Implementing Contextual Teaching and Learning: Case Study of Julia, a Middle School Science Novice Teacher
Deborah J. Tippins University of Georgia Final Report March 30, 2003 The work reported herein was prepared in association with the contextual teaching and learning in preservice teacher education and studies of novice teachers’ implementation of CTL approaches in the classroom projects at the University of Georgia, with funding support from the U.S. Department of Education, Office of Vocational and Adult Education, Contract # ED-98-CO-0085, 1998 – 2003. 2 Implementing Contextual Teaching and Learning: Case Study of Julia, a Novice Science Teacher Deborah J. Tippins University of Georgia Abstract Research has shown that school science is often taught as a decontextualized narrative that fails to take into account the experiences, skills, values and lifeworlds of students and their communities. This study grew out of an interest in expanding our notions of what might constitute ―contextual science teaching and learning.‖ In this interpretive case study, Julia, a novice science teacher, and Deborah, an experienced science teacher educator, collaboratively examined what it means to learn to teach science contextually. The tools of inquiry which were at the heart of this study included interviews, journal reflections and field notes from classroom observations. Secondary data sources included teacher-generated curricular materials, impressionistic tales and classroom artifacts. Findings of the study suggest that the strengths and weaknesses of a contextual teaching and learning approach are rooted in many factors including: the role of science teaching and learning within larger community narratives, tensions between the narrative of school science and contextual teaching and learning, and the teacher‘s role as a mediator of knowledge. Implications of the study shed light on criteria that are needed for a contextually-based, transformative science education that addresses the needs of middle school learners. 3 Implementing Contextual Teaching and Learning: Case Study of Julia, a Middle School Science Novice Teacher Deborah J. Tippins University of Georgia Introduction Increasingly, as science educators attempt to address the challenges of teaching diverse learners, they must think deeply about the purposes of ―science education.‖ Whose interests are addressed in current practices of science teaching and learning? What might science education be like if we seriously consider how it fits within the lifeworld of the broad community of learners who occupy K-12 classrooms? Over the past decade, science educators have begun to explore the substance of what it means to ―know‖ and ―learn‖ and the sorts of navigational challenges teachers and learners experience in the midst of the diverse interests and life histories they bring to the classroom. In recent years, the focus on preparing science teachers as technical decision makers has given way to preparing critically reflective practitioners (Anderson & Mitchner, 1994). The current interest by science teacher educators in contextual teaching and learning models stems from the increasing belief that teacher‘s knowledge is 1) contextual and situation specific, 2) interactive, and 3) speculative, involving many uncertainties and ambiguities. In contrast to traditional approaches to teaching and learning which emphasize the transmission of codified subject matter, a contextual teaching and learning approach emphasizes the importance of examining social structures, exploring community issues and helping others live meaningful lives. In their book Contextual Teaching, Kincheloe, Slattery & Steinberg (2000) stress that education 4 must ―help us connect students and their sociocultural environment through an emphasis on autobiography, community relationships, reflective and interdisciplinary practices, creative problem solving and social action in the schooling process‖ (p. 2). From our perspective, there is a critical need for a contextualized view of teaching and learning
which generates local knowledge and builds community memory. Thus, at the heart of this collaborative case study is a concern for examining common places that intersect the lifeworlds of children and the science education experiences they have in the classroom. Accordingly, the focus of this study was to understand contextual teaching and learning as it was practiced by a middle school science teacher within particular professional development and classroom communities. The study was framed within the following research questions: 1. What does contextualized teaching and learning mean to a practicing middle school science teacher? 2. What enabling strategies does a middle school teacher draw on to build relationships between school science and contextualized forms of teaching and learning? 3. What factors constrain the use of a contextual teaching and learning approach in the context of science teaching and learning? 4. In what ways does science teaching and learning in Julia‘s class differ from that of more traditional classes? Context of the Study This study is situated within the context of an on-going preservice teacher education model that was inductively derived and based on tenants of contextual teaching and 5 learning (CTL). Julia, a recent university graduate with a major in secondary science education, was a participant in the CTL program since its initial inception. One of the highlights of Julia‘s participation in the CTL program was her involvement in an internship experience at the Center for Disease Control (CDC) in Atlanta. Working with scientists at the CDC, Julia collaborated in developing a science education curriculum designed to engage middle school learners in the study of epidemiology. After graduating in the summer of 2001, Julia found herself in a period of professional transition. Unable to immediately assume a teaching position, Julia accepted a temporary position as a consultant and participant in the Altamaha Watershed Project, a professional development experience for middle school science teachers. The Altamaha Watershed Project frames professional development of science teachers in terms of two key organizers: service learning and contextual teaching and learning. One of Julia‘s major roles in relation to this project was that of ―curriculum-maker‖—drawing on her experience at the CDC, she was asked to design a model unit on endangered species of the Altamaha Watershed that could be adapted for use by middle school teachers working in counties situated along the Altamaha river basin. With the approach of the 2002 academic year, Julia assumed her first teaching position as a Grade 7 science teacher. She began her work in a nearby middle school, hoping to work alongside several experienced teachers who had been integrally involved in the Altamaha Watershed Project; however, by the beginning of the school year these teachers had already resigned or transferred to other middle schools. Julia was assigned to teach five sections of Grade 7 science in one of four middle schools located within a small city university community in Georgia. The school population consists of 68% 6 African American, 11% Hispanic and 23% Caucasian students. Approximately 85% of the students in the school qualify for free and reduced lunches for the 2002 academic year. As a new science teacher, Julia planned to draw on her CDC internship experience and use her ―Altamaha watershed: Pollution as a cause of extinction‖ unit and others like it as focal points for her Grade 7 science curriculum. This study explores how Julia attempted to translate her understanding of contextual teaching and learning theory into practice. Methods of the Study ―The methodologies and methods of research, the theories that inform them, the questions which they generate and the writing styles they employ all become significant acts‖ in the research process (Smith, 1999, p. 39). A careful consideration of perspectives, purposes and goals led us to choose an interpretive case study methodology which was collaborative in nature. An interpretive research approach (Erickson, 1986) was perceived to be appropriate for this study as the goal was to examine the nature of contextual teaching and learning in light of the perspectives of two co-researcher participants. An interpretive methodology allowed for exploration of participants‘ understanding of contextual teaching and learning and its meaning in the context of a 7th grade science classroom. This approach also enabled an examination of participants‘ views about contextual teaching and learning in the context of a project aimed at placing CTL at the center of reform.
Participants This case study involves members of two overlapping science education communities: a science teacher learning community and a science teacher education 7 research community. Participants in this study include two science educators—Julia, a first-year middle school teacher and Deborah, an experienced science teacher educator. Julia initially enrolled in the university as a biochemistry major in September, 1997. ―I had decided as a fourth grader that I would find the cure for pancreatic cancer so that no one else would have to go through the pain that I had when I lost my grandfather.‖ While working part-time in a pharmacy lab, Julia gradually began to experience a sense of isolation. She came to value the fleeting opportunities to interact with and assist others in the laboratory. Simultaneously, Julia began to recall her positive experience as a tutor for middle school students during her high school years. A short while later, Julia made the decision to change her major to science education. Julia noted that shortly thereafter ―I received a flier in the mail about a program called Contextual Teaching and Learning which promised a stipend at the end to assist in purchasing teaching materials. Being one to never turn down free money, I decided to give it a try. The more that I learned about the contextual teaching and learning approach, the more I began to wonder why more teachers were not using it in their science classrooms.‖ Deborah, a former elementary and middle school science teacher, and a faculty member in the science education department, first met Julia through her involvement in the CTL program. As the instructor for the CTL Seminar # 3: Contextual Teaching and Learning in the Schools, she had the opportunity to work closely with Julia and other students. Deborah initially became involved in the CTL program because of an interest in expanding her understanding of science teacher preparation and scholarship contextualized in the experiences, skills and values of the local community. During the early stages of this study, Deborah was a Fulbright Scholar in Iloilo City on the island of 8 Panay in the Philippines. Iloilo is a thickly populated province located along the shoreline of the South China Sea where the majority of the people earn their living through fishing and rice farming. In her capacity as a Fulbright Scholar at West Visayas State University, Deborah shared her understanding of the CTL principles with other faculty, which ultimately led to the development of a new course entitled ―Contextual Teaching and Learning through Community Immersion.‖ During this preliminary stage of the study, Deborah and Julia communicated regularly through e-mail and exchange of curricular materials. Data construction and data sources The primary conceptual tools we selected as investigative strategies for this study included interviews, journal reflections and field notes from classroom observations. Secondary data sources included teacher-generated curricular materials, impressionistic tales and classroom artifacts. Data collection initially commenced with a series of informal e-mail conversations between the two collaborators, leading to more formal phases of data collection and analysis. Procedures During the initial phase of the study, a semi-structured interview protocol was used to pose questions which guided subsequent interview conversations. At this time, Julia was working as a consultant on the Altamaha Watershed Project and developing curricula pertaining to endangered species of this ecosystem. More than 30 different definitions of ―curriculum‖ can be found in the science education literature. The workshop instructor, however, did not provide Julia with an a priori definition of curriculum; rather, Julia was encouraged to define curriculum in a way which personally 9 made sense. It was during this initial experience that Julia refined her previous understandings of CTL to generate a working definition. The primary phase of data collection began when Julia started her first teaching position as a middle school science teacher. Throughout the semester Julia kept a journal and recorded impressionistic tales related to CTL while Deborah observed Julia‘s classroom. The two co-researchers conducted conversational interviews to discuss their analyses and interpretation of data. Data analysis The concept-indicator model of grounded theory (Strauss, 1987) was used based on constant comparison of various data sources. Because the goal was to examine contextual teaching and learning in light of participants‘ perspectives, analysis began by independently coding primary data sources to produce indicators of concepts and categories fitting the data. No a priori set of concepts or categories were used; instead,
categories were derived from the different data sources. Categories representing convergences and contradictions were considered. Connections between categories were identified by returning to the data sources to confirm or negate possible connections. After completing independent analyses, the co-researchers discussed, clarified and negotiated categories. Themes were generated through further comparative analysis of the concepts and categories in relation to the questions of interest. The tenability of the themes emerging from one data source were ultimately tested against other relevant data sets. Theoretical Perspectives of the Study The theoretical perspectives of this study are drawn from assumptions surrounding notions of contextual teaching and learning and the situated nature of 10 teachers‘ knowledge. The concept of contextual teaching and learning frequently draws on the premise that science, mathematics, and other kinds of learning can more powerfully engage students when they are connected to workplace contexts. From this perspective, the emphasis is on making science more relevant and useful to the lives of children through applications of concepts and real-life examples across diverse workplace settings (Britton, Huntley, Jacobs & Weinberg, 1999). Other scholars conceptualize CTL in a broader philosophical sense, calling on the need for teachers to understand that ―no body of facts should ever be taught in isolation‖ (Kincheloe, Steinberg & Tippins, 1999, p. 22). Pointing out that students will unlikely be motivated to learn a body of abstract, unconnected facts, they call for a more holistic science education which emphasizes knowledge creation through experiences which ―clarify connections among political, religious, familial, environmental, social, economic, athletic, aesthetic and academic lives of students‖(Kincheloe, Slattery & Steinberg, 2000, p. 3). Taking this idea a step further, a number of scholars have suggested that teachers‘ knowledge is situated, social and distributed across individuals and tools (Cobb, 1994; Greeno, Collins & Resnick, 1996). They emphasize that what we know and learn is created, interrogated and questioned through the mutual conversations of members of diverse learning communities. This study recognizes the need for a more situated knowledge base. In contrast to a more generic model of CTL practice characterized by a ―one size fits all‖ approach, we are interested in thinking about generating situated teacher knowledge with relevance to contextual science teaching and learning. Common Places and Emerging Tensions 11 As a storied landscape, multiple narratives are interwoven throughout Julia‘s experience with contextual teaching and learning. The intersections of these narratives or tensions created common places or focal points for discussion. Some educational researchers (e.g., Abell & Bryan, 1997) frame what they learn in a study in terms of tensions that represent struggles as the basis of learning. We approach the use of tensions in a broader sense to include not only struggles, but the more positive aspects of teacher learning that took place for Julia in this study. Our use of ―tension‖ is one in which struggles are viewed as ―movements of excitement that spur us on to continue striving in our learning‖(Arellano, et al., 2001). In this section we first explore Julia‘s understanding of contextual teaching and learning; we then share and discuss the themes generated as commonplaces of understanding and emerging tensions in relation to the research questions of interest. Question 1: What does contextual teaching and learning mean to a practicing middle school teacher? As a new teacher, one of Julia‘s first goals was to get to know her students and their life worlds outside the classroom. ―I need to have an understanding of students‘ prior experiences and knowledge, of what interests and excites them. It means I have to try to understand their cultures and take time to go into their communities.‖ Julia quickly discovered, Most of my students come from the Nellie Dee housing projects and the surrounding trailer parks. My students are the ones that hang out in the ‗Iron Triangle‘ (a part of the community where the selling and buying of drugs is pervasive). These students are consumed with worry about who they will have to 12 fight in order to maintain a status which keeps them safe within this community. They could care less about the scientific method or the different kinds of cells that can be found in blood, what we know as QCC objectives (journal reflection). As Julia learned about the life worlds of her students she began to ask ―what kind of science do my students see at home—a small patch of grass between buildings falling
down from disrepair…a cockroach infestation?‖ Disturbed by what she was learning, Julia‘s understanding of contextual teaching and learning began to shift. Theme 1: A Question of Purpose Early in this study, Julia, in attempting to articulate her vision of contextual teaching and learning, integrated what she had learned from her previous CTL seminars and experiences into a definition that worked for her. Reflecting in her journal she wrote, I have come to the conclusion that everyone involved in CTL tries to create a definition that personally makes sense. While I have been struggling with my definition, I have come to view CTL as an approach used to identify student needs and then use students‘ real-life experiences to teach science lessons in the classroom. It‘s based on the idea that both students and teachers can engage in and have ownership for their learning. They can learn to reflect more deeply on their learning. As Julia‘s first semester of teaching progressed, however, her understanding of CTL also began to shift: 13 I am no longer thinking about CTL only in terms of how I can help them learn science through relevant experiences connected to the community, home and workplace. Instead, my goals and understanding of CTL has shifted from ―cells‖ to ―survival.‖ I want to see my students live beyond 25 years (e-mail communication). At the heart of Julia‘s changing understanding of CTL is a critical question: what happens to students when they leave the classroom community wherein scientific knowledge is no longer the centerpiece for their everyday knowledge and activities? In short, Julia is beginning to critically reflect on the question of what is meaningful science education in relation to students‘ life worlds beyond the classroom. Question 2: What enabling strategies does a middle school teacher draw on to build relationships between school science and contextualized forms of teaching and learning? This study sought to identify and describe CTL enabling strategies. An enabling strategy is one which can assist teachers in developing and implementing CTL-based science teaching and learning plans that are effective in helping students learn. Throughout the study, Julia tried many strategies and met with both success and failure. Several enabling strategies emerged as important themes and are described in detail in the sections that follow: a) connecting to students‘ interests, b) bringing the history and nature of science into the curriculum, c) enacting the work of scientists through simulation, and d) using alternative assessments. Theme 2: Connecting to Students’ Interests For Julia, one of the basic goals of CTL was to incorporate the cultural knowledge which all children bring to school into the science curriculum. She continually sought out 14 ways to make science relevant to the life worlds of her students. Several examples illustrate Julia‘s successful attempts to create culturally relevant learning experiences. Caught in a speed trap!: One of the concepts that students seem to struggle with is the idea of instantaneous velocity. I wanted students to see the application of this concept in their everyday lives. What came immediately to mind is the idea of speed traps. I invited a local police officer to my classroom. As a class, we went outside and stood next to the road that runs parallel to our school. Officer Martin showed us how to use laser speed guns to determine the average velocity of cars traveling between two points. He then placed students at each end of the road to time cars. Students were really interested in this practical application of an abstract concept. This activity really served as the basis for them understanding the whole idea of instantaneous velocity (conversational interview). Bacteria is everywhere!: On Monday I used a slide show to facilitate discussion about bacteria. At the end of the day, students left with the thought that bacteria could be present anywhere. Then yesterday we tested our theories about bacteria using blood agar that I obtained from the hospital. We tested either a hand or a mouth for bacteria (knowing that it would be present there). Because many of the students asked about the difference between bacterial and anti-bacterial soap, we decided to wash our hands using one type of soap or the other and then retest the same area. If a student had selected the mouth they compared Listerine with water in terms of cleaning. Today you saw us take this one step further by testing for bacteria at sites we had selected throughout the school. Some of the most popular selections were the lock on the bathroom stall, the water fountain, desk tops, 15
tables in the cafeteria and locker doors. Students used one of three cleaners to clear the area they had washed and re-swab it (conversational interview). Grocery store classification!: Classification is one of the basic processes of science and an integral aspect of the Georgia QCC‘s. However, most of the textbook examples used to illustrate classification are not connected to the experiences of students. I chose a different approach, a more contextual approach, to develop students‘ understanding of classification. As a starting point, I asked students about examples of classification they were familiar with. We discussed why these classification systems were used, and the system that students were most interested in was the grocery store. I decided that we could use the grocery store as the starting point for building our own classification system, rather than looking at the Dewey Decimal System or some other classification scheme (journal reflection). One of the most popular ways to study genetics is through the process of determining the blood types of children and adults. With the advent of the AIDS crisis, authentic experiences with blood typing were soon outlawed. At this point, scientific equipment companies began to produce ―simulated blood typing kits‖ for teachers. In thinking about how she could illustrate genotypes and phenotypes in a contextually meaningful way, Julia decided against using blood typing as the typical example. The genetics of dog breeding!: I try to limit the use of blood typing as an example as much as possible because of the diverse makeup of the families of many of my students—children who are adopted, families where every sibling has a different father…instead, I focus on traits such as dimples, widow‘s peaks, and attached 16 earlobes—but even these examples can be problematic. It was only when I took the opportunity to find out the personal interests of students that I came upon the idea of dog breeding. I found out that two of my students were in the business of breeding dogs. We took this opportunity to try to figure out what coloring the parents needed to have to get the coloring desired in the offspring. Unfortunately, the coloring on the coat was a little more complicated than we had expected, but all of the students learned a lot trying to figure out the alleles their dog might have—I found that every student could relate to dogs as an example (conversational interview). If science teachers are to truly prepare students through science to live in an increasingly complex world, they must move beyond the notion of cultural relevancy. Both Julia and Deborah agreed that it is necessary to consider how to connect curriculum to the lives of children as a starting point for creating contextual learning experiences. However, they concede that a relevant curriculum is simply not enough—what seems to be missing is students‘ personal sense of identity, a sense of who they are as individuals and as science learners—that ultimately will affect their success. Theme 3: Bringing the History and Nature of Science into the Curriculum Julia‘s emphasis on the history and nature of science was a powerful tool for helping students explore different interrelationships that connect the past, present and future of particular science issues. Reflecting on this aspect of her teaching, Julia stressed that The history of science allows for contextual teaching and learning. Scientists, for the most part, are simply individuals who questioned what went on around them 17 and how things come to be. Through their experiments they learned about the world around them. I think that our students must understand that some of the ideas that to us might seem silly were just beliefs of the time. This helps students to feel secure while experimenting in their own world (journal reflection). Drawing on her internship experience at the Center for Disease Control, Julia developed a powerpoint presentation to chronicle the historical evolution of epidemiology (the study of disease). Julia‘s goal was to help students develop a better understanding of how modern theories of disease have evolved and changed over time. The National Science Education Standards (1996) emphasize the need for students to develop an understanding of the nature of science. Julia felt that bringing history into the curriculum was an effective strategy for developing students‘ understanding of science as an ever-changing, dynamic construct which is characterized by the search for understanding. Throughout her powerpoint presentation Julia was able to engage her 7th grade students in a lively discussion, which almost bordered on a scientific discourse, of the following ideas: What is epidemiology?
Origin of the Word Early Ideas About Disease Causation Buddhism‘s Six Causes of Disease He Got Sickly, He Must Have Done Something Wrong Inhabited by Evil Spirits—African Native Healers Disturbances in Humors or Atmospheres (Florentine physicians of the 1600‘s) Supernatural Contract or ―Curse‖ (Burning German Jews accused of poisoning wells and causing Black Death) Using Leeches to Remove ―Bad Blood‖ from the Body Removing (cutting off) a Body Part that Causes Pain Development of Germ Theory Van Leeuwenhock‘s Description of ―Wee Beasties‖ (microbes) Louis Pasteur‘s Ideas of Fermentation, Anthrax, Spontaneous Generation, Silkworm Diseases and Rabies Vaccine 18 Robert Koch‘s Postulates for Disease Causation (tuberculosis, cholera and anthrax) John Snow as the ―Father‖ of Epidemiology (1854 outbreak of cholera) Development of Public Health Immunization Clinics of the Late 1800‘s Public Health Service Formation in 1912 STD‘s—Social Hygiene Commissions Rise of Public Health Departments Sanitation and Hygiene Movements (sanitary privies are cheaper than coffins) Smoking and Lung Cancer Communicable Disease Center of the Mid 1900‘s Polio Vaccines Epidemic Intelligence Service of 1951 Center for Disease Control in 1970 Legionnaire‘s Disease Agent Orange Studies Abestos and Mesothelioma HIV Infection Violence and Injury Prevention Bioterrorism (classroom observations and anecdotal records) Through an informal survey of her students, Julia learned that the inclusion of the history of science was very effective in terms of increasing students‘ class participation and interest in the subject. However, her discussions with Deborah highlighted several issues that still need to be considered with respect to this strategy: a) whose version of the history of epidemiology is being reenacted?, b) how can more student-centered strategies be used to incorporate the history of science?, and c) how can students‘ understanding of the nature of science be assessed? It was interesting to note that Julia‘s presentation of the history of science excluded the role of females as some of the earliest physicians to study disease. This presentation of history privileges a history of science emergent from ancient Greek and White European cultures—a type of science that might be described as masculine and objective. During their discussion of this strategy, Deborah shared with Julia some 19 additional resources that could be used to facilitate a more student-centered approach to the history of science. In particular, Deborah recommended Joan Solomon‘s series of historical role plays which provide a basis for students to dramatize such events as ―Jenner‘s Discovery of the Smallpox Vaccine‖ or ―Galileo‘s Trial.‖ A final point that came to light in their discussion of this strategy concerned the issue of assessment. While recognizing that student understanding of the nature of science was an important standards-based goal, Julia expressed some uncertainty concerning how best to assess this understanding. Theme 4: Enacting the Work of Scientists through Simulation “Pack your bags, EIS officer! Your first assignment is to find the source of a foodborne illness outbreak at a church supper. Church members who ate the supper reported symptoms of nausea, vomiting, diarrhea, and severe abdominal pain.” An authentic curriculum and assessment is one which is often described as
―mirroring the work of scientists.‖ Julia viewed activities which mirrored the work of scientists as an important strategy in building students‘ conceptual understandings. She emphasized that ―students do not have to know everything about a subject to experiment—as they experiment they can build their knowledge by using the same methods that scientists use.‖ The work of scientists is not something that can be captured easily in the brief, fragmented periods of science instruction that characterize the typical middle school schedule. Scientists‘ work evolves over time in a manner that is not neat and tidy. Julia believed that the best way to contextualize learning in the work of scientists was to engage students in simulations that mirrored current events in science. Drawing on her 20 CTL summer experience with the Altamaha Watershed Project, Julia designed a simulation to investigate ―Water Pollution as a Cause of Extinction.‖ Later, as Julia began her own teaching, she engaged students in the simulation study of ―Illness Strikes the County of Oswego.‖ This simulation corresponded with students‘ interest in the ―anthrax scare‖ that was currently headlining the news, and was a timely fit with the study of diseases in the 7th grade life science curriculum. Describing how she came up with the idea of an outbreak simulation to complement her unit on epidemiology, Julia stated: Many of my students have attended a potluck dinner so they are familiar with the concept of multiple individuals bringing in food to share with others. We could have one food product that is contaminated and every individual with a glow-inthedark marble would be infected. Once we have established the outbreak we will use the EIS Officer Handbook to figure out how the outbreak occurred. This handbook describes how an individual at the CDC would solve an outbreak if it was reported to them by a local health department. They will actively be gathering information to solve an outbreak of food poisoning (conversational interview). Over a period of ten days, Julia‘s students participated in an outbreak simulation that involved seven major themes: a) exploring possible causes of food-borne illness; b) collecting data: interviewing people to gather information about the outbreak; c) organizing and confirming information through the development of an epidemic curve (a type of graph); d) mathematically charting the range of incubation periods (incubation period=time of experiencing symptoms=time of meal); e) using tally charts to determine the attach rate of each food item served at the supper; f) calculating risk for food items 21 that were determined to be high risk; and g) interpreting data to support or refute initial hypotheses (anecdotal records). Julia points to her use of this simulation, and others like it, as a way of showing students that science does not always occur in a linear fashion. The work of scientists is far more complex and even involves a great deal of intuition and trial and error. Julia believes that students are often unmotivated because science is simply taught as a linear set of facts. Both Julia and Deborah agreed that contextualized knowledge is at the heart of motivation, and that facts are irrelevant unless seen as part of a larger context. Julia‘s use of simulation as a strategy was not without difficulties. Through the use of simulation, Julia hoped to show students how scientific methods are a part of everyday life. She notes, however, that at first ―students were just blown away…they could not fathom at all the abstract idea of scientific methods as a part of everyday life.‖ The role of mathematics in science learning created an additional dilemma. Julia believes that mathematics is a tool essential to learning science. Her simulations were based on an expectation of an average level of mathematical skill. However, as Julia soon found out, many of her students lacked what she considered to be very basic, foundational knowledge of mathematics skills such as division. While Julia saw simulation as a strategy which encourages curriculum integration, she was not prepared to deal with students‘ diverse levels of mathematics understandings. Nevertheless, this pedagogical approach does support a more authentic, contextualized view of science as a social practice—not just an activity of the intellectually privileged. Theme 5: Using Alternative Assessments 22 Julia felt that assessment of student learning should match the way in which science is taught. This type of seamless assessment can be illustrated by describing a lesson that Julia taught on force and motion. As part of a force/motion lab, Julia had students brainstorm examples where they could see different principles of force and motion both in the laboratory and outside the classroom. As part of this lesson Julia incorporated an alternative form of assessment which required students to build a roller
coaster containing two hills, two loops and two banked curves. As a form of assessment, students had to explain at least seven principles of force and/or motion present in their roller coaster and the importance of these principles to the functioning of the roller coaster. Later, as a summative assessment at the end of the unit on force/motion, Julia showed a video of one of the school‘s football games. Students had to explain what principles of force and motion were used in the context of this football game. Research Question 3: What factors constrain the use of a contextual teaching and learning approach in the context of science teaching and learning? The identification of conceptual, structural and epistemological factors that constrain teachers‘ ability to successfully develop and implement CTL practices is inextricably linked to the design of effective enabling strategies such as those discussed previously. In this section we describe some of the constraints that emerged as themes relative to Julia‘s attempts to design and enact a CTL-based science curriculum. Factors that constrained Julia‘s ability to fully enact her vision of CTL include: a) a disembodied learning community; b) the tension of high takes testing; c) inequities in terms of access to resources; d) the influence of textbooks; e) the domain-specific nature of science topics; and f) the tradition of assessing understanding for grades. 23 Theme 6: The Disembodied Learning Community For Julia, as a new teacher, an important starting point for preparing students to learn involved the cultivation of a classroom community for understanding science. At the beginning of the year, Julia assumed that students would already have the knowledge needed to participate as a member of a learning community. She soon realized that ―students do not know how to work together. They do not understand the meaning of collaboration.‖ Julia found herself taking the first part of the schoolyear just helping students develop strategies of collaboration, something she considered essential to effectively fostering an environment conducive to contextual teaching and learning. The importance of community goes beyond the four walls of the classroom. In Julia‘s classroom, as is the case in many classrooms, there was frequently little time for anything more than daily survival. Time for further learning and reflection in collaboration with peers was a pipedream given the crisis management atmosphere of the school and the immediate attention survival necessitates. Julia lamented this lack of collegial support, commenting, ―the CTL approach requires a lot of creativity—it is difficult to come up with novel ideas or workable projects without the input of other teachers.‖ When Deborah asked Julia about the mentoring support available to first year teachers, she was surprised to learn that there were very few experienced teachers in the school. Julia explained how low morale had contributed to a dramatic turnover in teaching staff, resulting in the loss of a historical memory. This in turn created a cycle where there was little support available for new teachers. This is a cycle that both Julia and Deborah agree must be broken. 24 Thomas Sergiovanni (2000) in his book The lifeworld of leadership: Creating culture, community and personal meaning in our schools, emphasizes the importance of place, memory, relationships, and practice for building community in schools. Julia also expressed the need for learning networks to be built between the school and the community, noting, ―for our team‘s open house only 15 out of 200 parents attended.‖ Julia emphasized that the school and community must join together in facilitating a vision of contextual teaching and learning, commenting, ―perhaps parents see no real purpose for involvement.‖ Julia felt that integrating parents as speakers within the classroom was an important way to bring together community and school. She encountered difficulties, however, when she tried to do this: Most parents, because of their work schedules, can only come in for one class period of the day. This does not fit with the way in which our middle schools are set up. Only one group of students will have the opportunity to benefit from the parent‘s knowledge (conversational interview). Theme 7: The Tension of High Stakes Testing As far as Julia is concerned, it is not what students learn, but how they learn that is fundamental to a contextual and quality education. However, as Julia experienced firsthand, schools are part of a larger system where educational change can not always be equated with quality. A question that I have no answer for right now is how to balance what I believe my students need to know in their lives right now with what they need to know to pass the CRCT [criterion-referenced competency test] at the end of the year. I am struggling to bring the QCC‘s [quality core curriculum] to their lives in a way that
25 they do not resist. However, it is taking me some time to work through what they need to know, what they want to know, and how we will struggle together‖ (journal reflection). In concert with her belief in the importance of a democratic learning environment, Julia would like to see students and teachers working together to design appropriate methods of assessment at the grass roots level. As Julia shared, this approach—the idea that assessment should not be isolated from the construction of knowledge—was modeled in several of her university CTL seminar classes. The tension of high stakes testing in the current era of reform seems to stand in stark contrast to the kinds of assessment called for in contextual approaches to teaching and learning. The premise of many high-stakes testing procedures is that ―we need to specify precisely what students need to know and then check to see if they know it. We need to specify precisely what teachers need to do and then check to see if they are doing it‖ (Kincheloe, Steinberg & Tippins, 1999, p. 240). Theme 8: Inequities in Terms of Access to Resources Equitable science teaching practice is not something that can be mandated. Julia held a vision of teachers, students, parents and community members working together to bring about learning in science. Her image of an equitable science was, in part, influenced by her CTL service learning class where democracy was a central organizer. Julia considered the notion of a democratic classroom to be an idea central to contextual teaching and learning. In trying to create such a learning environment, she found herself constantly experiencing structural, linguistic and epistemological tensions. Reflecting on 26 her struggle to encourage all students to participate in project-centered science activities, Julia commented: I have trouble finding a way for all students to participate in projects which require information gathering and discussions. Many students do not have resources at home--books or newspapers--where they can gather information. Often times these same students do not have access to a library or other resources (conversational interview). As Julia and Deborah discussed this tension further, they came to the realization that students‘ participation in science, particularly girls, was influenced by their role as ―othermothers.‖ In this sense, many of Julia‘s students had after-school responsibilities serving as surrogate mothers for younger siblings which prevented them from readily accessing information from outside the classroom. Julia was quick to point out that this phenomenon was not just a reflection of lower socioeconomic status. When students need a folder or other materials from home I have some parents that just send a note with some money, rather than helping their child secure these materials. For these parents, responsibility for helping their child develop a sense of accountability is often regulated to the background when juxtaposed with work and other child-rearing responsibilities (personal journal). Julia was also concerned with the growing number of students who speak little or no English. As an issue of equity, Julia felt that these students were particularly disadvantaged when it came to science. ―These students not only must learn the English language, they must also learn the specialized language of science.‖ In this regard, Julia pointed to the example of Celves: Fundamentals de la Vida. ―We have a CD Rom for 27 Spanish speaking students, but there are only two disks for 240 students. Furthermore, we have no computers with CD Roms!‖ Theme 9: The Influence of Textbooks For the most part, Julia felt that the required science textbook did not provide contextually appropriate content for learning. The school district had adopted the Prentice Hall Science Explorer as a textbook. Julia described this book as …consisting of guided reading and a study workbook. Essentially, students are supposed to write out definitions, and then copy sentences from the textbook into the workbook. Basically, this book does not seem to promote student thinking or transfer of knowledge to real-life situations (conversational interview). Julia described a first-hand experience with the limitations of this textbook as it related to a unit on genetics: After working through a problem in genetics in which we crossed heterozygous and homozygous parents using a punnett square, we began discussing mutations and how these mutations can be passed from one generation to the next. We talked as a group about how scientists use fruit flies to study mutations. I assumed
that students would have a clear concept of fruit flies, since there were many pictures in their textbook. As I passed around the tiny flies in vials I overhead Kevin ask ‗when they grow up will you be able to see the red eyes?‘ Similar questions followed. It took me awhile to realize that when students saw the tiny flies in the vials they assumed they were baby flies. The pictures in the textbook were enlarged and students did not realize that actual fruit flies would be much smaller. I was able to save this lesson by having students examine the fruit flies 28 under the dissecting microscope. Only in this way were students able to grasp the idea that the large pictures in their textbook were really the same tiny fruit flies under the microscope (anecdotal record). Even more problematic than the textbooks, themselves, was the way in which the books and other curricula served to exclude teachers from the design of science teaching and learning. In many instances, Julia was able to move beyond this constraint, choosing to engage in the process of creating and involving her students in creating meaningful units of study. Yet, at the same time, Julia continued to feel the tug and pull of ―teaching the book.‖ Theme 10: The Domain-Specific Nature of Science Topics Julia‘s major field of concentration in science education is biology. She has taken more biology courses at the undergraduate level than would typically be required of a biology major in the College of Arts and Sciences. Thus it would seem that Julia‘s strong preparation in this area would enable her to more easily incorporate contextual examples from biology than examples taken from the physical sciences. Much to the surprise of both Julia and Deborah, this was not the case. Rather, it was the domain-specific nature of the topics that most influenced Julia‘s ability to incorporate relevant examples. Julia used the topic of ―the cell‖ to illustrate this point. What we are required to teach in terms of the cell is basic—the parts of the cell and their functions. I had students create cell models using household items, but only 1/3 of the class showed any interest in that activity. I have struggled to find a way to teach about the parts of the cell in a contextually meaningful way. 29 At the same time, Julia declared how easy it was to come up with relevant examples from the physical sciences and chemistry. ―The nature of the topic is a big determinant in terms of how well it lends itself to a CTL approach.‖ Theme 11: The Tradition of Assessing Understanding for Grades Assessing student understanding for the purpose of assigning grades has long been a task of teachers. While Julia was eager to focus on assessing student understanding beyond the traditional focus of assigning grades, she was unclear about the skills that were needed to develop and analyze embedded assessments as an ongoing part of instruction. Repeatedly my CTL classes have emphasized that assessment is all about determining what students know, not what they don‘t know, and I agree with that. I also recognize that any kind of assessment should ideally consider the context in which students are being asked to create knowledge. At the same time I am not sure just how to go about this kind of assessment when it still boils down to the final grade. Research Question 4: In what ways does science teaching and learning in Julia‘s class differ from that of more traditional classes? At first glance, science teaching and learning in Julia‘s class might seem very similar to what can be found in middle school classrooms across the country. It was only as Deborah increasingly spent time in Julia‘s classroom that she came to understand and appreciate a significant difference: 30 What strikes me most is that students seem to have a genuine ownership in their learning. They are actually involved in making decisions about what, how and why they will learn particular science concepts (classroom observation notes). Theme 12: Student Ownership of Learning In a conversational interview with Deborah, Julia explained how the concept of student ownership for learning had become an integral part of her teaching philosophy: I remember during the first CTL seminar how I really had no understanding of the CTL philosophy. At first I hoped to just learn different perspectives on teaching and learning—some alternatives to lecture and recall. I knew that I like more interaction, hands-on activity and tactile experiences. But as my understanding of CTL grew I learned how teachers can transfer ownership for learning to students
(conversational interview). For Julia, the idea of student ownership in learning is what distinguishes CTL from culturally relevant approaches to teaching and learning. While this may not seem significant, Julia is quick to point out the difference: With culturally relevant curriculum the teacher chooses the curriculum and the way it is to be taught, and just incorporates culture into the various lessons. To me, CTL is quite different than the idea of culturally relevant curriculum. It centers around students and is intended to give them ownership in developing curriculum. It stresses more of a connection between former knowledge and new information (email conversation). The concept of student ownership was evident in Julia‘s use of alternative assessment practices. For example, as a way of assessing science projects, Julia involved 31 her class in creating evaluation rubrics. Students had a voice in the assessment process and developed a better understanding of what counts as ―quality‖ in terms of their work. Conclusion: Looking to the Future Julia is certainly a teacher who has come to understand contextualization and the opportunities for students to learn and grow in a democratic society. As she looks ahead to the rest of the school year, she is already beginning to work with her students in conceptualizing a CTL-based project. Through discussions with students and school social workers she has identified a need: many students living below the poverty line do not get nutritional, well-balanced meals during the summer months when school lunches are not readily available. The seed of an idea begins to grow—the cultivation and harvesting of a school garden. As Julia begins to plan for this CTL project she asks many questions of herself and her students: What skills and knowledge will be needed for this project? What areas of learning does this project encompass? How will knowledge be constructed? How does this project relate to the life worlds of my students? How does this project relate to myself as a learner? Who will be the participants and what role will they play in project development and implementation? What service will be provided? What preparation is needed? How will I evaluate and document student learning? What resources will be needed? 32 What timeline will be required? How will I reflect on my learning? How will the overall impact of the project be evaluated and by whom? Together with Deborah, Julia recently developed a proposal to secure outside resources for this project. The proposal entitled ―Learning to teach contextually: What really happens?‖ was selected for funding through the Georgia Systemic Teacher Education program (GSTEP). The proposal will provide Julia with project-related science equipment and supplies beyond that which is found in the classroom, giving her an added incentive to expand her knowledge of contextual teaching and learning. Expressing her enthusiasm for the CTL approach, Julia commented, ―to have students excited about what they are studying excites me as a teacher. My experience with the contextual teaching and learning project has allowed me to see and experience the rewards of this kind of teaching even before I entered the classroom.‖ In many ways, Julia seems highly atypical of many first year science teachers. At the same time, she is not unlike many new teachers who are struggling to find a balance between their personal and professional lives. A contextual teaching and learning approach envisions many more teachers like Julia who refuse to teach decontextualized information…teachers who continuously ask from where data came, and how this information can be used to help students confront the world and better understand themselves and the knowledge and skills they need in relation to it. At a time when many educational reforms reinforce the memorization and regurgitation of unconnected facts, contextual teaching and learning approaches hold promise for restoring meaning in the educational process. 33 References Abell, S., & Bryan, L.A. (1997). Reconceptualizing the elementary science methods course using a reflective orientation. Journal of Research in Science Teaching,
8, 153-166. Arellano, E.L., Barcenal, T.L., Bilbao, P.P. Castellano, M.A., Nichols, S.E., & Tippins, D.J. (2001). Using case-based pedagogy in the Philippines: A narrative inquiry. Research in Science Education, 31(1). Britton, E., Huntley, M.A., Jacob, G., & Weinberg, A.S. (1999). Connecting mathematics and science to workplace contexts: A guide to curriculum materials. Thousand Oaks, CA: Corwin Press, Inc. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13-19. Erickson, F. (1986). Qualitative methods in research on teaching. In M.C. Wittrock (Ed.), Handbook of research on teaching (pp. 119-161). New York: MacMillan Publishing Co. Greeno, J.G., Collins, A.M., & Resnick, L.B. (1996). Cognition and learning. In D.C. Berliner & R.C. Calfee (Eds.), Handbook of educational psychology (pp. 15-46_. New York: MacMillan. Kincheloe, J.L., Slattery, P., & Steinberg, S.P. (2000). Contextualizing teaching. In J.L.Kincheloe, P. Slattery & S.P. Steinberg (Eds.), Contextualizing teaching: An introduction to education and educational foundations (p. 3). New York: Addison Wesley Longman, Inc. 34 Kincheloe, J.L., Steinberg, S.P., & Tippins, D.J. (1999). The stigma of genius: Einstein, consciousness and education (2nd edition). New York, NY: Peter Lang Publishing. Sergiovanni, T.J. (2000). The lifeworld of leadership: Creating culture, community and personal meaning in our schools. San Francisco: Josssey-Bass Publishers. Strauss, A.L. (1987). Qualitative analysis for social scientists. Cambridge: Cambridge University Press.
Implementing Contextual Teaching and Learning: Case Study of Lynn, a High School Mathematics Novice Teacher
Heide G. Wiegel University of Georgia Final Report March 30, 2003 The work reported herein was prepared in association with the contextual teaching and learning in preservice teacher education and studies of novice teachers’ implementation of CTL approaches in the classroom projects at the University of Georgia, with funding support from the U.S. Department of Education, Office of Vocational and Adult Education, Contract # ED-98-CO-0085, 1998 – 2003. 2 Implementing Contextual Teaching and Learning: Case Study of Lynn, a High School Mathematics Novice Teacher Heide G. Wiegel The University of Georgia Abstract This is a case study of Lynn‘s student teaching experience and one semester of her first year of teaching. Lynn identified her experience with contextual teaching and learning before becoming involved with the CTL project as limited, including a high school geometry class and activities in a few college math classes. Lynn completed the entire UGA course sequence designed with a contextual teaching and learning focus. Her experience with InterMath, a service learning project that included working with classroom teachers, was a very influential component of her teacher preparation and shaped Lynn‘s perception of teaching that includes extensive use of technology. Lynn‘s student teaching experience can be characterized as predominantly conventional with CTL elements interspersed. CTL elements included writing assignments, portfolios, small-group work with presentations, and hands-on activities. Several of the factors that seemed to hinder CLT implementation for Lynn during student teaching were the use of a very traditional algebra textbook, lack of time for adequate planning, and problems with class management. Lynn, however, was generous in sharing her time with her students by being available for tutoring and by attending students‘ extra-curricular activities. Factors fostering CTL implementation during student teaching included the statistics
textbook used because Lynn saw it as promoting problem- and activity-oriented teaching, Lynn‘s past experiences in mathematics, and her ability to reflect on her actions and to evaluate them in light of her goals. Lynn was similar to many student teachers who are overwhelmed by the complexity of the daily teaching demands. What sets her apart is that she kept her goals alive, despite the difficulties she encountered. As a first year teacher, within the first month, Lynn started CTL student projects with three of her five classes and established a class website that includes, among other information, examples of the use of mathematics in the ―real‖ world. 3 Background Lynn entered the University of Georgia in fall 1998; she was admitted to the College of Education as ―unspecified.‖ Early on she worked toward becoming a teacher of mathematics taking calculus and physics in her first semester at the university. Lynn was admitted to Mathematics Education in fall 1999. In Summer 2001, after an undergraduate research experience in the mathematics department, Lynn added mathematics as a second major. She graduated May 2002 with a B.S. Ed. in mathematics education and in December 2002 with a B.S. in mathematics. Because Lynn did not start her first teaching job until January 2003, all but one observation took place during her student teaching in Spring 2002. Lynn‘s student teaching assignment took place in a local high school that, because of the large minority population, is considered to be an inner city school. Lynn felt comfortable in this environment because her own high school had been a racially mixed school. Lynn knew a lot about African-American culture that, in turn, helped her understand some of her students‘ difficulties in school in relation to their life situations. Methods Data Collection I collected the main part of the data during Lynn‘s student teaching experience. Lynn fulfilled her student teaching in an inner city school that was racially mixed, very much like her own high school. The school was on block schedule, that is, each course was taught daily for 90 minutes and completed in one semester. During the height of her student teaching experience, Lynn taught three classes: Statistics/Probability (seniors), 4 Beginning Algebra (Seniors), and Algebra 2 (mostly sophomores); the fourth period was her planning period. I observed Lynn four times during February and March of 2002, and once in January 2003. During each visit, I took field notes that I expanded on the day of the visit. After the observations (in 2002 only), we sat down for interviews. During the interviews Lynn had the opportunity to comment on all aspects of her student teaching experience, including class management issues, parent meetings, extra-curricular activities Lynn shared with her students, and general issues of teaching and learning mathematics. I did not use a specific interview schedule because I wanted Lynn to highlight what was important to her. In April of 2002, Lynn came back to campus for an extended background interview. This interview was more structured, in that it specifically asked for CTL-related experiences in her high school and college mathematics and mathematics education courses, as well as for Lynn‘s view on implementing the different CTL principles during student teaching. All interviews were audiotaped. At first I transcribed verbatim only the segments directly relating to CTL. I paraphrased general comments about school, college, teachers, teaching, the classes, etc. and expanded those segments as needed. In May 2002 Lynn graduated with a B.S. Ed. in mathematics education but did not enter the teaching profession in the fall of that year. She was still working on her second major, mathematics, which she completed in December 2002. For the spring semester 2003, Lynn was hired by a neighboring county to teach mathematics in one of the middle schools. 5 Analysis I analyzed the field notes and interview protocols using analytic induction. Analytic induction involves scanning the data, developing initial categories, and looking for relationships among those categories. Working typologies and hypotheses are developed by examining initial cases and modified on the basis of subsequent cases (Goetz & LeCompte, 1984). In a first step, I identified and coded segments of data by subject or issue discussed; e.g., prior experience, class management, ball activity, planning. I then
examined how the labeled segments related to CTL principles and strategies, and their implementation. Recollections of Lynn’s CTL Experiences Experiences in High School Geometry was the only high school mathematics class that Lynn identified as providing contextual learning and teaching experiences. She remembered vividly the activity of a polygon scavenger hunt that brought them out of the classroom into the whole school building and onto the school grounds. This activity stuck in her mind because it made her see mathematics around her; e.g., ―I started looking at water fountains and seeing parabolas‖ (Interview 4/3/02). Lynn also remembered that her geometry teacher used ―Problems of the Week‖ that often were contextual, and that they did a lot of teamwork. In summary, Lynn said about her geometry teacher, ―I think she was trying to do that without knowing it [CTL]. … I think she had an intuition about how she wanted her class to be and that she wanted it to be untraditional, but she, she wasn‘t 6 saying, ‗Okay I‘m gonna make this contextual teaching and learning‘.‖ (Interview 4/3/02). In general, Lynn experienced her physics classes and science academic team providing more contextual experiences than the mathematics courses and team. ―Even on the math team we were so focused on doing the problems, getting the right answer‖ (Interview 4/3/02). About the physics classes she said, ―They brought mathematics to life, even though it was a lot harder to see because everybody is intimidated by/of …word problems‖ (4/3/02) Experiences in College Math Courses Initially, Lynn could think of no college mathematics courses that she saw highlighting any of the contextual teaching and learning principles. She emphatically stated, ―No math classes. None.‖ Lynn finally mentioned word problems. Maybe—the word problems. There is one thing I am struggling with as far as going past word problems and seeing them as contextual. You can’t just make a word problem up and say, Oh I made this cultural—a different name that my students might relate to, instead of saying Billy Joe, if I was in an urban city I would use something like Derek or a different, maybe an African name and would be more conscious of cultures. (Interview 4/3/02). She wondered, ―But as far as the mathematics involved, what makes a conceptualized [contextualized] word problem different from a word problem that kids are seeing from a day-today basis‖ (Interview 4/3/02). 7 Lynn identified one specific activity as being contextual. In her calculus class, she had to write Maple1 programs that would simulate slicing a pizza in parallel cuts so that all slices had equal area, and cutting a watermelon horizontally so that all pieces had equal volume. Experiences in Professional Mathematics Education Courses Lynn identified several mathematics education courses that she thought had contextual elements. She mentioned that, in one of her curriculum classes, they did ―a lot of self-discovery and open mathematics‖ (Interview 4/3/02). She characterized the activities in that course as being authentic learning because ―we were discovering things for ourselves in a different way. He wasn‘t giving us the formula, he was having us find the solution and go backwards and see how we got the solution‖ (Interview 4/3/02). Hands-on experiences seemed to be the key for Lynn to characterize an activity as contextual. She mentioned an activity in which they had measured the height and depth of stairs, and tested whether the staircase was up to code. One cool activity that we did, my favorite one the whole semester, was the stair activity where we went and measured the height and depth of each stairs, and talked about the angle—of inclination, and whether the school was up to code or not. I did the exact same thing with my statistics class and, the reason I did that because now, if I walk up the stairs in Aderhold2, I think, “These steps aren’t up to code” (laughs). (Interview 4/3/02) 1 Maple is a programming language used in the labs of the first two calculus courses at the university. 2 Aderhold Hall houses the Schools of Teacher Education and Professional Studies in the College of Education. 8 Another memorable activity came from her statistics class in which they had measured their body parts and investigated whether ―they were square.‖
On the other hand, if an activity was too complex, Lynn tended to dismiss it. For example, she did not see the ―Ant-on-the-Wheel‖ activity from her second curriculum class as a model for contextual learning. This activity was an in-depth investigation of the cycloid and its component functions and required the pre-service teachers to use their knowledge of trigonometry in a novel situation. The activity also combined mathematical and physical concepts as explanatory constructs. Lynn also dismissed her work on a unit from the textbook series Interactive Mathematics Program (IMP). The highlight of the IMP series is that the mathematical topics, concepts, and procedures are embedded in unit-specific contexts. In Lynn‘s unit, the framing context was the Edgar Allen Poe‘s The Pit and the Pendulum with the overarching question of whether or not the prisoner had time to escape. In order to answer the unit question, students had to extract the mathematical information embedded in the provided excerpt of the story and make some assumptions about the pendulum and different pendulums. The mathematical topic embedded in the unit was that of data spread. Lynn commented about the unit, I may think about it sometimes, but I think that the whole concept was so huge, some of the concepts that we tackled were so huge, it was hard to take in a simple thing that I can go and apply to my life on a daily basis. (Interview 4/3/02) But she also thought that the work on the unit opened a door for her because ―see, I can make connections to literature now without having to use [this unit]‖ (Interview 4/3/02). 9 Finally, Lynn never thought to mention a field trip to Washington DC the junior class had taken as part of a mathematics education CTL course3. On this trip the preservice teachers‘ content study of transformational geometry was extended by visits to the Textile Museum with its collection of quilts and Arabic carpets, to a mosque, and to the Smithsonian collection of Arabic art. In all these exhibitions, pre-service teachers experienced mathematics in context of its use in different life situations. The trip was definitely memorable, but it did not enter Lynn‘s recollection of memorable experiences that were relevant to her immediate teaching situation. CTL Courses Lynn was one of four students who participated in and completed the entire CTL sequence and every course designed with a contextual teaching and learning focus. Upon my question of how these courses had shaped her image of teaching, Lynn responded with descriptions of the courses and the value they had for her development as a teacher. In particular, she highlighted three courses; a course on human growth and development, a sequence of seminars, and a class on academic community learning. Human growth and development. Lynn voiced contradictory feelings toward this course. On the one hand, she enjoyed the set-up of the class because ―it was like an open forum‖ (4/3/02). There were ample opportunities to talk, to interact with other students or the instructor, and to reflect on educational issues. In addition, the writing assignments gave her an outlet for ―things that were on [her] mind a long time‖ (4/3/02). Although, as a mathematics person, she hated writing, she did like these writing assignments 3 EMAT 3450: Practicum in Mathematics Education. The course was taught by a doctoral student in mathematics education who also organized the fieldtrip to Washington, D.C. A professor of mathematics, the students‘ geometry teacher, and I participated in the trip as faculty representatives. 10 because they valued what she wrote and did not criticize how she wrote. She was proud of her progress from the first to the last written reflection in the course. One the other hand, Lynn described some of the group activity as useless; ―Get into groups and talk, get into groups and talk, reflecting, reflecting‖ (4/3/02). She thought the group talks were not intellectually challenging enough to hold her attention. In addition, although Lynn valued the opportunity to observe instruction at a local high school, she did not always see the connection between her observations in the school and the instruction on campus. Okay, we are going out into the school systems, which is great, but what are we doing in the classroom that is connecting my experiences here [the college class] into the classroom and how are we learning about all this educational psychology stuff? And I remember being very frustrated with that part of that class. (4/3/02) Seminars. The seminars included several fieldtrips that were memorable to Lynn. She made connections to teaching on some of the fieldtrips, but not on others. For example, Lynn reported from the visit to a children‘s hospital, how someone from the leadership team had highlighted how she had to develop different ways of talking, depending on the audience. If she was talking to a parent, she couldn‘t use technical
terms, but had to communicate through pictures and everyday language. I did not see Lynn make the connection that as a teacher she would have to develop different ways of talking as well. On the other hand, Lynn made a direct connection during a visit to a convention of technology during which one of the guest speakers highlighted the value of experience-based learning. He asked a science teacher to read a paragraph on snakes, 11 what a snake looks like, feels like, that it does not feel slimy but smooth. He then took a snake out of a bag, handed it to the teacher and asked, what was the better way to learn, from the reading or from holding the snake. Lynn concluded, ―That‘s really what CTL is‖ (4/3/02). Academic community learning. Lynn labeled this course as democratic because, as a class, the students decided the way they wanted to be graded and what they wanted to do. They decided to take on one large project for the semester, and the grade would come from a portfolio they would assemble from that project. Lynn thought her project was amazing because she had to write her first lesson plans, and she had the opportunity to practice networking. With two other CTL students, Lynn worked in the InterMath project4. Because the project is housed in the mathematics education department, Lynn got introduced to the mathematics education community before she officially started with the professional course sequence. Lynn‘s service in InterMath was two-fold. First, she and her team members helped the InterMath group in that they tried out many of the items and problems written for InterMath. That is, they were guinea pigs. Second, her team was working with teachers who were learning to work with the InterMath items. Thus, the pre-service teachers were learning to introduce or explain an activity and to write lesson plans. In short, they were trying on their future roles as teachers. This service-learning project gave Lynn a lot of confidence, and it reassured her in her chosen career. It also extended her image of a teacher, in that this image now included extensive use of technology. 4 http://www.intermath-uga.gatech.edu/homepg.htm 12 Results Implementation of Contextual Teaching and Learning Principles Lynn‘s student teaching, as revealed in the observations and interviews, can be characterized as predominantly conventional with CTL elements interspersed. In all three classes, Lynn followed the curriculum as laid out in the textbooks. Teacher presentation of new concepts and guided student input were her main teaching strategies. To this conventional framework, Lynn added tasks and activities that she characterized as having a CTL flavor, such as writing assignments, portfolios, small-group work with presentations, and hands-on activities. Writing assignments. Lynn used two different kinds of writing assignments: articles and poems. For the articles, students had to find mathematical information outside the classroom, for example in a newspaper or on the web, and then write an article about the information they had identified. The first time I assigned that I said, you gonna have to find an article in a magazine, I want you to write about the math involved, write about the statistics involved, make sure it has numbers in it because that will help you out a lot and see if they’re talking about averages or different things like that. (Interview 4/3/02) Lynn related two reasons for the writing assignments. She wanted the students to have a mathematical writing outlet, and she wanted them to realize the amount and kind of mathematics found outside the classroom (Interview 2/21/02). At first, some articles were rather clumsy and not necessarily what Lynn had expected. For example, one of the 13 students from the Algebra 2 class simply described the numbers she found in an article on the Olympics, rather than analyzing the context. One of the students picked out something completely random, with Olympics, which she could have really tied in with math, but she said, she picked out a person, she said, […] “The age of the person, this is a whole number,” […] “This took place in 2001, 2001 has so many decades in it,” different stuff like that. (Interview 2/21/02) Lynn assigned articles repeatedly, and the writing became a routine of which she was proud. Articles and all other homework were due on testing days. Lynn saw the articles improve, and the students thinking more critically about ―government, about food, about politics, about everything‖ (2/21/02). For example, one student wrote an
article on the USA birthrate exceeding the death rate for the first time since 1971, another student wrote on spending habits for Valentine gifts (Field notes 2/21/02). Both articles were based on information students found on the Internet (CNN.com/health and flowers.com, respectively). Lynn was particularly impressed by the work of one student who analyzed the information on the back of a baseball card and wrote the essay about the stats on the card. She was impressed because the student brought things to her attention that she had never thought of before. Lynn got an idea about using poems from one of her classmates. She offered 5 extra points to the test score of anyone who incorporated ―at least 10 bold-faced words from the chapter‖ (2/21/02) into a poem, and turned the poem in by test day. Writing a poem did not serve the same purpose as the essays because the students did not bring mathematics into the classroom from the outside, but it gave them a way ―to express it 14 [mathematics] differently‖ (2/21/02). Lynn was surprised by the eagerness of the students and the quality of their work. The following statistics Haiku poem was written by a student who was president of the drama club and who intended to be drama major in college. Statistics Haiku An observation of the double-blind cricket reveals subtle joy The distribution of thin, variable clouds— random, much like life Each event, like the hand‘s independent digits, is disjoint, perfect And in addition: what‘s the probability of enlightenment? Portfolios. Lynn referred to portfolios only in connection with the statistics/probability class. Students assembled portfolios ―at least two or three times‖ (4/3/02). For the portfolios, students collected ―different activities that we had done, up to that point, that were involved in the chapter that they did‖ (4/3/02), including homework, the articles, and projects. Lynn referred to the grading of the portfolios as authentic assessment. Group work and class presentations. Lynn used the jigsaw model for many of her small-group learning activities. This model fit well the purpose of the small-group arrangements: studying for a quiz or a test. If, for example, the test was over four sections of material, Lynn would first divide the class in four larger groups, each of which was charged to study one of the four sections. She would give them about 20 minutes in which to become experts on the section, ―take notes, look at formulas, get examples 15 down, be able to teach it to other people‖ (4/3/02). For the second phase, students would assemble into groups of four so that the group consisted of one expert for each of the four sections. The designation into the groups of four required careful planning, which was complicated for large classes, and for classes with poor attendance patterns. In addition, some of the students did not like the small-group arrangements because ―there were slackers in the group that didn‘t pay attention during phase one, so they didn‘t teach it very well in phase two‖ (4/3/02). Lynn realized that it would take time to educate all students to be responsible group members. Nevertheless, she liked the model and would use it again, but not make it the sole context for reviewing (4/3/02). I observed two slightly different set-ups, although they were both based on the jigsaw model. In a review session on functions (Algebra 1), groups of students made presentations on function sub-concepts, such as end behavior, continuity, symmetry, and extreme. Each presentation included two quiz questions that the rest of the class had to answer directly after the presentation. In another instance (Algebra 2), different groups of students would work through a section and select three problems from that section to be worked on the board. Lynn worked most of the selected problems, but asked for student questions and elicited student input. Finally, some of the hands-on activities also provided a context for setting up a small-group working environment. Activities. Lynn tried to implement many of the activities ―that we have done within my math education classes that were contextual, I tried to bring them into my
statistics class‖ (4/3/02). Lynn was particularly fond of the staircase activity mentioned earlier. She said, ―I remember measuring these, like I have an experience to connect with 16 the stairs that I was looking past everyday before I did the experience‖ (4/3/02). Later in the interview, Lynn highlighted again the importance of experience, ―I think that I‘m gonna relate that from my learning experience and try to transfer it so that other people can have the same experience‖ (4/3/02). I observed the implementation of two activities, the blood-type activity and the ball activity. Lynn introduced the blood-type activity to her statistics class because the activity highlighted concepts from probability and statistics. She used two days, one for the initial introduction and one for the ―clean-up.‖ I observed only the second day. Lynn found the activity in the February edition of the Mathematics Teacher. The activity consisted of an introduction by the teacher, instructions for a survey to be completed at home before the activity, and a set of student activity sheets. Lynn assigned the homework then handed out the activity packets the next day. From what I could gather from the interviews, there was no verbal introduction or explanation of the different components. I handed them out a packet, and it was directly from the magazine […]. And I thought, and I really didn’t look over it that well because I thought that was pretty self-explanatory, I thought, oh cool, we get to do something with blood types, […] and I looked at it, while they were working on it, and I thought, “Oh, they can do that, they can make a bar graph. (2/21/02) As Lynn found out during the lesson, the activity was in no way explanatory. Well, I didn’t realize how un-self-explanatory it was, until they started working on it, and I had a flock of students coming up to me saying, “I don’t understand this, 17 this is stupid, I don’t, I don’t get this, why are we working on this,” and they were very frustrated, and it was because of my lack of planning. (2/21/02) For the activity, the students had to correlate and compare three sets of blood-type data; class data based collected during the survey, data collected through a random number game, and Red-Cross data provided in the activity package. The Red-Cross data were presented as percentages, whereas the survey data and the simulation data were raw data with different sample sizes. Because Lynn did not think through the activity in detail, she did not anticipate the confusion over the different representations of the data. After the rather chaotic lesson, Lynn went home and prepared a second handout with data and instructions. She said, ―I cleaned it up a lot, and I made it a lot more straightforward, and I really (with emphasis) read the introduction to this article more. And that helped a lot‖ (2/21/02). The next day Lynn handed out a work sheet that contained the introduction and instructions, which were more concise than in the original packet. The students read through the introduction and a brief discussion followed including what it means that two blood types match, are compatible or incompatible, and what is means to be a universal donor or receiver. She lead the class through the rest of the assignments, and the lesson ended with a survival game in which the class determined who of their classmates would have the best chance of survival in case of a natural disaster with no hospital blood supply available. It was pure coincidence that the school had a blood drive later that week, and thus the activity provided a connection between the wider realm of school life and the more narrow life within the mathematics classroom. At the time of the interview, Lynn had no clear image of how to take more conscious advantage of this connection. In the later 18 interview in April, however, Lynn considered more seriously how to extend the bloodtype activity and to take advantage of opportunities such as the school blood drive. She thought about taking advantage of student volunteer work for data collection, or finding out more about hospitals and how they work. The second activity I observed was the ball activity. A ball was dropped from a certain height, and the time it took the ball to bounce twice was measured. Thus, the initial height was the independent variable, and time was the dependent variable. Lynn had done in the activity during a workshop, and thought it suitable for her Algebra 2 class. The class was studying quadratics, and Lynn wanted to give her students an example of quadratic function ―outside the classroom.‖ The activity was performed on two days with some other class work preceding the activity on each day. The first day was planned for data collection; the second for graphing and data analysis. However, because most students did not keep their data sheet, data collection had to be repeated on Day 2. Thus, data analysis was cut short. There was
only time to enter the data from one group into a graphing calculator and run a quadratic regression. The regression parabola had a maximum in the first quadrant and opened downward. The correlation coefficient was above 0.9. However, as I thought about the regression function, I realized that the result did not make sense. Because the parabola opened downward and the maximum was in the first quadrant, the time had to be zero again at some future height. It made no sense that the time would decrease as long as the height increased (see Figure 1). 19 Figure 1: A parabola with maximum in the first quadrant an opening downwards with two x-intercepts. I discussed the activity with Lynn during the interview following the second lesson and again during the interview in April. As it turned out, Lynn did the activity as she remembered it; she had no written record. However, she insisted that the relationship was quadratic. But she also agreed that the quadratic relationship did not make sense. Lynn was not able to resolve the issue during the interviews. The graphs below (Figure 2, a-d) show that with a limited set of measurements the regression function can be ambiguous. Figures 2a and 2c show quadratic functions, Figures 2b and 2d square root functions. The general shapes are similar and both could be—considering measurement errors during the experiment—solutions to a small set of data. 20 Figure 2a: A quadratic function. Figure 2b. A square root function. y = -0.0156x2 + 0.4003x + 0.1212 R2 = 0.9798 0 0.5 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 16 Figure 2c. Experimental data with quadratic regression. 0 0.5 1 1.5 2 2.5 3 0 5 10 15 Figure 2d. Experimental data compared to a square root function. Like the blood-type activity, the ball activity was not well prepared and not thought through with all its consequences. This lack of thorough planning was one of the factors that interfered with a more comprehensive implementation of contextual teaching and learning. Factors That Hindered Implementation From the observations and the interviews, I inferred several factors related to extensive and thorough planning that hindered the implementation of CTL: the textbooks used in the Algebra classes, a lack of time, difficulties with class management, lack of thorough planning, and lack of experience. 21 The algebra textbooks. Both algebra classes used traditional textbooks with their usual two-page per lesson layouts. Typically, a lesson starts with an introductory word problem, followed by a how-to-do section, practice, more practice, and finally some more word problems. Within the lesson, the steps to be performed are small. Students can go through the lesson and complete the practice assignments with minimal thought. The lessons within a unit follow the same principle: small steps and few, if any, challenges. In short, work from most traditional textbooks can be boring. In order to turn a unit from such a textbook into a more exciting sequence of tasks with problem-solving emphasis, the teacher needs experience, has to invest considerable effort and planning, and has to be secure enough to tolerate some level of student
frustration inherent in problem solving. As a student teacher, Lynn did not have this experience. She was just starting to gain this experience. For example, she did not have previous teaching experience that would have facilitated her knowing which parts of a textbook unit to de-emphasize, which to expand, or how to consistently frame a presentation from a conceptual rather than a procedural point of view. In addition, it appeared that Lynn took the non-contextual approach of the textbooks as given. For example, she said about algebra, ―If you just give these kids just random functions that are abstract and only exist or are alive on a Cartesian plane, and that‘s it, there is no Cartesian plane that those kids can touch and feel and relate on a daily basis […], it‘s much harder to find that those abstract ideas in the real world‖ (4/3/02). I do not claim, however, that Lynn did not attempt to address the contextual development of her algebra students. For example, when the class studied factoring 22 quadratic functions into linear factors, Lynn introduced algebra tiles and guided the students to interpret the trinomial as the area of a rectangle, and the linear factors as the length of the sides of that rectangle. But, in general, the algebra textbooks did not foster a contextual approach. In addition, Lynn felt that her university courses did not prepare her well to deal with the kind of textbooks she had to use in the algebra classes. She highlighted the discrepancy between ―these interesting themes and projects that go on for four weeks‖ (3/8/02) and the charge to student teachers to ―using the books, [and] going by chapters‖ (3/8/02). The time factor. Time seems to be the most precious and scarce commodity for any teacher, and this is even truer for student and novice teachers. Lynn saw herself having more time problems than the other student teachers in the school. For example, Lynn accompanied her mentor teacher, who was the department head, to all meetings the mentor teacher attended. These extra meetings diminished her preparation time. Also, Lynn was generous in her time before and after school when students asked for help. In addition to the tutoring of her own students, Lynn tutored other students in order to earn some extra money. Finally, Lynn visited several of her students‘ extra curricular activities. She attended the presentation of the drama club, participated in senior night of the basketball team, watched a tennis match, went to a mock trial on a Saturday morning, visited some of her students at their work places, and intended to go to the graduation ceremony. As commendable as Lynn‘s interest in her students‘ life outside the classroom was, it again took a lot of time, time not available for planning. Class management. Classroom management was the single largest issue that permeated all aspects of Lynn‘s student teaching experience. For example, in the 23 interview after my first visit, classroom management dominated about 75% of the interview. The interview took place at the end of a week that had brought Lynn to tears after one particular lesson in the Algebra 1 class of seniors. It was just really sad, it got so chaotic, the class I have the hardest problem with—the other two classes were fine—but that one class, it messed up my whole week, that one class during that one period on that one day has messed up my whole week. And, and it was horrific. (2/21/02) Lynn‘s problems seemed to be greatest in the Algebra 1 class. Lynn saw several factors that contributed to her difficulties. First, with 32 students, this was the largest class she had to teach. The room was filled to capacity, and Lynn felt she had only limited options to rearrange the seating and accommodate students who wanted and needed to be in the front of the room (2/21/02). Second, most of the students were seniors who needed the class to graduate, and they simply wanted to finish it with the least amount of work. Third, Lynn felt her age and her tendency to be very casual contributed to her difficulties in this particular class. I’m so casual and that’s the way I am. The students I’m working with are mostly seniors and so they don’t look at me as teacher a lot of times—which they should, they look at me as a big sister or as a college student, or someone who is there who knows a lot about math. But they don’t take instruction very well. (2/21/03) Furthermore, the class—although a college-preparation class—was not an advanced class and was made up of students with a wide range of abilities. Lynn mentioned quizzes as one example of her difficulties with students of diverse abilities. 24 A quarter of the students will be done with it in three minutes, the majority will be done within five minutes, a few will be done with it in eight minutes. Between that interval, the ones who get finished first start talking. (2/21/02)
Again, Lynn thought more options to change seating of the students could solve the problem with ―the hot spots,‖ whereas a more experienced teacher would have chosen some productive work assignment for the fast-working students. Finally, the Algebra 1 class was the last class to be picked up by Lynn, and it would be the first one she would return to her mentor teacher.5 Lynn couldn‘t wait to turn the class back to the teacher. She felt that she was in a mode of ―survival teaching‖ (Field notes 3/1/02). The Algebra 1 class was not the only class she had problems controlling. In a break between classes (3/1/02), Lynn talked about how she had been called to the counselor‘s office. Several students from the Algebra 2 class had gone to the counselor and complained that they were not able to learn in the class atmosphere of constant disruption and talking. The counselor had recommended that Lynn use a circle discussion about the behaviors in the class, what she could do to improve the learning atmosphere, and what the students could do. Lynn had followed that advice for her first period class (seniors, statistics/probability) and her third period class (sophomores, Algebra 2), but not with the second period class (seniors, Algebra 1). From my perspective of a limited number of classroom visits, Lynn‘s primary problem was that she had a difficult time establishing a focused presence in the class. I 5 In a typical student teaching experience, a student teacher starts with teaching one class only, gradually adds more classes to her schedule until she teaches the full load of classes. After about two weeks of full teaching, the student teacher returns one class after the other to her mentor teacher. 25 observed several lessons as having sliding beginnings, unclear starting points of when students‘ attention was required. During the lessons, I noticed parallel activities that I saw as distracting. For example, Lynn used the time during individual seatwork to return papers to the students. By going from student to student, commenting on the work done, she introduced some restlessness that then translated into student-student conversations. Another time, Lynn interrupted a quietly working class with an unrelated theme. She was, however, able to reestablish the working atmosphere in the class. Possibly, my interpretation of Lynn‘s unfocused presence and her view of being casual, ―the way I am,‖ describe the same phenomenon from two different perspectives, an outside view, and an inside view. Lesson planning. I already highlighted the lack of thorough planning for the blood type activity and Lynn‘s insights into the consequences of this. Similarly, the ball activity was not thoroughly prepared. Her preparation was limited to the surface features, that is, getting balls, stopwatches, tape measures and yard sticks for the lesson, determining the different groups, and producing the worksheets. What she failed to do was the deep, conceptual work on the mathematics involved. That is, Lynn did not think through the meaning of the independent (height) and dependent (time) variables, and the appropriate function that would express the relationship between these variables. However, in this particular case, this lack of conceptual preparation was not visible within the lesson itself. It only surfaced during the interview when I asked her to clarify the mathematics of the activity. I observed a few smaller incidents when Lynn‘s insufficient preparation was visible. In a quiz, Lynn wanted the students to find the roots of a quadratic equation by 26 applying the quadratic formula. However, she did not determine ahead of time if the function she provided actually had any real roots. As Lynn presented the quiz, she had to change the function twice to make it work for the intended purpose. In the same context of developing and working with the quadratic formula, Lynn introduced imaginary and complex numbers. The students were hesitant to accept those numbers. They called imaginary numbers ―fake numbers‖ and did not see any reason to invest time and effort into something ―fake‖ that did not even exist. A brief excursion into the history of mathematics and the conceptual development of imaginary and complex numbers (indeed, of all numbers) as ―answers to questions‖ could have provided a context for students to attach meaning to this new kind of numbers and thus accept them more willingly. Finally, Lynn felt that she was not prepared to produce effective lesson plans under time pressure. The development of a plan for a single lesson and a sequence of lesson plans for a 5-6 day unit had been requirements during the methods semester preceding student teaching. For both assignments, students had ample time, resources, and the support and advice of the instructors and a cadre of doctoral students. Although the ―the lesson plan was really good‖ (3/8/02), Lynn rejected the assignment as a model
for future planning because, Spending the three weeks to work on a one-week lesson plan was not realistic, […]. Neither did it prepare me for student teaching. I don’t write out day-by-day lesson plans with the five-bullet thing like we were talking about, I don’t do it, I don’t do it, I don’t have time to do it. (3/8/02) 27 In addition to feeling unprepared, lesson planning had not been the ―super duper focus during my student teaching‖ (3/8/02). However, I do not claim that Lynn did no planning for teaching. She planned her lesson to the detail that she felt comfortable with at the time. Lack of experience. Many of Lynn‘s problems can be seen as problems typical for a student teacher who simply does not have a wealth of experience on which to draw. With continued teaching experience, Lynn will know that instructional packages are not self-explanatory. She will be able to foresee student questions and difficulties and thus avoid frustration because of students‘ uncertainty with a task. She will know her textbooks, and will be able to evaluate a textbook lesson in context of the unit and the unit in the context of the year‘s curriculum. She will be able to distinguish between important new concepts that need to be highlighted, such as the quadratic formula and it‘s derivation and use, and side issue that could be postponed, such as the imaginary numbers. With more experience, classroom management issues will fade into the background of her attention and planning will move into the foreground. Factors That Fostered Implementation The following factors fostering instruction in the spirit of contextual teaching and learning evolved from the analysis of the interview transcripts and field notes; the textbook used, some of Lynn‘s mathematical experiences during high school, experiences in her professional college classes, and her ability to reflect on her actions and to evaluate them in light of her goals. The textbook. In contrast to the textbooks used in the algebra classes, Lynn saw the statistics textbook as promoting problem- and activity-oriented teaching. She said, 28 It’s so much easier for me to find activities for them to do, because they’re talking—their entire book is just laid out differently. Number one, it’s in paragraphs, it gives over and over examples, all they’re doing is word problems, that’s what they’re doing. (4/3/02) It was obvious that the layout of the textbook was quite different from the two-page, onelesson layout. Because statistics is an applied science that naturally relies on context, students have to read and deal with the context before they can engage in the mathematics. Word problems are not the dreaded section at the end, but make up the meat of the text. In addition, probability lends itself naturally to experiments, and Lynn introduced several of the experiments she had encountered in her university math ed professional courses and her statistics course. Finally, in preparing her lessons Lynn found herself reading through a whole section before attending to details, similar to what she had been requested to do during an investigation of a contemporary textbook series (Interactive Mathematics Program, IMP) in one of her curriculum courses. The thing that helped me out a lot is with the— even though we’re not using those kinds of books, those IMP books and all that stuff,…the way I had to go through the chapter is what I have to do for the stat class. (3/8/02) That is, Lynn had to read through and evaluate a chapter as a whole before she could attend to any details or design the first lesson. She also needed to work out the examples herself before she was able to use them in a lesson. However, Lynn did not use this kind of holistic and detailed preparation for the Algebra classes because ―the book is set up 29 differently in that it gives all the formulas outright and give problems to work on‖ (3/8/03). The IMP books, on the other hand, are set up with a theme, and this was similar to the set-up of the statistics book. Thus, Lynn‘s preparation in the curriculum course with one particular set of books was valuable for her teaching the statistics class, but not for teaching the algebra classes. Experiences in mathematics. The second factor that fostered Lynn‘s attention to CTL principles in her teaching was her memory of own positive mathematical experiences. These experiences had made a difference for Lynn in her view of mathematics and of mathematics in the world. For Lynn, the scavenger hunt in high school was a pivotal experience that opened her eyes for mathematics in the world around
her. She would look at a water fountain and see a parabola. Se would draw a coffee cup and think, ―This is an ellipse, where would the foci be, depending on the perspective, that kind of thing‖ (Interview 4/3/02). Like a staircase, the water fountain and the coffee cup are everyday objects that had become mathematical objects for her. It was important for Lynn that her students have similar experiences so that their world also would expand in a mathematical dimension. The second facet of Lynn‘s previous experiences that was influential was the way the mathematics concepts were taught. Lynn cherished the way she was allowed to discover concepts on her own and the ―open mathematics‖ in her first curriculum class. She remembered the hands-on activities and how much they changed her view of doing mathematics. Lynn wanted her students to have similar experiences and to remember the mathematics through those experiences. This seemed to be one of the reasons that she chose several activities as one way to bring CTL principles to life. 30 Reflection and openness. As long as I have known Lynn, I have always been impressed by her ability and willingness to look at herself and to reflect on her thoughts and actions. This willingness to reflect contributed to some valuable insights that surfaced during the interviews. For example, as she was reporting on the first day of the blood-type activity, she was also analyzing why the lesson had been so chaotic. She realized that her lack of preparation was one of the reasons for the students‘ confusion, and she went back to the activity and cleaned it up. Similarly, Lynn‘s preoccupation with classroom management led her to experiment with different strategies and to constantly evaluate these strategies. She was open to advice from the counselor and willing to follow this advice. Finally, I value Lynn‘s disposition of seeing more in her students than what was visible in class. Although Lynn‘s visits to her students‘ extracurricular activities and workplaces did take valuable preparation time, it did contribute to a more positive relationship between her and her most troublesome students: I sat with my, with my students that give me the hardest time, kind of blend, I don’t know, “Hey, Ms L., how you’re doing, Ms. L.,” that kind of thing, so they knew I was interested in what they were doing. (2/21/02) Lynn knew important details about her students. She recognized that some students did not have the luxury of coming for extra help before or after school because their out-ofschool work schedule did not allow for extra time in school. In addition, the out-of-school work was a necessary contribution to the family household. Lynn‘s openness to her students was influenced by one of her own experiences and her reflection on that experience. While Lynn was in college, a student was murdered 31 in her home, which was only a few houses away from Lynn‘s home. For some time Lynn was haunted by this seemingly random murder, and consequently her grades suffered. In her CTL portfolio, Lynn wrote: By reflecting on my own experiences, I will be able to understand more easily where some of my students are coming from. If one of my students are [sic] having problems at home, or in their community, hopefully I will be able to pick up on this, and help the student however I can. I think this experience will help me to be [a] more aware and sensitive teacher. (http://www.coe.uga.edu/ctl/model/stud_portfolios.html, see link: Problem Based Learning) Lynn‘s reflection on a personal life experience opened her eyes to her students‘ experiences as individuals. This contributed to her perspective that being a teacher of mathematics involves more than teaching mathematics, which, in turn, was a major factor in her approach to instruction. Discussion Dependence of Factors The factors that hindered implementation of CTL principles are not independent of each other. Although it is difficult to establish causal relationships between the factors, mutual influences among them are noticeable. Figure 3 depicts these mutual influences and relationships. 32 Lack of experience Algebra textbooks Lack of thorough planning Class management Lack of time Figure 3. Relationship among factors that hindered implementation. Algebra textbooks and planning. The designers of typical mathematics textbooks
make it easy and time efficient for teachers to use the textbooks without a lot of serious preparation. The two-page sections suggest a linear progression through the book, that is, two sections per day for schools on 4x4 block schedule. The teacher editions contain the answers to every question, exercise, and problem. Again, the teacher does not have to work the problems assigned. Thus, the teacher will miss the opportunity to anticipate difficulties for the students, and a time estimate of how long it might take to complete an assignment. On the other hand, a teacher does not have to accept the restrictions inherent in the design of the book. For example, the teacher can discard the teacher‘s edition, evaluate a unit as a whole, set priorities, bring in outside materials, and design instruction with a problem-solving focus. Although Lynn made some modification to the textbook and brought in activities; overall, she did not invest the kind of planning necessary for 33 problem-solving oriented teaching. The design of the algebra textbook let her get away with minimal preparation, whereas the design of the statistics book did not. Class management, time, and planning. These three factors reinforced each other and led to a cycle that made teaching more and more difficult, in particular for the Algebra 1 class. Issues of class management occupied much of Lynn‘s attention inside and outside of the class. In turn, time spent on worrying about management issues was time not spent on planning the next lesson, which then led to more management problems. Lack of experience. I see Lynn‘s lack of experience as the single most important factor. Lack of experience let her believe that the instructions for the blood type activity were self-explanatory. Lack of experience led to many of her management problems, and lack of experience made it difficult for her to divert from the convenient path of the algebra textbooks. In her lack of experience, Lynn was similar to many student teachers who are overwhelmed by the complexity of the daily teaching demands. What might have set her apart was that she kept her goals alive, despite her difficulties. Transfer of Learning For me, the teacher educator, Lynn‘s case highlights an important lesson. If I want to make experiences during the professional teacher education courses relevant for preservice teachers, then these experiences have to be similar to the situations they will encounter in schools. For example, it is not enough to introduce pre-service teachers to textbooks that model contextual, problem solving- and communication-oriented teaching such as the IMP textbooks. What Lynn learned from her work with these textbooks was only of limited help in her student teaching situation. When I asked student teachers to 34 read through a whole unit and determine and verbalize the overall goal of the unit before attending to any kind of detail, I intended to provide them with a planning principle useful for any textbook. For Lynn, however, this principle was useful only for the textbook that was similar to the IMP books. It was not helpful for the work with textbooks that seemed worlds apart. Thus, because most pre-service teachers will encounter conventional, skill-oriented textbooks, we, as teacher educators, also need to provide explicit models of how to transform these textbooks into problem- and contextoriented planning and instruction that pre-service teachers can transfer into their own teaching situations. It seems that transfer from one situation to the next was only effective if the situations were similar to each other. Similarly, I wonder how the lessons learned in the specific CTL courses transfer into the pre-service teachers‘ teaching environments. Lynn only connected a direct teaching situation—the episode with the snake—to her own teaching. She did not make a connection to teaching when the speaker in the children‘s hospital talked about communication. It might be up to us, the teacher educators, to make those connections more explicit. Coda In January 2003, Lynn started to work in a middle school in a neighboring county. She is teaching five 7th-grade classes, three regular (on-level) classes with about 17 students in each, one low-level class with 10 students, and one high-level class with 30 students. The school is not on block scheduling. Within the first month, Lynn started a CTL-like activity for the three on-level classes. The students had studied scale and scale drawings. As an application of what the 35 students had learned, Lynn asked the students to design their dream house, and to present a model, that is, front view and floor plan, to the class. The students could choose whether they wanted to work alone or with a group of students. Lynn‘s instructions for
the project are attached in an appendix. Lynn invited me for presentation day, and I attended the presentations in all three classes. As can be expected, the presentations and the models were of various qualities. But it was obvious that most students were very involved in the project and had put considerable thought and time into their designs. Many houses included an indoor half- or full basketball court. Two students, both working alone, had designed log cabins, thus documenting their love for outdoor adventures. The dream house project seemed to have captured the interest of the 7th grade students! Lynn had started the class project while she was still setting up classroom routines and learning about lunchroom and bus duties. In addition, she has already established a class website6 that contains syllabi, general assignments, expectations, group pictures, examples of mathematics in the world, and the description of the project. It seems that Lynn‘s start in her first teaching position has provided her with renewed dedication to provide contexts to her students that make mathematics meaningful for them. References Goetz, J. P., & LeCompte, M. D. (1984). Ethnographic and qualitative design in educational research. San Diego, CA: Academic Press. 6http://jwilson.coe.uga.edu/emt668/emat4680.2000/parker.Lynn/msparkersclass/oconeem athclasspage.html 36 APPENDIX BIG PROJECT : DREAM HOUSE Due: Day after Chapter 6 Test (Approximately Jan. 21st) The object of this project is to use your knowledge of scales and measuring ratios and fractions to create the house of your dreams. 1. I want you to be creative and inventive. 2. Your dream house should be accurate using proportions and scale drawings, A scale must be included and therefore is required. 3. The actual scale drawing of your dream house must be done on graphing paper. (I have some if you need it.) The major parts of the house should include – a. Kitchen b. Bathroom c. Living room d. Bedroom e. Dining rooms, decks, patios, and garages are optional 4. A visual representation of the house must also be included in your project. (I want to see what you imagine the front of the house looking like.) 5. Project must be presented in a poster form to a class. a. You may work individually, in pairs, or in groups of 3. NO GROUPS OF FOUR. b. Organization and information on the board will be assessed. THIS COUNTS AS A TEST GRADE. A rubric of how you will be graded follows: 1. Scale drawing of house (with scale included) - 40 pts 2. Neatness/creativity – 10 pts 3. Picture of the front of the house – 10 pts 4. Overall area of the house and outside perimeter of the house – 5 pts 5. Pick one room of the house and find – 30pts: 1. Cost for the walls 2. Cost for the flooring (hardwood or carpeting) 3. Perimeter and square footage of the room. 6. Reference for the flooring and wall prices. – 5pts (What store did you actually talk to, and what prices did the give per square foot?) 7. Bonus points will be given if you take the initiative to find out more about the pricing for building such a house. – 5pts Examples include: 1. How many bricks did it take to build the house 37 2. Give other statistics for other rooms 3. What about windows ~~~~~~~Good Luck and Have Fun !!!~~~~~~~
Dream House Rubric Name(s): ___________________________________________________________________ ___________________________________________________________________ Period: ____________ Date: _____________ Category Possible Points Points Received 1. Scale Drawing 40 2. 1 Room Stats- Cost of walls, floors, perimeter, area 30 3. Front of the house Drawing 10 4. Neatness/Creativity 10 5. Area/Perimeter of House 5 6. References 5 7. Bonus 5 OVERALL POINTS 105 Comments by Ms. Parker: ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Implementing Contextual Teaching and Learning: Case Study of Nancy, a High School Science Novice Teacher Catherine Teare Ketter and Jonathan Arnold University of Georgia Final Report March 30, 2003 The work reported herein was prepared in association with the contextual teaching and learning in preservice teacher education and studies of novice teachers’ implementation of CTL approaches in the classroom projects at the University of Georgia, with funding support from the U.S. Department of Education, Office of Vocational and Adult Education, Contract # ED-98-CO-0085, 1998 – 2003. 2 Implementing Contextual Teaching and Learning: Case Study of Nancy, a High School Science Novice Teacher Catherine Teare Ketter and Jonathan Arnold University of Georgia Abstract The goal of this study is to examine how Nancy, a student teacher in high school science, implemented contextual teaching and learning (CTL) into her classes. This was done by observing Nancy during her teaching, interviewing her after each observation, and reviewing the class materials she prepared (e.g., lesson plans and student assignments). Nancy‘s supervising teacher was also observed to identify differences between CTL and traditional teaching. A native of South Africa, Nancy became a strong supporter of CTL, stating that, ―If I had not gone through CTL, I would be a very traditional teacher.‖ Now, ―for every content topic I am always trying to figure out how things relate to the student‘s everyday life.‖ Nancy focused on using CTL in several ways in her classes. She used a case study approach to each science unit, providing students with an open-ended problem and tasking them to discover a plausible explanation. Students often worked in teams and had access to multiple resources for their research. Also, unlike traditional lecture and drill, Nancy focused on her students‘ ability ―to do science.‖ Whenever possible, students were asked to relate their studies to their own lives (e.g., connecting mononucleosis to the study of the lymphatic system of a fetal pig.) In addition, students
applied skills learned in other classes (e.g., math and English) to their science projects. Researchers also identify facilitators and barriers to Nancy‘s CTL implementation. 3 Implementing Contextual Teaching and Learning: Case Study of Nancy, a High School Science Novice Teacher Catherine Teare Ketter and Jonathan Arnold University of Georgia Introduction The goal of this study is to examine the process of implementation of contextualized teaching and learning instructional strategies in a secondary science classroom and laboratory setting by a student teacher participating in the contextualized teaching and learning (CTL) teacher preparation model at the University of Georgia. Towards the end of CTL training in the teacher education program, students have the opportunity to assume the role of a student teacher in an educational community, an internship experience by which pre-service teachers acquire on the job training prior to entering the teaching profession. The purpose of this model program is to provide preservice teachers with a context in which to frame their content (e.g., http://www.coe.uga.edu/ctl). The CTL model places specific emphasis on: Delivery of curriculum through contextualized teaching and learning strategies Use of community-based experiences, workplace experiences, and school contexts to inform teaching and learning Preparation of teachers to implement contextual teaching strategies CTL practice typically involves the use of one or more of the following seven teaching strategies (http://www.coe.uga.edu/ctl/theory): 1. Problem-based learning 2. Project-based learning 4 3. Inquiry-based learning 4. Service learning 5. Collaborative learning 6. Authentic assessment 7. Engaging students of diverse backgrounds Nancy is completing her training in science education and will be one of the first graduates of the U.S. Department of Education funded contextualized teaching and learning (CTL) contract in the College of Education at the University of Georgia. We observed Nancy beginning the fourth week of her internship and set plans to continue observing her once she has found a permanent position. The objective was to observe how she included and implemented CTL strategies within the curriculum specified by her supervising teacher and the state of Georgia. Four classroom observations were scheduled when Nancy was responsible for teaching a unit; she was interviewed immediately following each lesson. The interview questions focused on CTL principles, how she used them, her observations regarding her students‘ performance, and her feelings about her student teaching experience and CTL. At the end of this study, we conducted an exit interview with Nancy and her supervising teacher at Cedar Shoals High School, Mrs. Mary Bailey. Nancy was asked to submit lesson plans, outlines of student assignments, and other documentation, which supported her classroom CTL strategies. We also had the opportunity to observe her supervisor, Ms. Bailey, an award-winning science teacher. This provided an opportunity to compare traditional instructional paradigms as implemented by an experienced teacher with CTL strategies used by a novice teacher, Nancy. There are five research questions addressed by this case study. Classroom 5 observations and teacher interviews are designed to collect information about the efficacy of CTL practices in the secondary high school science classes by pre-service and novice teachers. 1. Which CTL strategies do first year CTL-trained teachers use in the classroom? Why? To what perceived or measured outcomes? 2. What are the facilitators and barriers to implementation of various CTL strategies in actual classroom practice in school settings? 3. How does the teaching practice of CTL-trained first year teachers differ from more traditional approaches to teaching the subject matter? 4. What effect does use of CTL strategies have on student engagement? 5. What effect does use of CTL strategies have on mastery of subject matter content?
Community Athens-Clarke County (ACC) is located approximately 72 miles north and east of Atlanta, Georgia. It is a unique community in which city and county governments have merged to provide residents with the best in governmental services. ACC is home to the University of Georgia, a large state research university with an enrollment of approximately 32,000. The large number of university students in ACC shifts the population toward a young demographic group. Athens and the University offer county residents with a large number of cultural programs, excellent libraries, and community education programs. The ACC School District currently serves 12,127 students enrolled in 19 schools. There are 13 elementary schools (grades K-5), four middle schools (grades 6-8), and two senior high schools serving grades 9-12: Clarke Central High School and Cedar Shoals High School. Athens-Clarke County also has state funded pre-kindergarten programs in 6 place in many of the elementary schools. All 19 schools in the ACC District are accredited by the Southern Association of Colleges and Schools; additionally all the schools meet Georgia Department of Education standards. Currently, almost 14% of the students registered in public education in Athens-Clarke County are enrolled in gifted education programs. The average student to teacher ratio in the elementary schools is 23:1 with an average daily attendance rate of 94.9%. ACC employs 820 teachers, 250 paraprofessionals, and 900 professional support personnel. Approximately 60% of the teachers and school administrators hold advanced degrees. Of the Clarke County high school students who completed Advanced Placement (AP) courses during the 1999-2000 academic year, 74% earned sufficient scores on the AP exams to merit college credit. This level of AP success compares favorably to the state of Georgia average of 56% AP college credit for all Georgia high school students enrolled in Advanced Placement courses. School Setting Cedar Shoals High School (CSHS) is one of two public high schools in ACC. There are currently 1,516 students attending CSHS. The student body in 2000 was comprised of 559 freshman, 389 sophomores, 299 juniors, and 269 seniors. There are 88 teachers at Cedar Shoals with a student to teacher ratio of 17.2 to 1. Demographically, the majority of students who attend CSHS are Black, non-Hispanic students (877 students or 57.8%). White, non-Hispanic students comprise 37.1% (562 students) of the student body. Hispanic students are 3.4% of the student body (51 students), Asian/Pacific Islanders are 1.6% of the student body (24 students), and there are currently two Native 7 American high school students at CSHS (0.1% of the student body). The average Scholastic Aptitude Test (SAT) score for Cedar Shoals High School students was 1035 in 2000 as compared to 980 for all Georgia high school students and a national mean of 1020. CSHS college prep students averaged 1044 on the SAT in 2000, and the top 10% of CSHS seniors earned a mean SAT score of 1269. The current school building was completed in time for the 1999-2000 academic year replacing an aging facility, which opened in 1972. The building is brightly lit, open, and inviting. There are security checkpoints at all of the main building entrances. Students must have hall passes to walk the corridor during class periods. Visitors to Cedar Shoals High School must have prior clearance, and they must obtain a pass to visit a specific classroom. The current athletic facilities are a combination of new and existing buildings. Cedar Shoals High School has a fine arts program, which includes a theatre program, an active band and orchestra, and a visual arts program. There is a large career and technical education program with its own dedicated wing of the building. The various offerings place students in internships with local business while preparing students for a career following the completion of high school. Cedar Shoals High School has a large college prep program that offers many Advanced Placement courses for students who wish to earn college credit. CSHS also participates in a joint enrollment program with the University of Georgia. Qualifying CSHS students may enroll in courses at the University of Georgia and earn college credit that is applied to their high school course of study. Student Teacher Nancy is a student teacher finishing the CTL program with a degree in secondary 8 science education. A native of Port Elizabeth, South Africa, Nancy moved to Georgia as a teen. She completed high school in Peachtree City, Georgia before coming to the
University of Georgia to pursue a college degree. Initially, Nancy was enrolled in a nutrition/dietetics program because she wanted ―to make a difference in people‘s lives.‖ After her freshman year, she changed her major to secondary science education. She hopes to combine her love of the outdoors with her interests in epidemiology. Currently, Nancy has completed these CTL courses in teacher education program: Learning and Development in Education (Instructor: Knapp) Disiciplinary Knowledge (Instructor: Schell) Situated Cognition Theory and Implications for Teaching (Instructor: Schell) Academic Community Learning (Instructor: Pate) Contextual Teaching and Learning in Schools (Instructor: Tippins) Internship at CDC, Fall 2002 Teaching Internship at Cedar Shoals High School in Athens, GA, Spring 2002 She needs to complete content courses in genetics, biochemistry, and cell biology to graduate. We observed her teaching internship at Cedar Shoals High School. Nancy‘s initial and exit interviews provided a view of her goals, teaching philosophy, her background, insights on what the CTL focused courses meant to her and her personal goals for the future. Nancy’s Background Nancy said, "I always knew that I wanted to teach. I used to line up the stuffed animals and teach them." She developed a portfolio of case studies for use in her classes as part of her CTL curriculum. These included a whale portfolio and a CDC case study portfolio. She has taught middle school science using CTL strategies with a case study focusing on whales. As part of her internship, she has attempted to implement CTL in 9 introductory high school biology in a "rowdy," college-bound class; a well-behaved (2nd period) class, which we followed in this study; and an anatomy and physiology class in which she used the CDC case study she developed. She has also garnered teaching experience in Gainesville, Georgia. Once she finishes the remaining content area course work, she will enter the job market. Nancy’s Teaching Philosophy The following quotation gives a suggestion about what Nancy would like to do in the classroom and how she would approach the classroom in an ideal world, "Epidemiology, diseases and plagues, oceanography, microbiology in a big spacious classroom, with stations (lab benches) around the back and tables or nothing in the center. I'd like a monochromatic room, like a museum, in black and white, with displays that the students made which I could rotate. I'd like the big projector, like at UGA, where you push a switch and the screen comes down. I want a lot of autonomy on the content; I don't want to have to follow a state-mandated curriculum on a specific day. I would also start with a field trip where the students can use a field trip as a starting point for the course." She also said, "I love hands-on learning. I am a huge fan of PowerPoint, the students were probably sick of it by the end of the term.‖ Her description of the ideal classroom in many ways matches the description of the classroom at Cedar Shoals High School where there are multiple resources supporting innovative teaching practices (see Figures 1-3). This statement includes many CTL elements such as project-based learning, case-study research, multidisciplinary learning, and students doing real science at a lab bench and in the field. When asked to list the characteristics of a good teacher, Nancy said that ―a good teacher for her was someone 10 who was passionate, had the ability to sell content, engage students, questioning, challenging students to think beyond the classroom, scaffolding, guiding, inspiring, genuine with students, intellectually exciting." Her view of a good teacher is someone who makes content fun, meaningful, and presents the material in a real world context. For Nancy, the CTL program has changed her views on teaching, "If I had not gone through CTL, I would be a very traditional teacher. Dr. Knapp did a great job showing me that there were very different kinds of learners (in CTL Course, Learning and Development in Education). Dr. Schell's class really help me to think about my curriculum in a more practical manner." Nancy’s Perceptions Regarding CTL Use Nancy articulated her view of CTL, "How to relate to every day life — for every content topic I am always trying to figure out how things relate to the students' everyday life. I am trying to work on inquiry-based lessons." During our classroom visits we observed her efforts to include daily life in the context of each lesson. She engaged the students on a personal level by relating her life to the curriculum. The hope is that when students are engaged, the science content becomes meaningful to the student. It is hoped
that providing each learner with information that he or she can relate to and remember, we are helping them to develop scientific literacy. The structure of her lessons mirrors the process of scientific inquiry. Questions were posed to students concerning fetal pig organs systems, and students were required to make the necessary observations to answer these questions. In another example, Nancy asked the students to provide possible explanations for population fluctuations on an imaginary island. As part of this exercise, students had to develop testable hypotheses from which evidence is collected to support 11 or refute their explanation. For Nancy CTL teaching requires the teacher to connect biology to student lives, connect lesson content to other disciplines, and the lesson must have an inquiry-based learning design. Nancy said that you had to "ask for input from your students so that when you are incorporating everyday life experiences from the students, you are incorporating things that are pertinent to them" (student engagement to the world). ―Actively try to pull things in from other disciplines" (contextualizing science with respect to other disciplines). ―Don't be afraid to be wrong" (inquiry-based learning). In order for students to engage in inquiry-based learning, they need to see a teacher who is willing to try multiple approaches and learn from failure. At first, Nancy‘s students seemed to be uncomfortable watching her fail at doing something new. She emphasized that sometimes failure is part of the process involved in searching for an answer. Many real problems do not have a single correct answer, and the practice of science does not generally produce a single right approach or correct answer. Part of the scientific process includes the formulation of a hypothesis; frequently the hypothesis is not supported by data collection and analysis. Inquiry-based learning involves encouraging students to think on their own, allowing students the freedom to find individual and different solutions to a problem. Our observations in the biology and anatomy and physiology classes at Cedar Shoals High School suggest that contextual teaching and learning became part of these students‘ everyday experience in Nancy‘s class. The following vignette illustrates student engagement in the 2nd period class. Some of the class is engaged in learning about the function of different organ systems. Nancy interacts with a student. She shakes her head up 12 and down as the student answers. She asks about the heart and demonstrates with her own body. She interacts with two more students and asks them what organ system circulates oxygen. Several students joke about organs. One of the students asks what system makes you go to the bathroom. Nancy asks what system removes toxic waste? (reference field notes). Nancy’s Life Goals In Nancy‘s own words, "I see myself teaching in public school while I am working on my masters and continue working on curriculum for the CDC. I like internship opportunities." She hopes to have the opportunity to enrich her classroom with case studies drawn from real world examples and personal experience. In the development of a case study unit on whales, Nancy used her personal experience as a participant in a whale watch off Stillwagon Bank in the Atlantic Ocean near the coast of Massachusetts. She has developed this unit as part of her CTL curriculum portfolio, and she presented this lesson during her teaching internship. Classroom Nancy fulfilled her internship requirements by teaching introductory biology in 1st and 2nd periods and anatomy and physiology in 4th period. We observed her in 2nd period biology class. The class met every day on a block schedule. Class observation began at 10:00 and finished at noon. The classroom layout included a central seating area flanked by laboratory tables so that lectures, student discussions, group work on projects, and laboratories can be conducted in one classroom (see Figure 1 for classroom layout and Figure 2 for flanking laboratory area). There were several computers in the classroom as well as VCR, overhead, and computer projection capabilities (see Figure 3). 13 Figure 1. The classroom layout, where student work areas can function both as classroom and laboratory area. More computers can be seen in the background. Figure 2. Flanking laboratory area at the back of the classroom pictured in Figure 1 allowing laboratory science in the classroom 14 Figure 3. Computers in the classroom for integration of mathematical sciences with the teaching of biology. Curriculum
Nancy described the biology curriculum as increasing in complexity from the cell to kingdoms to ecosystems. The curriculum is structured using levels of biological organization: organism, individual, community, and back to the cell. The class progressed from small to large biological organizational units, returning to small units (the cell) when Mrs. Bailey resumed teaching responsibilities. Students were given a diversity of assessment instruments including a standardized test in biology administered to all high school biology students in the state of Georgia. Nancy's instructional goals for the ecology unit are best captured in her own words, "I would like to focus on the 15 environmental things that they can do - earth friendly cleaners - use human hair and test bacterial growth - I want to tie it all into the whales, the Beluga whales in the St. Lawrence." Methods Table 1. Classroom observation and interview schedule for Nancy. Date Topic Interviewer Notes January 31, 2002 Initial Interview Jonathan Arnold Outside class February 6, 2002 Permission Jonathan Arnold With Mrs. Bailey February 15, 2002 Fetal Pig Lab Jonathan Arnold In class February 26, 2002 Community Web C. Teare Ketter In class March 1, 2002 Imaginary Island Jonathan Arnold In class March 4, 2002 Imaginary Island Jonathan Arnold In class May 20, 2002 Exit Interview C. Teare Ketter Outside class January 30, 2003 Follow-up Interview C. Teare Ketter With Mrs. Bailey Data were collected as outlined in Table 1 above. The two investigators, Dr. Jonathan Arnold and Dr. Catherine Teare Ketter, observed Nancy's class from 10:00 a.m. to 12:00 noon, immediately conducting an interview with Nancy following the class that day. Fortuitously, we also had the opportunity to observe Mrs. Bailey teach which facilitated the comparison of CTL practices implemented by a student intern with the classroom practices of an experienced professional. Nancy worked with four different classes, but we elected to observe 2nd period because Nancy indicated that this class would probably be similar to the students that she would be teaching on her first job. We felt that should Nancy complete her degree requirements and become employed as a teacher during the time of this case study, we would be more likely to observe her using her CTL portfolio during her first year in a paid teaching position. We did not consider visiting multiple classes for a planned three 16 visits because we wished to become familiar with class behavior and the individual students in a specific class. An additional benefit to the selection of the 2nd period class was that Nancy had lunch/planning period following the class, providing us with time to interview her immediately after class. At the end of the fourth classroom visit, Dr. Arnold felt he was observing a large fraction of recurrent classroom behaviors. No additional class observations were made. There were two independent observers for data collection in this study. Dr. Arnold took a laptop into the class, and notes were taken as events unfolded in each class. Dr. Arnold always sat in the same location in the class (near the computers in the background of Figure 2) and was limited in what he could overhear and see of the students. Dr. Teare Ketter sat in a different location and took notes by using her laptop to record classroom events. We tried to evaluate each visit from Nancy‘s perspective as well as from our viewpoint. The initial, permission, and exit interviews had different research objectives. The initial interview was conducted to encourage Nancy‘s participation in the study and to explain the purpose of the study. The permission interview with Mrs. Bailey had the same objectives. The exit interview was conducted to solicit Nancy‘s views on CTL and to elicit her personal and career goals for the immediate future. Additionally, we reviewed the artifacts used in class by Nancy. The transcripts of class observations and interviews conducted by both researchers were combined. The data were evaluated using the constant comparative method of case study analysis (Merriam, et al, 2002; Merriam, 2001) by Drs. Arnold and Teare Ketter. Summary of Findings 17 Direct observation of student learning in the 2nd period biology class at CSHS suggests that student learning was stimulated by an inquiry approach. A problem-solving paradigm or a case study approach was used for each unit. Student problem-solving
skills were developed as a direct result of practicing science. They were provided with an open-ended problem, explaining fluctuations in population size for example, and asked to construct an ecologically plausible explanation. Students were engaged in collaborative learning by "partner study," teamwork in laboratories, and the presence of multiple sources of authority in the classroom. Facilitators of CTL practice were a classroom/laboratory, new school, block scheduling, and an award-winning mentor already practicing elements of CTL (based on her experience of what works with students). Barriers included were "time pressure to cover the material," cost of laboratories, discipline issues, administrative interruptions from the main office, and lack of time management skills by the novice teacher. Student engagement was apparent in the classroom, and student engagement was achieved by connecting science to student lives, community, and world and by having them constantly "doing science." Differences between traditional classroom practices and CTL instruction included content presentation using a traditional lecture approach followed by a question and answer drill (passive learning) and one-on-one interaction between student and teacher required to implement a case study unit (active learning). The student teacher performed student assessment on a nominal, functional, structural, and multi-dimensional scale by assessing the student's ability "to do science." Observer Perspective Dr. Jonathan Arnold is a professor in the Genetics Department who holds 18 appointments in three additional departments: Mathematics, Statistics, and Physics and Astronomy. He is actively involved in teaching undergraduate science students in an introductory biology course and in an upper division genetics course. His research interests include the use of CTL practices in college courses and their impact of the development of student communities within a large research university, student achievement, and problem-based learning in an introductory biology laboratory course. Dr. Catherine Teare Ketter has spent the past twelve years teaching introductory biology courses, training life science graduate teaching assistants in effective teaching methods, and designing introductory laboratory curricula for biology and marine science courses. Prior to completing her Ph.D. in Educational Research, Catherine was a secondary science teacher in Alabama. Findings CTL Strategies Used by CTL-Trained Novice Teachers CTL practice typically involves the following pedagogical methods (Resnick, 1987; http://www.coe.uga.edu/ctl/theory): Problem-based learning Project-based learning Inquiry-based based learning Service learning Collaborative learning Authentic assessment Engaging students of diverse backgrounds There are several fundamental aspects to contextualizing science in the science classroom/laboratory: Students doing real science; students relating the science to themselves, their community, and their world; and students relating science to other 19 disciplines. We observed the contextualization of science being practiced by the students in the CSHS biology classroom. In addition, we analyzed how students practiced science. The practice of science includes these student behaviors: Observing natural systems Formulating a hypothesis through exploratory analysis Following a scientific protocol in observation or experiment (i.e., a recipe) Keeping a laboratory notebook Carrying out an experiment with controls Testing a hypothesis Writing up the findings Relating the findings to the literature Presenting the findings to colleagues Project-based learning was a central theme in this high school life science course. Project-based learning "is a comprehensive approach to classroom learning designed to engage student investigation of authentic problems" (Berns & Erickson, 2001; http://www.coe.uga/ctl). We observed Nancy supervising students in several projects: a laboratory dissection of a fetal pig, the analysis of an imaginary island population, and a
case study on Whales focusing on the trophic structure of an open ocean community. An extension of one of the units included the students constructing their own community ―web‖ describing their interaction with people in their daily lives. The whale case study unit was part of Nancy‘s CTL portfolio prepared in her CTL teacher preparation. The fetal pig dissection project was designed for completion during a single class period. Student enthusiasm for the project slowed Nancy and her class so that the project was extended for four class periods. Nancy posed a series of questions requiring the students to make observations of the internal anatomy of the fetal pigs. Only through 20 careful observation were the students able to answer all of the questions. The students worked collaboratively in small groups to complete the dissection exercise. Assessment for content mastery included a practical exam using student-dissected pigs. The students were asked a series of questions requiring recall identification of internal organs and organ functions using the pigs. This provides the students with concrete experiences that anchor abstract concepts. This anatomy unit also required that the students summarize their observations in writing. The entire unit was organized so that students hear, then say, see, then say (Hear/Say/See/Say). This instructional strategy provides auditory, kinesthetic/tactile, and visual sensory input for learning so that no learner is left behind. The fetal pig anatomy unit illustrates contextualized learning in several important ways. Mrs. Bailey introduced an analysis section of the laboratory with the statement "Explaining is learning." Students were asked to write two paragraphs about what they saw during the dissection answering questions including, but not limited to, the distinction between anatomy and physiology, the relationship among differing levels of biological organization, and the relationship between the level of organization and complexity. An important aspect of science is the written and oral communication of research findings. Writing skills learned in English class were transferred across disciplines to science class. Implicitly a link was made between disciplines. This link is emphasized as essential to employers. Lastly, students related what they had learned in biology class to themselves. They observed internal organs, and they identified the reproductive organs of both male and female pigs. They related the organs they observed to the food that they eat. Students who had contracted infectious mononucleosis located the pig spleen and noted 21 the location of lymphatic vessels and lymph nodes. The students had a personal connection to that which they found. There were multiple sensory modalities actively used to master this material. This visceral experience for one student was overwhelming. He nearly fainted. The fetal pig was a first in this class, and the students were videotaped as the class moved through the unit, presumably for evaluation and later use. The second major project class project was a population growth exercise in which students are asked to follow a human population on an imaginary island for 90 years. The physical characteristics of the island were described including the size of the island and island topography. Island events, physical and biological, were presented as part of the problem. Students were asked to analyze the pattern of population growth and to provide an explanation for the numerical fluctuations observed in population size. Ecological concepts including environmental carrying capacity, predator-prey interactions, density-independent limiting factors to population growth, and densitydependent limiting factors were to be incorporated into their explanation of the data. This investigation required multiple class periods to complete. Students were provided with a data table summarizing population size as a function of time, in years (refer to Table 2). They were asked to present their results graphically. They were required to apply the concepts of independent and dependent variables to their data analysis. These concepts had been mastered in a previous problem-based unit, and the application of these concepts in a new situation required the students to extend their current understanding of experimental variables. Table 2. Human population growth data from Nancy’s “Imaginary Island” unit (Reference Notes lines 959-975 (in Appendix)). 22 Time Point (Yrs) Change Population Size 0 +25 25 10 +35 60 20 +25 85 (correction here) 30 +25 110 40 +10 120
50 0 120 60 -20 100 70 +20 120 80 -30 90 Cannabilism? Eat humans they say. 90 -90 0 Nancy circulated through the class as students plotted their data on a graph using the data table (in Table 2) presented on an overhead. Perturbing events such as cannibalism were introduced. A series of challenge questions were posed using the overhead projector, and the students were left to address the questions individually. ―What is the density on the island? What is the limiting factor? Define carrying capacity. What major event during the study was an example of a density dependent factor? When is the population growing exponentially?‖ The students were introduced to abstract concepts using questions and asked then to apply their answers in a unique way to explain the data. Traditional lecture format was not a part of this unit. The content was placed in a personal context for the students. They used the scientific inquiry paradigm to formulate their own hypothesis about the population fluctuations over time. They used their hypotheses to make predictions. They had to evaluate their predictions using the longitudinal population data. To summarize the unit, the students were asked to prepare a written analysis of the process they used to evaluate the problem. This unit required the transfer of quantitative skills learned in mathematics to the science classroom. Students 23 began to understand that mathematics is central to conducting scientific research. Students were required to apply mastered computational skills in a new context. This problem-based unit required the students to transfer written communication skills from English class. As the Imaginary Island was analyzed, Nancy asked students to define growth rate (on the island) and calculate it. She asked about the death rate. She introduced the concept of exponential growth and when did exponential growth occur on the island? She explained that rate is how fast something happens. (field notes). Due to time constraints, Nancy was unable to use her third unit centering on the trophic position of whales in open ocean ecosystems. She has successfully used this unit in a middle school classroom at St. Mary's. In the exit interview with Mrs. Bailey, she stated that Nancy‘s implementation of CTL practices had impacted student learning. Student engagement was high, and student attitude toward the content and the class was positive. Mrs. Bailey did feel that CTL strategies as practiced by Nancy were an inefficient use of time. The problem-based units all had to be extended to multiple class periods because Nancy required all of the student teams to complete all parts of the problem rather than assigning a different subset of information to each student group. Student groups could then summarize their findings for one another, and facilitated discussions would be used to piece together the larger puzzle. Mrs. Bailey felt that Nancy‘s lack of adequate time management skills was a function of inexperience in the classroom and not a direct result of CTL practices. Problem-based learning is a key element in CTL teaching practices. "Problem based learning is an instructional approach that uses real-world problems as a context for students to learn critical thinking and problem-solving skills." (Berns & Erickson, 2001; 24 http://www.coe.uga.edu/ctl). During the fetal pig anatomy unit, the students were required to master the organs systems before they began to dissect. The instructional method to present this material was lecture and drill which facilitates shallow cognitive processing through rote memorization. For many classrooms, that would be the end of the lesson. Then the pigs were introduced, and the students had to apply what they had learned in the context of the pig; the unit suddenly became problem-based. Real organs similar to the ones in the students‘ own bodies were displayed on the lab bench. The students made visual observations. They could touch the pigs. Students also had to describe what they saw. In each group, there was usually one student who took charge of the cutting. Some students were unable to handle the dissection and were put off by the smell of the preservative agent. With the human population fluctuation problem on an imaginary island, the instructional method was solely problem-based learning. The objective of the lesson for each group of students was to provide an explanation for the data in the table. They needed to relate island events with fluctuations in population size. They needed to propose a hypothesis explaining their observations, and they employed the scientific method to test the hypothesis. Formulating a scientific hypothesis meant applying
concepts such as carrying capacity to the situation and distinguishing among the different kinds of growth limiting factors that may or may not affect population size. Nancy asked a student, "Is there a predator coming in?‖ A student asked what scale should I use for their interpretation. The vignette that follows illustrates the use of problem-based learning in Nancy‘s 2nd period life science class during the ecology unit focusing on population growth (refer to Table 2). 25 Nancy comes in with colored paper for graphing and population numbers over time of human beings on an Imaginary Island. She says we are going to graph the population today (and figure out what is happening). The students choose the color they prefer. The students are quiet and focused on graphing the data table of population numbers over time. Students choose a dependent variable for the Y-axis and time as the independent variable. They choose a scale for the axes and a range. Some ask whether or not it should be a line graph. She walks about the room spot checking the graphs. She begins to ask them questions to interpret the graph. What is the population density on the island? What is the carrying capacity? What is the limiting factor? How do you explain the rise and fall in numbers? They are being challenged to explain the results, and this involves problem solving. She visits with individual students and examines their charts. The population drops in the last time interval. She asks a student for an explanation. (field notes). "Inquiry based learning engages students in "what if" scenarios and investigations to construct mental frameworks that adequately explain their experiences." (http://www.coe.uga.edu/ctl). Inquiry learning is a primary strategy in CTL practice. While Nancy taught the class, there was very little in the way of traditional lecture. In the 2nd period classroom, students were engaged in a laboratory exercise or an overhead transparency projected a list of questions to be answered. Nancy interacted with students one-on-one. In many of these interactions, she would use the Socratic method and return a question with another question in an effort to assist the student in solving the problem or answering the question with the knowledge they had at hand. In the fetal pig unit, inquiry was directed at visible organ system identification. In the population growth unit, inquiry was directed to explaining the observed fluctuations in island population size. 26 The process or inquiry was discovery-driven with the students in the driver's seat. "Service learning is a method of instruction that combines community service with a structured school-based opportunity for reflection about that service emphasizing the connections between the service experiences and academic learning." (Berns & Erickson, 2001; http://www.coe.uga.edu/ctl). Service learning is another strategy often identified with CTL practices. There was the potential for service learning, although we did not directly observe service learning while we were visiting the classroom. Mrs. Bailey had the students visit an old field site on Morton Road prior to our first observation of Nancy. The students surveyed the field in an effort to observe vegetation succession on the site. Nancy described that one of the major objectives of this lesson was to develop student observational skills (about their own environment). If Nancy had sufficient class time, several of per projects, including cleaning up the field, could have resulted in a service learning project. The discussion of whales and oceanic trophic structures could have provided a segue into the effects of pollution on ocean ecosystems. Ecology is about communities. As Nancy said, "Go up to biosphere. Tie into pollution. Like whales." "Cooperative learning is defined by a set of processes which help people interact in order to accomplish a specific goal or develop an end product." (Berns & Erickson, 2001; http://www.coe.uga.edu/ctl). There were multiple ways in which learning was collaborative in the CSHS 2nd period life science class. The laboratory projects were done in groups of three to four students. Students were engaged in partner study. Student partners were usually paired by the instructor, assuring effective group work and limiting nonproductive student pairings. The pairings mirrored teacher-student classroom 27 interaction. Using a study partner approach, the students would each answer the questions on the overhead, and then the student partner would grade it. They would quiz each other. Study partners were used to complete homework assignments. In this classroom, there is more than one authority figure. This strategy encourages peer tutoring. One student helped two other student groups with the fetal pig laboratory. As
Nancy said, I encourage them "to think like a teacher. They swap problems. They do a partner study. They took quizzes in class and graded themselves for immediate feedback." There appear to be multiple benefits to study partnering including immediate feedback, active learning, multiple sources of information, and learning in a social context. Students worked in self-selected teams of three and four students during the fetal pig laboratory. The groups were segregated by gender by student choice. They had the option to work with their friends. Students who needed to take an active role in order to learn effectively could volunteer to take charge of the actual dissection. Other students who were not comfortable with dissection could watch. Students were required to take notes. The social structure of this lesson provided three different learning activities for student groups: active participation, recording data, and analysis of their observations. There were multiple sources of authority in this classroom. Students engaged in cooperative learning learn from each other. They used personally meaningful language to attach new content to previously mastered concepts and facts. Facilitators and Barriers to CTL Implementation at Cedar Shoals High School Cedar Shoals High School is located in a beautiful new building with the 28 classroom equipped to do bench science. As Mrs. Bailey suggested, "The old school was a sick building, and each day when I come in the morning (now), I pause and am grateful." The classroom is set up to do laboratory work right around the periphery of the room with a central seating area for note taking, class discussions, and lectures (see Figures 1 and 2). Students can switch back and forth between academic study and laboratory study without leaving the room. Audiovisual support is excellent (See Figures 1 and 3). Another major facilitator was the block scheduling system in place. Block scheduling permitted Nancy the time to give students the opportunity to explore, discover, and solve problems on their own. Case studies, laboratory experiments, and projects are time-intensive. Nevertheless, even with block scheduling and thus more time each day, Nancy felt constantly under pressure to "cover the material." I asked her where do you see the pressure on time. She responded, "Not figuring out yet how to plan. Classroom management. Meaner in first period. Certain units need to [be] covered. These include research methods, basic chemistry, organization, cellular level.‖ Another major facilitator to the implementation of CTL instructional strategies was that Mrs. Bailey was an award-winning teacher who had "arrived" at a number of CTL practices as a function of her teaching experience. As a result, Nancy used many of Mrs. Bailey‘s ideas as a foundation for her lessons. She adopted the practice of student projects, student notebooks, "partner study," and designing field studies in cow pastures. Mrs. Bailey served as a positive model to emulate. As Nancy commented, ―Ms. Bailey is doing whole lot of CTL practices, especially incorporation of English and math skills. Very effective.‖ 29 Perceived lack of authority was a barrier to learning for Nancy‘s students. She commented that generally the 2nd period class was an attentive class, but she does not have the same level of authority as Mrs. Bailey. She has more difficulty with the 1st period class. She explained, "Mostly males. Computer to put in one class. All friends. Putting out little fires. Mrs. Bailey can control. (It is) good, when Mrs. Bailey is there. Bad when gone. (They are) whiney. Talkative. Poor kids in bad mood. Not staying on task is a barrier.‖ Another barrier: Contextualizing science means first and foremost doing science "in the laboratory." Laboratories are expensive. Setting up a classroom/laboratory, such as in Figure 4, involves a significant commitment of resources. Buying a bucket of fetal pigs is a major expense. In doing the laboratories, students came to understand the process of science and that science is more than a collection of unrelated facts. Another barrier: Some scientific skills can be easily assessed using standardized tests. Others skills — particularly learned through CTL strategies — are more difficult to directly assess. How does one rate the power and quality of observation? How do you grade the ability to do an experiment? Some people have a natural gift for working in a laboratory. How does one assess curiosity? These are all important scientific skills requiring indirect and creative assessment methods. But ―indirect and creative assessment methods‖ are not used on state standardized tests. 30 Figure 4. Doing science in the classroom involves a significant commitment of resources.
Nancy, by her own self-assessment, felt her time-management skills were a barrier. She drastically underestimated how long it would take to graph the population data from the imaginary island. She did not have enough experience to redirect student questions in a way that made the students feel that their questions were important but preserved class time. Mrs. Bailey felt that many of Nancy‘s time management issues would resolve with increased experience in the classroom, with both content and students. Related, there are some unplanned events that just happen that fall under the heading ―acts of God'. There was a chemical spill in the school that forced an evacuation. This cut into the Nancy‘s class time and, coupled with her poor time estimates on several 31 project-based units, may have led to the loss of the whale unit. The implementation of CTL practices by Nancy required considerable one-on-one interaction to enhance learning by all students. This was enabled because her 2nd period class size was about twenty-two students. Small class size facilitates CTL practice while large class size impedes the practice of contextual teaching. At some point, class size would prohibit any meaningful interaction on a one on one basis between student and teacher. Differences in CTL-Trained Novice Teacher Practices and Traditional Instruction Traditional instruction is classroom and teacher centered. All learning occurs within the physical confines of a high school classroom. Nancy and Mrs. Bailey moved instruction outside the classroom using several nontraditional strategies. The field study of old field succession observed in a local cow pasture in the ecology unit required that students leave the school grounds to complete the activity. Nancy used "A Bug's Life" as a data source for students to observe a community food web. The CDC infectious disease study and the open ocean trophic structure units were themselves drawn from the real world experiences and anchored to real world problems. The use of current instructional technology such as PowerPoint to present content is a nontraditional approach. An example of the application of this technology in the 2nd period class was the series of PowerPoint presentations on whales and whale feeding behavior. The PowerPoint presentation used actual photographs of whales to make it real to the students. The presentation introduced the value of a single individual as an object of study and its relation to the community. Pollution (our impact) was introduced to talk about ecological disturbance. Students were engaged by these real world examples. 32 Another example was Nancy‘s CDC case study used in anatomy and physiology. The problem of public health and the associated issues became a vehicle for contextualized learning: how biology can be used to solve real health problems. This represents the last in the triad of aspects to how biology is contextualized. She drew on real life case studies to engage the students. Nancy was raised in South Africa under Apartheid. She was teaching a class made up principally of minorities. She brought her personal experiences and a unique perspective into the classroom. She had a module on the individual, using whales as an example. At first students were surprised that an individual could be a unit of study in ecology. She stressed how each individual is unique. She opened up and told the students things about her home environment. She asked them to construct a concept map with themselves at the center and then to choose ten items in the map. She illustrated the principle using herself and a unit of study and her dog Rudy. In this way, she had them build a picture of themselves as a member of a biological community. During our period of observation, we were able to observe another teacher teach the same students in this 2nd period class. Nancy‘s supervising teacher, Ms. Bailey, was nominated for a state of Georgia teaching award. An evaluator from the State Department of Evaluation was present in the class to observe her teach and assess her teaching skills and effectiveness. The ―lecture‖ lasted about thirty minutes and was part of the ecology unit. Mrs. Bailey began where Nancy ended. The style of delivery was quite different from Nancy‘s. Working from the overhead, she used a series of questions and worked herself through the problems related to population growth rate. She introduced a 33 definition of growth rate and then worked an example of how growth rate was calculated. She created a variety of examples including parrots and cats as populations to illustrate the concept and its calculation. She called on students to fill in the calculations. Students were actively engaged in a question and answer format. There were a number of ways in which Mrs. Bailey‘s teaching differed from Nancy‘s. She utilized the lecture format and then a question-response follow-up. She
asked a question, and students were expected to provide an answer. What operationally defined, traditional teaching practices in Mary Bailey‘s classroom was the inclusion of lecture formatted lessons, note taking, rote learning, passive learning, question and answer drills, and standard quiz and test assessment methods. What was largely absent from Mrs. Bailey‘s class was the one-on-one interaction driven by the laboratory experience. Mrs. Bailey begins a twenty-five minute lecture. She has two questions. How are birth and death rates different, and what are two problems facing human populations? She instructs them to create solutions and no sharing of solutions. She tells them, ―Get your work done, and then you can gossip.‖ One student was finished, and others worked quietly. Students are finishing their answers. Mrs. Bailey now indicates that we will now work through several population growth scenarios. She asks how would you express growth rate? Look at your numbers. They could be increasing or decreasing. She gives them a definition of growth rate. She puts a problem up for them to solve. In 1975, 800 parrots existed in a rain forest. In 1980 there are 1100 parrots. What is the growth rate? She lets them fill it in. She asks the students for an answer. She begins with a similar new problem. (field notes). 34 Effect of CTL Teaching Practices on Student Engagement If you do not have the students‘ attention, you will not be able to teach them. Recognizing and responding to student diversity in the classroom increases student engagement. The majority of students in the 2nd period class belonged to a minority group. At the beginning of each class, there were little testimonials and stories given. One was about the release of many colored balloons. At the end of the story, the announcer (probably the principal) indicated that it is what inside that makes the balloon rise. In this school, there is an institutional stance on the importance of diversity in learning. Recognizing and supporting student diversity is an integral part of student engagement and the American educational experience (Botstein, 1997). When students connect to the content as people, then the material becomes real for them and a part of their lives. Aspects of the fetal pig dissection exercise in the anatomy unit provided students with personal experience in the practice of science. They were actively engaged in making direct observations using the pig. The laboratory work is team-based, mirroring the common collaborative research paradigm (Hurd, 1997). Student engagement during the fetal pig unit was high. One student commented, "See chittlins that you eat?" Another student commented, "Is that what we look like? Gross." The material caught and held the students‘ attention. As Nancy noted in the interview after class, "The fetal pig was new. Cutting it open engaged them. They have been anticipating this. They keep asking about the pig." I observed that the students were focused on the pigs during much of the laboratory. The vignette below describes the high level of student engagement and enthusiasm for the dissection portion of the anatomy unit. 35 The pigs are here! Almost every day they ask about the pigs. Nancy says that we are cutting today. Your grade depends on your following directions. You are to explain what we are doing. Take notes. The purpose is to look at (identify) all of the organ systems. Pull the tray and scissors out. Keep the pig in the tray and follow directions. Play with the organs. Move them. She asks one of the students to begin with a pelvic cut. Feel the ribs. Trace out the ribs on your own bodies. Nancy draws a picture of Piggy, and they laugh. She shows them the cutting lines. Students choose their own groups. There are four female groups and two male groups formed. One guy in one of the male groups begins cutting. The second male group isn‘t doing much; one male student almost faints. All of the female groups are intent. They are cutting. One group sexes their pig and identifies the ovaries. Nancy comes over and helps them identify intestines. (field notes). While student empowerment is not an explicit element of CTL instructional strategies (http://www.coe.uga.edu/ctl), it appears to be an important characteristic of successful CTL practice. Mrs. Bailey summarized the idea this way when she spoke to a student, "You have the right to study and the right to fail.‖ They were treated as adults,
and if they chose to tune out, they knew the consequences. In Mrs. Bailey‘s and Nancy‘s class, students must assume responsibility for the direction of their own learning. They were presented with choices daily which included the option of nonparticipation. They were free to choose the famous scientist to research and display in a poster. They were encouraged to choose their own approach in cooperation with others to analyze experimental and research results. They were allowed to choose a role as part of a student group completing the fetal pig dissection. The creation of their own notebook for study for quizzes and tests (an approach by Mrs. Bailey) gave the students ownership of what 36 they learned, provided them with a tangible product, and a produced sense of personal accomplishment. As Nancy said "Ask for input from your student so that when you are incorporating things that are pertinent to them; it helps with the motivation factor." Student empowerment is necessary for relating what they learn to what they know. A final very important part of student engagement was student ownership. They had their notebook. It was their own, and their notebook reflected all their work and was a resource for tests and quizzes. Effect of the Use of CTL Strategies on Subject Area Mastery CTL practice includes the use of authentic assessment as a means of documenting content mastery. "Assessment is authentic when we direct examine student performance on worthy intellectual tasks" (http://www.coe.uga.edu/ctl). Ultimately authentic assessment in science is based on observing students practicing science by applying what they have learned and doing science. Traditional assessment in the classroom including homework, quizzes, and tests were in evidence. There were alternative assessment tools in use as well such as portfolios, laboratory notebooks, and class projects with written reports. Mrs. Bailey organized the student reports, stapling together all the student reports after each section and bounding them in a notebook. Each student received a notebook copy containing all of the reports. This gives the students a sense of ownership for the work and rewards their individual efforts collectively. This notebook represented a history of what each student had learned over the course of the academic year. Nancy plans to adopt this strategy in her teaching practice. While the fetal pig laboratory was in progress, students were assessed for their ability to follow a scientific protocol in addition to the internal anatomy of the pig. Their 37 ability to use good observational skills was assessed. Nancy told the students "your grade is dependent on following directions. You are to explain what we are doing. Take notes." In the population growth unit, the learning endpoint was to explain the data in Figure 2 using ecological concepts. Students were assessed on their ability interpret the data using written reports. Work resulting from previous projects covered the classroom walls. There were many modalities to assessment in the classroom/laboratory. There were the standardized tests at the end of the class. There were the traditional question and answer sessions in class, homework, tests, and quizzes. There were also instruments that allowed authentic assessment of the process of science. This included a multi-week poster, conducting laboratories, completing data analysis, and following a scientific protocol. Finally, there was the creation of a course/project notebook for each student. There were families of CTL strategies being used to create "biological literacy," an informed citizen able to utilize biology in their everyday lives (Figure 4). Students were assessed for mastery of biological concepts at a nominal level, as in question and answer about the organ systems. They were assessed at a functional level by being asked to apply what they had learned identifying the internal organs of a fetal pig. They had to master the material at a structural level by writing an analysis of what they saw in the fetal pig laboratory or provide a scientific hypothesis to explain the population data on the imaginary island. 38 Figure 4. CTL strategies for biological literacy. I am indebted to Dr. Loving for this figure derived from BSCS (1996). There were applications of what they learned to their personal lives as in the cow pasture vegetation, or in preparing a poster presentation on a minority scientist. They were practicing scientific skills and utilizing the information from class to connect with their lives. The analysis of the possible effects of abstract ecological concepts such as predator-prey interactions and environmental carrying capacity to a theoretical population requires the mastery of higher order cognitive skills such as application, evaluation, and synthesis. Further, formal operational cognitive skills such as combinatorial and proportional reasoning must be used to arrive at an answer. They used the scientific
process to analyze human population explosion. They were using mathematics and 39 communication skills to summarize their findings. The result was that students were asked to pursue self-sustained scientific inquiry. Mastery was being assessed in a much more extensive manner than simply taking a standardized test. Finally, differences in student content mastery as a function of instructional practice was tested statistically by comparing student scores on teacher-made instruments for both the unit lab practical and the unit exam. Unit exams were constructed to include both objective multiple choice questions and open-ended essay questions. To compare student differences in content mastery, operationally defined as lab or lecture exam score, as a function of instructional practice, CTL versus traditional, an Analysis of Variance (ANOVA) (Glass & Hopkins, 1996; Keppel, 1991; Kirk, 1995) was performed on the variable of interest using a general linear model solution. Hartley‘s F-max test was used to ensure that the underlying assumption of homogeneity of variances was met. For the test of the hypothesis that content mastery is related to curriculum type in secondary science at CSHS, 2nd period student scores for the lab practical and the unit exams did not differ significantly from one another (a =0.05). The omnibus F test of hypothesis for lab = method was not statistically significant (refer to Table 3). The probability associated with the calculated test statistic was less than or equal to 0.2701. The R-square value, 0.026375, suggests that only 2.6375% of the total variability in 2nd period life science student lab practical score can be attributed to instructional practice. For the test of the hypothesis that 2nd period life science student unit exam score is related to instructional practice, no statistically significant differences in unit exam grades were observed. There was so little variability in unit exam grades among the students for the ecology unit which Nancy taught and the cell unit which Ms. Bailey taught, the calculated F statistic 40 was minute (refer to Table 4). While no statistically significant differences in student content mastery were observed in this study, the sample size and duration of the observation period may have been too limited to produce significant gains in test scores. Underlying differences in student science achievement were controlled for by comparing student performance on lab practicals and unit exams within a single class. The limited time frame of Nancy‘s teaching internship coupled with her poor time management skills meant she completed a single content unit. This limited the number of lab and lecture unit scores which could be used for quantitative comparison. It should be noted that important changes in student behavior and student engagement were observed during this short time period. Table 3. Analysis of Variance for laboratory practical score as a function of instructional practice. Source DF Sum of Squares Mean Square F value Pr > F Model 1 1242.49 1242.49 1.25 0.2701 Error 46 45865.51 997.08 Corrected Total 47 47108.00 R-Square Coefficient of Variation Root MSE 41 0.026375 39.47064 31.57651 Source DF Type III Sum of Squares Mean Square F value Pr > F METHOD 1 1242.49 1242.49 1.25 0.2701 METHOD LAB Std Err Pr > /T/ Pr > /T/ LSMEAN LSMEAN H0:lsmean=0 H0: LSMEANS1=LSMEAN2 1 84.880 6.315 <0.0001 0.2701 2 74.696 6.584 <0.0001 Table 4. Analysis of Variance for unit exam score as a function of instructional practice. Source DF Sum of Squares Mean Square F value Pr > F Model 1 0.08523 0.08523 0.00 0.9908 Error 46 29368.91 638.45456 Corrected Total 47 293683.99 R-Square Coefficient of Variation Root MSE 0.0000003 29.98758 25.26766 Source DF Type III Sum of Squares Mean Square F value Pr > F
METHOD 1 0.08522645 0.08522645 0.00 0.9908 METHOD UNIT EXAM Std Err Pr > /T/ Pr > /T/ LSMEAN LSMEAN H0:lsmean=0 H0: LSMEANS1=LSMEAN2 1 84.220 5.0535 <0.0001 0.9908 2 84.304 5.2687 <0.0001 42 Implications for Future Research Secondary Science Education In the exit interview conducted with Nancy‘s supervising teacher, Mrs. Mary Bailey, she indicated that if teachers could be convinced to take the time to use CTL pedagogy, the increased time investment would produce greater student content mastery. She felt that the use of problem-based learning and inquiry-driven teaching methods would improve student mastery of the concepts contained in the QCC‘s (Quality Core Curriculum for the state of Georgia). This should translate into improved student science test scores on the Georgia High School Graduation Exam. Mrs. Bailey mentioned that the Cedar Shoals High School improvement plan would be well served by the application of CTL methods to content instruction. The school‘s long-term educational goals include requiring more oral and written student presentations, an increased number of cross-discipline units, and the development of student problem-solving skills. Mrs. Bailey said ―I need more information on CTL, and I would like to know who to contact to get our teachers involved. We need a summer workshop where CTL units could be developed and piloted by current teachers.‖ If postcertification teachers have the opportunity to try a new approach to their curriculum during the summer, then it is more likely that they will incorporate this approach into their teaching strategies during the academic year. Mrs. Bailey asked for the CTL web site so that she could search for science units developed by CTL student teaching interns as part of their teacher training. 43 Post-Secondary Science Education The application of CTL instructional principles to college science courses provides an additional opportunity to observe the benefits of increased student engagement and motivation on content achievement. Drs. Arnold and Teare Ketter have incorporated the CTL model in an introductory biology aimed college freshmen and sophomore students over the last two years (http://www.coe.uga.edu/ctl). The student audience for BIOL 2107/2107L is not much different from the high school juniors and seniors in Nancy's class. Drs. Arnold and Teare Ketter have utilized a research-centered curriculum that has introductory biology students engaged in inquiry project-based biological research. The "biology class" is part of a twelve semester-hour credit cluster course, where the same community of students is in a philosophy, history/speech communication, and English class together. All four courses in the cluster have one theme, genomics and society, and have integrated curricula, problems, and student activities. They reflect on the "science they are experiencing" in English. They are challenged to think about the nature of science and bioethics in the philosophy course; they examine public perceptions of science in the history/speech communication class. The laboratory component of the biology class utilizes project-based learning. Students work in teams on a semester-long project both within the context of the laboratory class and outside of class on their own time. Barriers to learning encountered in the implementation of the college course included considerable resistance to trying a new approach to teaching by immediate supervisors and colleagues in contrast to traditional lecture format to a large class with small laboratory sections and cost of laboratories. 44 References Berns, R. G., & Erickson, P. M. (2001). Contextual teaching and learning: Preparing students for a new economy. Columbus, OH: National Dissemination Center for Career and Technical Education, The Ohio State University. Botstein, L. (1997). Jefferson's Children: Education and the promise of American culture. Doubleday, NY, NY. Glass, G. V., and Hopkins, K. D. (1996). Statistical Methods in Education and Psychology. (3rd ed.). Boston: Allyn and Bacon. Hurd, P.D. (1997). Inventing Science Education for the New Millennium. Teachers College Press, NY,NY. Keppel, G. (1991). Design and Analysis: A Researcher's Handbook. (3rd ed.). Upper Saddle River, New Jersey: Prentice-Hall.
Kirk, R. E. (1995). Experimental Design: Procedures for the Behavioral Sciences. Pacific Grove, California: Brooks/Cole Publishing. Merriam, S. B. and Associates. (2002). Qualitative Research in Practice. JosseyBass, Inc., San Francisco, CA. Merriam, S.B. (2001). Qualitative Research and Case Study Applications in Education. Jossey-Bass, Inc., San Francisco, CA. Resnick, L. B. (1987). Education and learning to think. Washington, DC, National Academy Press.
IMPLEMENTING CONTEXTUAL TEACHING AND LEARNING: MIDDLE AND HIGH SCHOOL STUDENT PERCEPTIONS OF CLASSES TAUGHT BY CTL NOVICE TEACHERS
Nancy F. Knapp University of Georgia Final Report March 30, 2003 The work reported herein was prepared in association with the contextual teaching and learning in preservice teacher education and studies of novice teachers’ implementation of CTL approaches in the classroom projects at the University of Georgia, with funding support from the U.S. Department of Education, Office of Vocational and Adult Education, Contract # ED-98-CO-0085, 1998 – 2003. 2 Implementing Contextual Teaching and Learning: Middle and High School Student Perceptions of Classes Taught by CTL Novice Teachers Nancy F. Knapp University of Georgia Abstract In Fall 2002, students' perceptions of their learning experiences in classes taught by five of the novice teachers participating in the contextual teaching and learning (CTL) study were accessed in two ways. First, each teacher administered a course evaluation survey in a target class, asking students to compare that class on 11 CTL-related dimensions to other classes they had taken in the same subject area. Second, a subset of students from each target class (generally those with parental permission) were interviewed to capture their descriptions of classroom procedures and activities and what they felt they had learned in the class. These interviews were then analyzed for evidence of the overall pervasiveness of the same 11 CTL principles in the class. One difference in the two data collection methods is that the surveys asked students to compare, for example, a science class to other science classes they had taken. In contrast, the interviews were used to evaluate CTL use independent of subject area or earlier experiences. Although the classes had varying strengths and weaknesses, data from student course evaluation surveys across all classes reveals an impressive record. On all but three of the survey questions, students rated these classes as embodying CTL principles to a greater degree than most classes in the same content areas. In addition, students clearly and consistently rated these classes as more interesting, and they felt strongly that they had learned more in these classes than in most classes in the same content areas. This record is all the more remarkable when one considers that these classes were all taught by novice teachers. At a stage when most novice teachers feel lucky simply to survive, these teachers were able to both engage their students' interest and significantly facilitate their learning. Students from all classes also perceived their teachers as caring deeply about them and their learning. Each teacher received above average ratings on this quality on student surveys, and examples of effective teacher caring, the kind that supports students in their efforts to learn and also
communicates to them strong expectations for their success, abound in the student descriptions of these classrooms. Unlike the case for so many novice teachers, this caring has not come at the expense of discipline. One of the unexpected results to emerge from the qualitative data is that students also describe these teachers as highly effective classroom managers who have developed classroom management techniques that enable them to simultaneously control and motivate students to behave appropriately. Their mastery in this area is not incidental to the subject of this study, nor is it simply because they are "good teachers." Data from student surveys show that, as compared to others in their content areas, these teachers are particularly strong in their abilities to actively engage students in learning, adapt instruction to diverse students' needs and interests, enable students to do real world, critical problem-solving, and create a caring community of learners in the classroom. In focus group interviews, students described active learning as either a major part of or pervasive within in all but one of the target classes. Adaptive teaching and critical problem-solving were described as significant or pervasive features of all the target classes. These key features of contextual teaching and learning are also identified as key needs in recent educational policy discussions, such as those around the federal No Child Left Behind act. When students are given the opportunity to do contextual teaching and learning--that is, to actively engage in critical thinking around real life problems in a collaborative, inclusive classroom community--they want to learn, and they can learn. In such classrooms, students experience little of the boredom and frustration that leads to most classroom misbehavior. Contextual teaching and learning techniques enabled these novice teachers to manage, to motivate, and ultimately to teach their students. 3 Implementing Contextual Teaching and Learning: Middle and High School Student Perceptions of Classes Taught by CTL Novice Teachers Nancy F. Knapp University of Georgia Purpose Student feedback is an important source of information on the nature and effectiveness of teaching practice. In studying a model for teaching practice which is intentionally studentcentered, as is contextual teaching and learning (CTL), students‘ perceptions of their learning experiences in the classroom become especially significant data. In Fall, 2002, five of the teachers participating in the University of Georgia's CTL novice teacher study were working as regular teachers in their own classrooms. Student perceptions of their learning experiences in a target class taught by each of these teachers were accessed in two ways. Teacher participants administered a course evaluation survey to all students in target classes, as part of their regular self-evaluation of teaching practice. In addition, focus group interviews were conducted with all students in each target class who turned in consent forms reflecting personal and parental consent to be interviewed. This document reports the results of the course evaluation surveys and the qualitative analysis of the focus interview data. Following a brief section on methodology, a portrait is drawn of each teacher's target class, as perceived by his or her students, including the strengths and weaknesses of that class in relation to core principles of contextual teaching and learning that have been used throughout the University of Georgia CTL project (see Figure 1). A cross-class discussion follows, which includes additional findings not directly related to the CTL principles. Finally, conclusions and questions for further research are addressed. Methodology The survey and interview instruments were piloted during Spring, 2002, with two of the participating novice teachers who already had full time, regular teaching jobs. As a result, both instruments and administration procedures were slightly revised so as to ensure maximum 4 effectiveness in the Fall data collection. This report describes data and findings from instruments used in the final data collection.
Student Course Evaluation Survey The survey given consisted of two open-ended questions and 18 Likert-scaled questions based on core principles of contextual teaching and learning (see Figure 1) that were adapted from the original CTL project framework (1998-2001). These adapted principles were used successfully to analyze student learning in the first CTL class attended in 1999 by many of the participants in this novice teacher study when they were just starting their pre-service teacher education program (see www.coe.uga.edu/ctl). All of the CTL principles were addressed in at least one survey question; several were addressed in two questions, one stated positively and one stated negatively. This was done to avoid the development of a biased response pattern on the part of students. Two final Likert-type questions addressed students‘ responses to the class as a whole. To avoid transfer errors, students circled their responses directly on the survey sheets and answers were later tallied by hand. The two-open-ended questions were intended to capture any additional student perceptions of the class. A copy of the survey is attached as Figure 2. Students in each teacher's target class completed these surveys on a voluntary, anonymous basis and returned them to the teacher, who gave them to project personnel for analysis. Classes were of different sizes, but more than 80% of students completed surveys in all but one of the classes. Table 1 shows frequencies of each response for each Likert-type question in each class, with response means for each question in each class and across all classes. All questions asked students to compare their current class to other classes they had taken in the same subject, using a 1-5 scale, where (1) = Not much at all, (2) = Only a little, (3) = About average, (4) = More than average, and (5) = A lot! Thus, for most questions, (1) is the least favorable answer, while (5) is the most favorable. Questions 7, 10, 12, & 14 were worded negatively, so that for those questions, response frequencies were reversed, so that (1) is consistently the least favorable response, while (5) is the most favorable. 5 In appraising these data, it is important to remember that students were asked to compare their current class with other classes they had taken in the same content area. Thus, their ratings do not represent a comparison to school classes across the curriculum, nor do they represent how the class might be perceived in relation to a criterion-based measure. For example, a rating of (4) (More than average) in response to Question 3 (Compared to other classes you have taken in this subject, how much time did you spend in this class working or discussing with other students?) in a math class would indicate that the student perceived himself or herself as collaborating with other students more than he or she had in other math classes, but this still might not be a large proportion of class time, given the individualistic nature of most math classes. The same answer in relation to a class in family and consumer sciences (FCS, formerly known as home economics) might reflect a far greater proportion of class time spent working with other students, while a student might answer (3) (About average) to the same question in the FCS class even though they worked in student groups most of the class time, because student group activities were the norm in the student's previous FCS classes. Thus, means across the target classes cannot be directly compared because different content areas may lend themselves more or less easily to the implementation of various aspects of contextual teaching and learning. Research Questions The questions of interest in this analysis are: 1) Did students perceived the target classes as embodying CTL principles to a greater degree than most classes in the same content area; in other words, were novice teachers who had participated in the CTL project enabled to use contextual teaching and learning in these classes more than might be the norm in their general content area? 2) Did students therefore perceive these classes to be more interesting and more effective for their learning than typical classes in the same content area? Focus group interviews One or two focus group interviews were conducted for each class, depending on school schedule constraints and how many students had returned signed parental permission slips for 6 each class. These interviews were all conducted by the same researcher at the students' school, but not in the target classroom or in the presence of the teacher. Students were assured of the confidentiality of their responses. The interviews were semi-structured and deliberately conversational in nature, following the students' lead in the order and depth to which various questions were addressed to allow students to emphasize what they perceived as important
aspects of the class and to avoid influencing or restricting their reports through a rigid question protocol. A copy of this semi-structured interview protocol is attached as Figure 3. All interviews were audiotaped and transcribed, and transcriptions were subsequently analyzed by the author using HyperQual III (Padilla, 1991), a HyperCard-based program for analyzing qualitative data. Initial categories for the analysis were based on 11 CTL principles at UGA (see Figure 1), with the addition of categories for students' descriptions of general classroom processes, themselves, and their classroom peers and a category for general attitudinal expressions of like or dislike for the class or teacher. During iterative analysis of the sort described in Bogdan and Bicklin (1992), the following themes emerged as additional categories: specific comparisons between this teacher/class and others in the students' experiences; evidence of class or teacher effectiveness in promoting learning; relationship between class content and local, state, or federal standards; displays or descriptions of teacher content knowledge; and comments related to classroom management. Data that spoke to more than one category were sorted into all appropriate categories; thus, the categories were deliberately not mutually exclusive, and there were no forced choices during the sorting. All data that addressed each category were included in it, whether the data spoke positively or negatively to the theme of the category. After sorting was completed, and following another review of the data in each category and the entire transcript of each class focus group, data in the 11 categories based on the CTL principles were assessed for each teacher, and rated as fitting into one of the following four classifications: None - Students describe no evidence of this characteristic in this class 7 Minor - Students describe only minor or occasional evidence of this characteristic in this class. Some - Students describe one or two major projects or occurrences evidencing this characteristic but do not describe it as typical of this class OR this is characteristic of one regular feature of the class but not of the class overall. Pervasive - Students' descriptions indicate that this characteristic is pervasive in this class. A summary of these ratings appears in Table 2, while Figure 4 gives illustrative examples of data summaries that fell into each rating classification for the category "Meaningful Assessment." In appraising these results, it is important to remember that focus groups were composed of a self-selected group of students, since only some students in each class returned the required permission forms. Also, although every effort was made to invite students to address all the CTL principles during the interviews, time was necessarily limited. Therefore, these ratings should be interpreted as minimal ratings for these classes, indicating that the relevant CTL principle was evidenced "at least this much" in students' descriptions of the class. In particular, a rating of "None" or "Minor" should be interpreted cautiously; focus group students may simply not have mentioned significant elements of the class that would have evidenced a particular principle more clearly. Unlike the responses on the student course evaluation surveys, these qualitative ratings from focus group interviews are criterion-referenced. They do not compare each class to other more typical classes in the content area. Another difference between these two forms of ratings is that these qualitative ratings, while based on students' perceptions of the classes as they described them, are not directly reflective of students' judgments of those perceptions, as were the survey responses. Rather, they reflect the author's characterizations of these classes on the 11 CTL dimensions after listening to and reading students' descriptions of class activities and conditions. Thus, reasonable triangulation can be expected between these two ways of summarizing and rating class characteristics, as it would be odd indeed if students rated a course 8 as offering "above average" opportunities for student collaboration, but then described no collaborative activities during the focus group interview. However, direct correlations between these two ratings should not necessarily be expected, due to differences in their data sources and analyses. A final caution: all of the data presented in this report must be interpreted in the contexts of the specific target classes. Class differences that may be attributable to content area focus have already been discussed above. But student populations in each class also differed importantly by age, socioeconomic status, minority status, ability level, and experience in and motivation toward class content. Not only would we expect seventh graders in a required, general-level life science course to describe and respond to instruction based in contextual teaching and learning principles differently from high school juniors and seniors in an elective engineering course with three prerequisites, but we would also rightly expect their teachers to use
different forms and degrees of CTL-based instructional strategies with these different student populations. All of these limitations highlight the need to avoid using these data to compare or rank these teachers. Rather, these data can speak richly to the strengths of each class, the potential benefits of and issues surrounding the use of CTL-based strategies in various content area classes by novice teachers, the areas where future efforts supporting the implementation of CTL principles might best be focused, and the questions that arise for future research in this area. Findings from the Five Classes Sarah's seventh-grade Life Sciences class Students Although all seventh-graders in this middle school were required to take Life Sciences, Sarah told me that this was her "gifted" class, so they sometimes "got to do more" than the other classes. The school is located in a small city in Northern Georgia and serves a diverse population from the city and surrounding rural areas. Seventh-grade teams this year were tracked, with all the "low" students assigned to a different team which had smaller than average classes and used specialized instructional techniques. The "average and above average" students assigned to 9 Sarah's team were not officially grouped for science, but scheduling constraints resulted in all of the advanced math students being placed in this science class. The principal requested that the course evaluation surveys be completed by only those students who had returned permission forms to participate in the focus group interviews, so only 15 of the students in this class completed surveys. Two focus group interviews were held, the first with eight girls and the second with four girls and three boys. Most of these students were Caucasian, although several were African American and one boy seemed to be of Asian or Indian ethnicity. Class processes Students said that once or twice a week, "if the overhead is out, it probably means we are going to take notes." "She'll have everything like an outline written out on the overhead, then she‘ll go through it and have like specific points and we just copy it, what we feel [we need]." But she makes it fun, . . . like, we're talking about budding and stuff, and she'll go into certain things that have happened lately . . . like red tides. She was explaining [what] causes red tides, and how it [makes a] seafood shortage and what happens to the beaches. They said that twice Sarah did not do the chapter notes herself, but "she divided us into groups and assigned each a section of the chapter. We‘d read it and know the information really well, and then we‘d [tell] about it . . . [and] that‘s where she would get our tests, from our notes." She had promised to do this again soon. On days they are not taking notes, they might be answering questions on a textbook chapter or "doing vocabulary." There are usually "about 30" vocabulary words to learn for each chapter. They learn them by writing out the definitions (found in the textbook glossary) and then doing worksheets or "word finds or crosswords" using the words. Tests require that they either "fill in the blanks," write the words next to their definitions, or write the full definitions after the words, although "sometimes she gives half credit for writing part of it." 10 The students described three "labs" they had done this semester. Their least favorite was one in which they had to classify "50 objects in the room . . . to understand classification more." In another lab activity, they made up, drew, and wrote about their "own" imaginary invertebrates that "could survive in the salt marshes." One student said hers was "half ant and half octopus," while another's was "half squid and half butterfly." But their favorite lab to date involved taking swabs in different areas of the school, including water fountains, lockers, and the boys' and girls' bathrooms. They grew bacterial cultures from these swabs, and vividly recalled how "disgusting" they were, with one that looked "like chex mix," and another a "type of broccoli," while from "the boy's bathroom there was this big jello blob." Several students said that they washed their hands much more frequently in school after doing that lab. But students also agreed that the labs were not a major part of the class. Strengths Students' responses to Questions 4 (m = 3.14) and 12 (m = 3.47) on the course evaluation surveys indicated that this class helped them connect science content to issues in the real world content somewhat better than most of their previous science classes. The focus groups specifically described some activities with this emphasis, including the "red tide" discussion and the "bacteria" lab mentioned above. On the surveys, students also indicated that Sarah cared more than the average science teacher about their learning (Q13, m = 3.67). Focus group participants confirmed this general impression, saying Like the first few days I was scared to death. She came across strict, but once you
get to know her, and as long as you're not being completely terrible, she‘s a really good teacher. . . . She gives you [credit for] efforts. Say like you bomb a test, she‘ll let you go back and correct it. She‘ll explain and let you ask questions. Sometimes she‘ll give partial credit, sometimes not, but she always makes sure we know. Overall, students rated this class as somewhat more interesting (Q17, m = 3.47) than previous science classes, and clearly felt they had learned more in it (Q18, m = 4.00). 11 Weaknesses Although focus group students described some class activities and features related to some of the CTL principles, no principle was seen as pervasively expressed in this classroom. In fact, both the student survey results and the focus group comments suggested that this 7th grade life science class embodied CTL principles least of all of the five classes studied. On the surveys, students indicated there were fewer than average opportunities for group work or collaboration (Q3, m = 2.71) and particularly little chance for self-direction or choice in their work (Q11, m = 2.07). Focus group comments corroborated these findings. The only two group activities mentioned were the group work generating chapter notes and the "bacteria lab" described above, and even in the bacteria lab, students were told which areas in the school to swab; they were not encouraged to come up with their own ideas about possible bacteria-laden sites. Students' choices in this class seemed to be limited to whether they would copy all or just some of the notes from the overhead and which "imaginary invertebrate" they would design. Finally, in both their survey responses and focus group comments, students indicated that the class required a great deal of rote memorization of facts and definitions (Q10, adj. m = 1.20). Students in one focus group listed the following advice for students taking Sarah's class next year: "Get ready for a different science class." "Bring packs of paper; three packs is not enough." "Be prepared for quizzes." "Don't talk, and learn your vocabulary really good." Students in both focus groups agreed they would like to do "more labs," "less worksheets," and "less bookwork." David's Manufacturing and Engineering III class Students This was a small elective class for high school juniors and seniors, most of whom had taken three prerequisite courses, Drafting and Engineering I and II. The high school serves a diverse, urban/suburban, student population in northern metro Atlanta. The one African American and four Caucasian students in the focus group were all male, as were all the students in the class. Although the high school serves a substantial population of limited English speaking students, none of these were in this class, according to the focus group participants. They 12 characterized the students in this class as "good," mainly students who "know what we want to do" and "have goals." Three of the focus group students planned to be engineers, a fourth wanted to be an architect, and the fifth did not indicate a career goal. Class processes Students described this class as focused around a series of projects that required them to learn and apply principles of engineering and manufacturing in realistic contexts. For each project, first there would be an introductory session or two, where David has PowerPoint, and he says, "This is what‘s happening." He‘ll give us specifications for the project we‘re doing, and the time limit, and like why we‘re doing what we‘re doing, and background info and all, and how it‘s used in real life. And then we usually get a sheet, just like a job, but it‘s fun." Then student teams work together to accomplish each project, which can take from "two to three days up to three weeks" to complete. Following completion, each team typically prepares a Power Point presentation for the rest of the class, showing "how we came up with our design, our problems, what everyone did to help. The problems we faced, the tools we used." Students described two projects in detail: designing and building a boat to compete with engineering students at neighboring schools in a sort of technical regatta, and designing a prototype gumball machine and mass-producing five copies within 30 minutes. Here is an excerpt from the focus group interview in which students are describing the gumball machine project: Student: We just built a gumball machine, and that lasted a long time, because that was a major project. Student: We built a prototype, and then built five like it. Student: We had to have drawings, and then we cut out all of the wood, and we had to figure out how to put it all together, and make sure it worked. . . . Interviewer: Did all the gumballs come out? Student: Yes.
13 Student: All but one. You had to shake it. Interviewer: Why are you building gumball machines? What does that do for you? Student: It teaches about manufacturing. Student: Assembly line. We had to figure out the quickest way to put it all together and the best way. Interviewer: Was the time factor tough? Student: Yes. Student: A lot harder than we thought. Interviewer: Is there different ways you design it because you had to build a lot of them? Student: Our original design was way too hard. Student: We had to cut off all the fancy stuff on the bottom. Student: It took longer to get all the parts ready than it did to build it. To draw the [plans] and get everything cut. . . . Student: We had one day for a pilot run; we could prepare everything. Interviewer: So, because of the time limit, you had to cut out a lot of the stuff? Student: Yeah, we had to move from glue to screws, and that messed some things up. The glue took too long to dry. Strengths On the course evaluation surveys, students rated David's class above the average technical class on all questions. Likewise, qualitative data from the focus group interview showed almost all the CTL principles as pervasive in this class. Obviously, this class had many strengths from the viewpoint of contextual teaching and learning. On the survey, students gave the class particularly high ratings in the use of multiple contexts for learning (Q2, m = 4.27), emphasis on connections to real world experiences (Q4, m = 4.27 and Q12, adj. m = 4.33), and learning that went beyond memorizing towards understanding and working with real problems (Q15, m = 14 4.44). All of these qualities are demonstrated in the "gum ball" excerpt above. In the following discussion of the "boat" project, these characteristics are again evident, and one can also see the students' excitement. Well after its completion, the students are still actively wrestling with the problems they faced in the project, still developing new ideas and solutions. This project clearly sparked the kind of learning that becomes self-sustaining and life-long. Interviewer: What were the requirements for the boat? Student: It couldn‘t be over eight feet long, and it had to hold at least one person, no motors or anything, and it had to go and turn around and come back. Nothing can be pre-manufactured; you had to produce it all yourself, from scratch, basically. Student: Some people use the…it‘s like plastic cardboard. Student: It‘s not good for boats. Student: Ours was made out of wood. Student: Some people made theirs out of metal, but they lost. It wasn‘t that good. It would sink. A little heavy, not good hydrodynamics. Student: There were some cool designs, though. Student: Ours was pretty good. We had a whole process to building one of those. We had to bend the wood. It was probably a three-week project. Student: We drew it up on AutoCad first, and came up with ideas, and did the whole problem-solving process. Interviewer: Did David say, "OK, here‘s different things people use for boats."? Student: He showed us pictures, and the basic designs, and all of that, but basically he was like, "Make a boat, under these specifications, and go!" I liked that because it let us do whatever we want. . . . Student: The boat that beat us, their dad was a boat maker. Student: It looked like a real boat, a little fishing boat. They showed pictures of them in the process of making it, and they were like welding it together, and 15 having rivets and stuff, and we were just like…they didn‘t even get first, they got second. They probably spent $200 to $400, and we spent like $80. . . . Interviewer: Did you have to finance it yourself? (They nod.) That makes a difference. So which boat won? Student: We got third. . . . We sank. That was the only reason we lost; we had them. Student: We started taking on water.
Interviewer: I was going to ask you how you sealed the seams on the boat. Student: We used caulk that turned out to be not waterproof. Student: It wasn‘t that bad until we were paddling. A lot of it was coming back over the side. It was good. I took it down the Chattahoochee about 3 times. Student: You would keep a cup with you, and about every 5 minutes you‘d scoop up what‘s in the bottom and throw it out. Student: When you think about it, you could have used a metal sheet from Home Depot. Students also rated David as caring much more than the average technical teacher about their learning (Q13, m = 4.44). In the focus group interview, they described how he would encourage reluctant students to learn, saying, "Well, this is what you need to have, if you want to go to college. You want to do things with your life; well, here‘s what I‘m trying to show you." One student explained how the goal of a college education is emphasized even in the room décor: You should see in the class, there‘s different schools-- you cannot come to class and not look at that college board that has all the colleges on there--license plates, and little tags, a whole bunch of schools in Georgia, and different states, like Florida. It just shows that he‘s putting education first. Students respond to this emphasis, even those who come into his classes without strong educational goals. One student explained how 16 A lot of people have electives, and they don‘t want to take band, or stage craft, so they just come to [David‘s] class, and then they learn something. I‘ve talked to a lot of people, and they‘re like, "Yeah, I want to go to college for this. I want to go to college for engineering. I want to be an architect." On the final two questions of the survey, students rated this class as "a lot" more interesting than most technical classes (Q17, m = 4.67), and indicated they had learned "more than average" in it (Q18, m = 4.33). One student in the focus group summed the class up by saying We get to design it, and we get to build it, and cut everything out, and make sure it works, and it gives us free will. You know how some projects, it‘s like, "Make a poster of this person." So you‘re limited, whereas here, he‘s like, "Make this go." There‘s not much that holds us back; we get to use our imagination. and another added, "I love projects; it gets your mind rolling!" Weaknesses Though there is no doubt room for improvement in some areas, students did not identify any particular weaknesses in this class in either their survey responses or focus group comments. The only CTL principle not judged to be pervasive in the class was the principle of social responsibility. Though students spoke frequently about the importance of being responsible on the job and "making something" of their lives, they did not speak specifically about doing things to benefit the larger society. Julia's seventh-grade Life Sciences class Students Julia's class was a regular-level, required seventh-grade Life Sciences class in a middle school in that serves a primarily low-SES, minority student population in a small city in central north Georgia. Only six students in the class returned their interview permission forms, so only one focus group interview was conducted. These students were all girls, and all but one were African Americans; Julia characterized them as "average students, but hard-workers." Sometimes 17 the students' dialect was difficult to understand and transcribe, but none of the focus group participants was limited English speaking. Class processes Students described covering many of the same topics as were covered in Sarah's class, but they did not seem to take notes off the overhead as often, and class was enlivened by more discussions and alternatives like "hands-on" activities, slide shows, movies, and songs. Students described how, in most classes You take notes on the overhead. They don‘t let you do nothing that‘s fun; all you do is work, work, work. In Julia‘s class, she‘ll give you time to catch up on your work, and let you conversate as long as you‘re quiet. . . . She makes hands-on projects, stuff like that. The other teachers, you got to read out of the book, copy off the board, take notes everyday . . . . Most of her class didn‘t understand about bacteria and stuff, so we did a research project with another class. We got grouped up, and we learned how bacteria and viruses connected."
Another student agreed, saying She does stuff like let you talk about stuff. Like other teachers say stuff like 'shut your mouths'; she let you talk about what you have to say, then she say what she has to say. . . . She has slide shows [with] directions and stuff. She shows more pictures and stuff; it's easier to understand." One student talked about how, "Julia, she‘ll make up like a song or round or something that make it fun, so it make you remember, like you might have a test. She makes sure that we learn stuff," while another gave the example of "'King Phil came over for great spaghetti' . . . that be, 'Kingdom, phylum, class, order, genus, species.'" Students also enjoyed watching videos, "mostly science videos." To prepare for tests, Julia often had students, . . . write 4 or 5 or 15 facts under a certain section and then answer the questions. . . . When the test comes, she gives you back the facts: then you can learn, then 18 you be thankful about it. If the facts ain‘t right, she‘ll tell you which ones ain‘t right first, [so] you can study for the test. Students reported doing much of this work in groups. Like she‘ll say '"two to a group," or "three to a group," or "four to a group" and you get with whoever you want, unless you and that person be acting up all the time. Sometimes she‘ll give you a chance even if you all do, but if you all keep on acting up, that‘s the only time she put you in a group. It should be noted that the seventh grade classes at this school use a management system in which students get punches on a "ticket" for inappropriate behavior; students receiving more than a certain number of punches in a week forfeit the privilege of participating in "fun Friday" activities--hence the references to "tickets" and "taking your ticket" in students' comments. Strengths As can be seen from the above descriptions of class activities, Julia's class offers students the opportunity to learn in a variety of contexts and through a variety of media. Students recognized this on the class evaluation surveys, indicating that they did different activities more often than in previous science classes (Q2, m = 3.59). They also saw Julia as more willing or able than most science teachers to adapt instruction to diverse students' needs (Q8, m = 3.76). Focus group participants gave multiple examples of her creativity in doing this, including several cited above and the following: If you are failing, she‘ll give you some extra work or give your work back and you can redo them, and she‘ll make copies, and when you redo them, she‘ll give you your grade, and your grade goes up. . . . When you tell her what you got wrong, she‘ll help you with it. . . . because you learn from your mistakes. Say like you're not doing so good, she‘ll put you with someone else that‘s doing real good, like got a 100 in the class. She‘ll let you team up, and you be learning, I know. Sometimes you think you just copy, but you still learn; you‘re looking at the answers. 19 She uses stuff like candy that we can have fun with. She‘s cool, like, she makes stuff fun. She be dancing in class; she‘ll be laughing, and everybody will calm down. She makes up songs about what we‘re doing like "My class is so bad, let‘s learn science, oh yeah"; she‘ll make cheers; she makes everything fun. She be doing crazy junk. Although focus group participants did not mention any related examples, students in the class also rated it as emphasizing ways they can contribute to the community and society more than the average science class (Q5, m = 3.94). Finally, students in the focus group described many ways that Julia demonstrated her caring for students and their learning. One student explained that [Julia] don‘t rag all the time; she don‘t cut you. Like if she heard you talking about, "Oh, girl, we went to the movies, and he was doing this," then she‘s going to take your ticket because you're off task, but if you ask for a pencil, like "Shawna, can I get a pencil?" then like the other teacher will come over, like "Give me your ticket," but [Julia] she, like, give you a warning, or, "If you need a pencil, ask me." While another confided that We can go to [Julia] and talk to her about something, and she will understand what‘s going on, but you won‘t want to go talk to another teacher about it. . . . Like I had got in trouble one day, and then I was fixin' to get mad. Then [Julia] . . . she let me go on back to her room and make some little cartoons to calm down. . . . . She'll let you sit in the back of her room and cool down. . . Say you get in trouble seventh period, and don‘t have her classroom eighth period, then while you in
there calming down, she‘ll go tell the teacher like well, "Janeice is in the back of my classroom," and then she‘ll bring my work over there, like "Do this." She makes sure we get our work done, she ain‘t going to excuse you from no work, but she‘s going to give you time to cool down, too, and then do your work. 20 On the final two survey questions, students rated both their interest (Q17, m = 3.94) and learning (Q18, m = 4.00) in this class as definitely greater than in the average science class. Weaknesses On the evaluation survey, students reported that they spent more time "just listening" in Julia's class than in the average science class (Q7, adj. m = 2.06). This survey result seemed somewhat contradictory to the many activities and open discussions described by the focus group students. Students' survey responses also indicated that kids in this class were "mean and nastily teasing" each other somewhat more than an average amount (Q14, adj. m = 2.50), but paradoxically indicated that students worked well together and helped each other more than average as well (Q16, m = 3.94). Students in the focus group reinforced the latter impression, giving several examples of helpful or harmonious student interactions and none of hostile interactions. This class had no areas of weakness that were evidenced in both survey responses and focus group comments. Cindy's high school Food Fundamentals class Students Cindy taught at a high school in north metro Atlanta which served two distinct student populations: one group of middle-class, urban/suburban, though ethnically diverse, students and one group of immigrant students, many of whom were poorer and limited English speaking. This dichotomy arose in part from the inclusion of a strongly immigrant area in the school's catchment zone and in part from the school's history; until the previous year, it had been designated officially as the "ESOL school" and had served all the limited English speaking students in the district. Although this year ESOL students were supposed to attend their local schools, those who had begun at this school were allowed to continue there if they wished to do so, and many remained. Finally, this high school offered an International Baccalaureate program, which drew a somewhat different group of international and immigrant students to the school. Cindy had students representing each of these groups in her Food Fundamentals class, which was the first in an elective cooking sequence in the Family and Consumer Sciences 21 department. Most of the students in her class completed the course evaluation survey, but only four students were available to participate in the focus group interview. These students included 3 girls — one African American, one Caucasian, and one Hispanic — and one boy whose family had come from India; all of them spoke standard English fluently, without any noticeable accent. Thus, in this class, the focus group was demonstrably not representative of the complete classroom population. Class processes This high school is on a modified block schedule, which means that this class meets for 90 minutes every other day. Students described the typical class schedule as being pretty evenly divided between "days we take notes" and "labs," with quizzes and tests occurring occasionally. They said, "At the beginning of the year it was more notes, just because we have to learn the basics before we could get into the kitchen and start cooking, but after the first two months" it was more cooking. On note-taking days, Cindy puts typed out notes "on the overhead projector, and we just copy them. We do it in sections, where we‘ll copy something, and [then] she‘ll talk about it and we‘ll discuss it, . . . and then we‘ll copy some more, and we go like that." Usually, the notetaking will not go on for a full 90-minutes, and in the remaining time Cindy might demonstrate the cooking lab for the following day, or have students complete a worksheet or answer the questions at the end of a textbook chapter. On lab days, about two out of every five, they work in selfchosen groups of four to six students to prepare and cook one or more dishes from recipes in their textbook or provided by Cindy. Before the students start the lab, Cindy "makes sure you know what you‘re doing, so you don‘t burn the recipe. . . . She gives you pointers, that she realizes classes before have messed up on, so she tells us so we know." Often different groups are told to prepare the same food in different ways, or groups might experiment with minor alterations to a recipe's ingredients or preparation instructions. Students particularly remembered a long-term project on regional foods in the United States. 22 She broke the United States up into different regions. Every group she handed out packets. Some groups got the Southwest, others got the Northeast, and she said, "If you want to, two groups can trade. . . . We researched the region, different
foods from that region, and we picked a food to make from that region. We made posters. We got some other recipes, just as popular foods that are eaten in that region. . . . The history was in the book, and . . . there was a menu-type thing in our book, and that‘s where we were to pick the recipe for what we were going to make, but the recipes that she wanted us to get to see what type of popular foods there were, we could get off the internet, or in a cookbook, or something. They also remembered a time when Cindy invited a restaurant owner who . . . gave food to the poor people of Atlanta, and he came in, and we made about 300 bologna sandwiches for homeless people. So, I think that was good because we interacted with the community, because when the class found out there was a real practical use, like that somebody else would benefit from me cooking or making a sandwich, something we could do whenever we want, but they don‘t have the option to, I think they got more spirited in their sandwich-making. You know there are always those class clowns that don‘t think it‘s cool to make a sandwich or something, but they were really into it after that…. It might have been the fact that the restaurant owner was encouraging everyone, [but] I think they also felt good because they were doing a good deed, and they realized it, and they don‘t get that chance every day. Strengths Students identified the real world applicability of their learning as one of the major strengths of this class, both through survey responses (Q4, m = 4.06 and Q12, adj. m = 4.06) and focus group comments. While only one student in the focus group was considering a career as a chef or caterer, all four students enjoyed the practicality of what they were learning. One student said she likes 23 taking my recipes home, and trying to make them for my family, because they like to cook . . . like, "[Cindy] taught me how to do that," and it‘s like, "Good, cook it!" Different utensils, like some of them I never knew the purpose of, it was like, "Why do we have this?" Like a broiling pan. I have one at home, we have the bottom pan and the top thing with the slits. I never knew what it was. Now I know what that is. All the stuff I get to take home, and share my knowledge with my family, cooking stuff. Another said I never get to cook at home, my mom is usually in charge with that, so its good to be able to experience cooking somewhere else. . . . She doesn‘t trust me with the oven. She‘s saying after this class, she‘ll let me try to do a couple of things. The boy from India said, "At my house, I cook, but my grandmother taught me, and she‘s from India, so we I know all this Eastern stuff, but . . . Cindy, she educated me on how to cook [American foods] like muffins." Students also appreciated the class's many opportunities for collaborative learning (Q3, m = 3.75), feeling that most students worked well together, helped each other and "learned from our mistakes" (Q16, m = 3.71). As with the other novice teachers in this study, Cindy's students also felt that she cared "more than the average" FCS teacher about their learning (Q13, m = 4.06). As the focus group students said She's not like any other teacher, where she‘s like, "Get your work done! Do this!" She talks to you. [She] interacts with us, I mean they all do, but she interacts more like on our own level. . . . She comes to you up front. Like some teachers, they have mood swings sort of, they can get very tense and evil, sort of, but I think what makes a good teacher is that she makes it fun for you to learn, but you also assimilate the knowledge. . . . I think it‘s good when a teacher, when you know that the teacher likes what they‘re doing, they‘re not just there to get it over with. She likes her job, I can tell, and it makes us like it more. 24 On the final two survey questions, students rated their both their interest (Q17, m = 4.18) and their learning (Q18, m = 4.12) in Ms. M's class as well above average. Weaknesses The only weakness students identified on the course evaluation survey for this class was a lack of different kinds of learning activities as compared to other FCS classes (Q2, m = 1.75). This perception might be due to students' previous classes (mostly in middle school) having been more general "survey" classes, covering a variety of topics in family and consumer sciences. Students filling out this survey may therefore have lumped all "cooking" activities together as a single learning context, perhaps not realizing that the same concept could be studied in the contexts of multiple, different foods and recipes. In fact, the focus group students described
exactly such a project. When we were learning about the dry heat and moist heat methods, she went around and every group picked out of a hat what you were going to do, and each group had a different thing. Our group had baking . . . some groups had broiling, others had stir-frying, and then we all cooked chicken and broccoli. Every group had chicken and broccoli, it was just cooked by a different method. Once it was all done, every group put it on a plate and we put it on the table and compared them to each other. You could see the difference between each method. The moist heat methods, like steaming and boiling, it keeps the color more vivid. The broccoli seemed greener. The dry heat was like dryer; it wasn‘t as good. Students in the focus group also expressed a feeling that the class was not sufficiently flexible in adapting to differences in students' prior knowledge of cooking or even of American kitchen appliances. As one girl said, "Half of our class is ESL, and they needed to learn the basics of what things are and what they‘re used for. I wish they had more of a higher class for people who already know the basics." 25 Rhonda's Honors Algebra II class Only freshmen and sophomores in the Honors program at the school where Rhonda taught were eligible to take her Algebra II class. This high school is located in one of the fastest growing counties just outside of Atlanta and serves a primarily middle and upper-middle class population. Sophomores taking Rhonda‘s class had been accelerated one year in mathematics, having taken algebra in eighth grade and geometry as freshmen. Freshmen in the class were accelerated two years, having qualified to take algebra as seventh-graders and then taking geometry in eighth. Fourteen students in the class returned interview permission forms, so two focus groups of seven students each were interviewed, each containing both male and female students. One group included an East Indian student, and the other included a Hispanic student. All the other students interviewed were Caucasian; there were no African American students in either group. Class Processes This high school is on regular block scheduling, which means that classes meet daily for a semester in 90 minute blocks. Students in both focus groups said that there was a regular daily routine in this class. First students check their homework using the teacher's manual at the front of the room. "Every day one girl goes up to the board; she‘s like the designated homework number checker. She writes down all the numbers people need help on, and then people who got them right [volunteer to] go up to the board and write [their problems] on the board." Students then explain how they did their problems, while the other students can ask questions. After they go over the homework, they "take notes" from the overhead projector. Students first copy each section of notes silently, and then Rhonda works one or two examples on the overhead which she explains. Students who finish copying a section faster than the rest "just make comments and have a class discussion or something. It‘s not like we just sit around silent. . . . (laughter) sometimes it's [about] math. We‘ll talk, and then when everyone has had enough time to take the notes down, then the discussion will end, and she‘ll explain." This goes on for most of the rest of the class, and "sometimes if a few minutes are left, she‘ll let us start on homework, or if we have 26 a test or something she‘ll hand those back." The homework is only collected occasionally; students realize that its purpose is to prepare them for the tests. Note-taking is also optional; although most students write all the notes, one boy shared that he never takes notes, but spends his time "read[ing] Harry Potter." He thought Rhonda probably didn't mind this. "She doesn't say anything negative. . . . I think it is OK as long as I‘m doing OK, and I am." Students also recalled doing several different activities in the class this term. One was an activity on random numbers. "She read us all this cool information about phone numbers, and like we had to find the probability of having the same last 3 digits of your phone number as your best friend, and stuff like that." Another activity was done with M&Ms, to find the probability of getting a yellow M&M from a bag. "She gave us all a big pile of M&Ms, and we got to count them out, and we got to eat them." Another time, students said We were doing conic sessions and like she was trying to make it fun, so she made each period a cookie cake, and you had to make an ellipse. So she put candles in the cake with a string, and you had to draw the ellipse with the icing, then we got to eat the cookie cake. She really tries to make it fun. The final activity they remembered was more of a party. They had just finished learning about using the base of a logarithm, and it was midterms, so they had an "E day. We all brought in candy or I think she brought in cookies. We all had "Es" decorated on them. . . . We reviewed during it; it wasn‘t just a party." Before tests, students also play "review games." Once Rhonda made "each row a team,
and one by one, you have to go up to the board and whoever finishes the problem first [wins]. Another time they worked in groups of four on problems she read out, and whichever group answered correctly first got a point. "Once we went around with a partner, and she had questions and answers on the wall and that was fun. You had to do a question then go find the answer around the room." 27 Strengths In both their responses on the course evaluation surveys and their focus group comments, students indicated strongly that Rhonda was better than most math teachers at adapting to different students' needs (Q8, m = 4.08). In addition to her flexibility on note-taking, students felt a good deal of freedom to ask questions during the homework reviews and lectures. They emphatically agreed that, unlike Rhonda, many other teachers "get annoyed" when students ask questions. They said that Rhonda also makes herself available to help students in the mornings before school and on regularly scheduled afternoons. Students appreciated the clarity and depth of Rhonda's explanations and the notes she gives them. They felt that her explanations actively engaged them in learning and critical problem-solving (Q1, m = 3.83 & Q15, m = 3.67). A girl in the first focus group explained, "Rhonda is very, very good. . . . I've understood every single thing that we‘ve learned this year. . . Like when we learn an equation, we know why that equation is how it is." Another added, "It helps me learn better. If you know why stuff is that way, it's easier to learn." Students in the second group said similarly that, "usually when she works an example, you can understand it and why it happens." Students survey responses indicate a high degree of comfort with both their fellow students (Q14, adj. m = 4.50) and Rhonda (Q13, m = 4.42). They see her as caring both for their learning and themselves as individuals. A student in the first group said, "I like Rhonda; she's really great," and the following conversation ensued: Student: She‘s just so casual about it. She lets me sit at her desk because the chair‘s so comfortable; not too many teachers would do that. She has a person every period who sits at her desk. She gives up the desk for the whole day because we like sitting there. Student: The thing I always like about Rhonda is she treats us more like equals. I really have a problem with teachers who are condescending and treat you like, You‘re my student, I‘m the authority figure; you must do what I say." Whereas 28 even while maintaining that effective authority she still treats us like we are people. Student: Rhonda obviously realizes we are people, too. I don‘t think she has ever gotten mad in our class. Student: That was what I was going to say. One time, like if I get in trouble, she won‘t give me a detention, but she‘ll like take me outside and that makes me feel so much worse. She‘s like, "You betrayed me, and I trusted you." They also were happy that She‘s not completely out to destroy our grades. . . . I‘ve had teachers tell me they don‘t want anybody with an A. If you have an A, you should be in a harder class. . . . I mean, she really does understand that if we really do understand this material, we should have an A, and I really appreciate that. She really does get excited when like 15 people get A on the test. . . . That says stuff about her." On the final two survey questions, students rated Rhonda's class as somewhat more interesting than most math classes (Q17, m = 3.58), and students believed they had definitely learned more than in the average math class (Q18, m = 4. 17). Weaknesses Students did not perceive many real life connections to much of the material in the class (Q4, m = 2.96 and Q12, adj. m = 2.83). Nor did they see how their learning of this material might eventually contribute to society (Q5, m = 2.67). They saw the extra activities more as "little fun projects." One girl said, "I probably prefer doing actual math problems and then explaining them . . . 'cause I don‘t really feel like a lot of the stuff connects very well. I think it‘s just kind of like busy work." Another agreed that, "It does seem a little superficial sometimes to do these other things, playing with M&Ms." A third partially disagreed, saying I just think that they are fun, fun. I think that the labs are like good, and things like that, but sometimes the questions that follow just don‘t, [they're] weird. You‘ve learned things already, and the questions are just kind of boring, writing random 29 procedures down and everything. It depends on the lab; sometimes they help and sometimes not.
One student thought Rhonda "did a good job of giving us real life examples where [she] can find it. It may not pertain to everyone's career choice," but another replied, " After hearing the real life applications, it makes it seem more ridiculous than if there were actually no applications. The applications are so absurd, like you would never do that." One student in the first group said, " I tried to do a combination the other day just to figure out my chances for doing something," but added, "I do math a lot. I‘m the kind of person who enjoys doing my math homework." When directly asked, no student in the second focus group could think of any time or place they might use knowledge from the class, except maybe in "Science Fair," while they were still in school. Finally, when asked how they would change the class if they could, students said they would prefer fewer notes and more opportunities to work out example problems, possibly with other people in the class. But they wouldn't like having to figure out how to do new types of problems themselves; they wouldn‘t like it if Rhonda didn't explain how to do the problems first. One student said, "I would cry," and another said That was like our geometry teacher. . . . We used to like, you‘d look over the section, and do a couple of examples she put on the overhead, and then we go through it, and I thought that was kind of a waste of time because I need things explained to me. So it was just wasting like half an hour with us just sitting there trying to do it, and really not getting anything done. I like the way [Rhonda] does it. Cross-class discussion and conclusions Although the classes had varying strengths and weaknesses, a review of the data from student course evaluation surveys across all classes (Table 1) reveals an impressive record. On all but three of the survey questions, students rated these classes as embodying CTL principles to a greater degree than most classes in the same content areas. 30 In addition, students clearly and consistently rated these classes as more interesting (Q17, overall m = 3.97), and they felt strongly that they had learned more in these classes than in most classes in the same content areas (Q18, overall m = 4.12). Every one of these five classes was rated above average by their students on both of these vital qualities. The individual frequency totals tell an even more impressive story: out of 81 total respondents on these summary questions, only 10 rated their class as less interesting than the average class in the same content area (Q17), and only 5 felt they had learned less than the average amount for classes in the same content area (Q18). This record is all the more remarkable when one considers that these classes were all taught by novice teachers, two by second-year teachers and three by teachers teaching their very first semester in the schools. At a stage when most novice teachers feel lucky simply to survive, these teachers were able to both engage their students' interest and significantly facilitate their learning. Clearly, the research questions originally posed on p. 3 of this document can be answered with a resounding, "Yes!" Another strong commonality that bears further discussion relates to Question 13, which asks, "Compared to other classes you have taken in this subject, how much did you feel the teacher really cared about you and your learning?" Again, students in all five classes rated their teachers as above average on this characteristic, and only 7 out of 81 students felt their teachers cared less than the average teacher in that content area. Examples of effective teacher caring, of the kind that supports students in their efforts to learn and also communicates to them strong expectations for their success, abound in the classroom portraits described earlier in this report. Unlike the case for so many novice teachers, this caring has not come at the expense of discipline. One of the unexpected results to emerge from the qualitative data is that students also describe these teachers as highly effective classroom managers. Consider the following excerpts from focus group interviews with each of the classes in this study: 31 Sarah: Once you get to know her, and as long as you not being completely terrible, she‘s a really good teacher. . . . she always makes sure we know. David: We're a lot more independent compared to other classes where the teacher‘s always telling us exactly what to do and always on us. . . . He teaches us the basics, but then he lets us go off, and I really like that. . . .most of the teachers wouldn‘t even let us use those tools. He let us. We have two or three days when we go in there and he teaches us, like, "This is what you‘re supposed to do," and safety, and by the time we‘re getting it, we‘re actually safe. Julia: She‘ll be laughing, and everybody will calm down. She makes up songs about what we‘re doing like "My class is so bad, let‘s learn science, oh yeah"; she‘ll make
cheers; she makes everything fun. She be doing crazy junk. (Interviewer: But do you all behave for her?) Yeh, because she's nice, we like her. . . . Like, if you gives us that, you get it back. We give her respect, and we get it back. Cindy: I think she has control, but I think one reason why she does have control is maybe we can get along with her so well. We respect her more than a teacher who acts superior to you and puts you down and stuff. [People] like her, and so if she asks you to be quiet, they‘re going to be quiet. Rhonda: She has really good control. I mean it‘s like an open class; it‘s not, nobody feels like if they do something they are going to get in huge trouble or anything, but at the same time, everybody behaves. . . . I don‘t know if we didn‘t behave if she would be more strict. She‘s pretty open, so it kind of makes you want to do what she tells you to. These novice teachers seem to have mastered the single facet of teaching that is most challenging for novices and most often leads to teachers quitting in their first or second year of practice: they have developed classroom management techniques that enable them to simultaneously control and motivate students to behave appropriately. Their mastery in this area is not incidental to the subject of this study, nor is it simply because they are "good teachers." Data from student surveys (Table 1) show that, as compared to others in their content 32 area, these teachers are particularly strong in their abilities to actively engage students in learning (Q1), adapt instruction to diverse students' needs and interests (Q8), enable students to do real world, critical problem-solving (Q15), and create a caring community of learners in the classroom (Qs 13,14,15). Focus group data (Table 2) confirm these teachers abilities in these specific areas. Students described active learning as either a major part of or pervasive within in all but one of the target classes. Adaptive teaching and critical problem-solving were described as significant or pervasive features of all the target classes. In all but one class, the teacher's caring for students and student learning pervaded the class. All of these are key features of contextual teaching and learning, and they are also identified as key needs in recent educational policy discussions, such as those around the No Child Left Behind act. The findings of this study suggest that these teachers' understanding and implementation of these key features of contextual teaching and learning has enabled them to gain their students' "cooperation" in both behavior and learning, what Woolfolk (2001) calls the "essential" task in classroom management. Simply put, when students are given the opportunity to do contextual teaching and learning--that is, to actively engage in critical thinking around real life problems in a collaborative, inclusive classroom community--they want to learn and they can learn. In such classrooms, students experience little of the boredom and frustration that leads to most classroom misbehavior. Contextual teaching and learning techniques enabled these novice teachers to manage, motivate, and ultimately teach their students. Further questions Closer comparative analysis of the cross-class student data summarized here leads only to new questions about the conditions under which novice teachers can implement the various principles of contextual teaching and learning most effectively in public school classrooms. For example, the two classes that were rated highest in both the quantitative and qualitative analyses were electives in career and technical education areas, rather than traditional core academic subjects. Is contextual teaching and learning easier to do in elective classes (a reasonable possibility)? Or is it easier to implement in career or other electives, rather than required classes, 33 perhaps because students in the former have chosen to take those classes? Students in both seventh grade Life Sciences classes tended to feel that they spent a lot of time memorizing facts and sitting and listening to the teacher. Does this finding simply reflect these teachers' professional styles, is it just the nature of beginning classes in Life Sciences, or is it somehow related to the age of the students? All of these questions and many more will provide material for significant future research in this area. References Bogdan, R.C., & Biklen, S.K. (1992). Qualitative research for education: An introduction to theory and methods. Boston: Allyn & Bacon. Padilla, R. (1991). HyperQual III (a software program facilitating qualitative analysis on the MacIntosh). Chandler, AZ: Author Woolfolk, A. H. (2001). Educational Psychology (8th ed.). Boston: Allyn & Bacon. 34 Core Principles of Contextual Teaching and Learning Active engagement: Students are actively engaged in constructing knowledge and solving problems. (Resnick & Kopfler, 1989) Multiple contexts: Learning in multiple contexts gives students experience in using what they
have learned to identify and solve problems in new contexts (transfer). (Hatano & Greeno, 1999; Winne, 1995) Student collaboration: Students learn from one another through cooperation, discourse, teamwork, and self-reflection. (Vygotsky, 1978) Real world connections: Learning is closely tied to "real world" issues through outsideofclassroom experiences and simulations. (Cronin, 1993; Newmann & Wehlage, 1993) Prior experience basis: Students‘ prior experiences are valued and seen as fundamental to learning. (Greeno, Collins, & Resnick, 1996) Adaptive teaching: Teaching is flexible and adapted to the needs of diverse learners. (Sternberg, 1997; Stodolsky & Grossman, 2000) Social responsibility: The ways in which students can contribute to the improvement of society through their learning and resultant actions are emphasized. (Bilig, 2000; Wade et al., 1999) Meaningful assessment: Student learning is assessed in multiple meaningful contexts. (DarlingHammond, Ancess, & Falk, 1995; Shepard, 2000) Critical problem solving: Higher order thinking and problem solving are emphasized above meaningless memorization and recitation of facts. (Anderson, 1993; Bruner, 1990) Self-direction: Students are encouraged to make choices, develop alternatives and be selfdirected, sharing with the teacher responsibility for their own learning. (Ames, 1992) Caring classroom community: The classroom context evidences the kind of caring, respectful relationships between teacher and students and among students that are conducive to learning. (Noddings, 1995) *(adapted from the University of Georgia CTL Conceptual Framework, 1999, www.coe.uga.edu/ctl) Figure 1: Core principles of Contextual Teaching and Learning (CTL) 35 Your comments count! Directions: This survey is anonymous & voluntary. You do not have to fill it out, and it will not affect your grade or my opinion of you in any way. To keep it anonymous, please DO NOT put your name on it. I am asking these questions because I am working with some colleagues on some new ideas about teaching, and I am really interested in your impressions of your experiences in my classroom this term. So, please CIRCLE THE RESPONSE THAT HONESTLY REFLECTS YOUR PERSONAL IMPRESSIONS OF THE CLASS, and take some time to make comments at the end. THANK YOU for your input—this is one of the ways I try to become a better teacher every year. 1. Compared to other classes you have taken in this subject, how much time did you spend in this class actively discussing, working on things or solving problems? Not much at all Only a little About average More than average A lot! 2. Compared to other classes you have taken in this subject, how many different kinds of activities did you get to do in this class? Not many at all Only a few About average More than average A lot! 3. Compared to other classes you have taken in this subject, how much time did you spend in this class working or discussing with other students? Not much at all Only a little About average More than average A lot! 4. Compared to other classes you have taken in this subject, how useful do you feel what you have learned will be in your life outside of school? Not useful at all Only a little About average More than average Very useful! 5. Compared to other classes you have taken in this subject, how much did this class emphasize ways you can contribute to your community or society as a whole? Not much at all Only a little About average More than average A lot! 6. Compared to other classes you have taken in this subject, how much were you encouraged to think about your own prior experiences, in and out of school, to help make sense of what you were
learning? Not much at all Only a little About average More than average A lot! 7. Compared to other classes you have taken in this subject, how much time did you spend just sitting and listening to the teacher? Not much at all Only a little About average More than average A lot! 8. Compared to other classes you have taken in this subject, how much was the teacher able to offer extra help or adapt activities to the different needs or interests of different students? 36 Not much at all Only a little About average More than average A lot! 9. Compared to other classes you have taken in this subject, how many different or unusual kinds of tests or activities did you do that counted toward your grade in this class? Not many at all Only a few About average More than average A lot! 37 10. Compared to other classes you have taken in this subject, how much memorizing of facts did you have to do in this class? Not much at all Only a little About average More than average A lot! 11. Compared to other classes you have taken in this subject, how much choice did you have about which topics you studied or the way you did projects, assignments or activities in this class? Not much at all Only a little About average More than average A lot! 12. Compared to other classes you have taken in this subject, how much of what you learned seems pretty useless outside of school? Hardly any useless stuff A little About average Mostly useless Almost all useless! 13. Compared to other classes you have taken in this subject, how much did you feel the teacher really cared about you and your learning? Not much at all Only a little About average More than average A lot! 14. Compared to other classes you have taken in this subject, how much were kids mean or nastily teasing to each other? Not much at all Only a little About average More than average A lot! 15. Compared to other classes you have taken in this subject, how much did you go beyond just memorizing facts, toward understanding and working with real problems in this class? Not much at all Only a little About average More than average A lot! 16. Compared to other classes you have taken in this subject, how much did kids work well together or help each other? Not much at all Only a little About average More than average A lot! 17. Compared to other classes you have taken in this subject, how interesting was this class? Not much at all Only a little About average More than average A lot! 18. Compared to other classes you have taken in this subject, how much do you think you learned in this class? Not much at all Only a little About average More than average A lot! 19. Please tell me about any ways you feel this class was different from most you have taken in this subject, or at this school. 38 20. Please tell me anything else you want to say about this class. 39 Student Focus Group Protocol
(NOTE: This is a semi-structured interview protocol. The questions below are intended as a guide for the conversation.) 1. Your teacher, Mr./Ms. X, is taking part in a project studying different ways to teach in schools. You‘ve been in Mr./Ms. X‘s class for about a semester now, and I am really interested in how you see your experiences in the class. To start off, could you describe how your teacher teaches in a typical day in the class? P: Get pattern of activities and their participation P: How did kids respond to the teacher‘s strategies in the class? (e.g., cooperation/collaboration, interest, conflict, teasing?) 2. What would you say was the best part of the class (or thing about the class) for you? P: Why was it the best? P: What did you do? P: Why do you think Mr./Ms. X had you do that? P: What did you learn from that? P: Do you think other kids in the class felt the same way? 3. What would you say was the most important thing you learned in the class? P: Why was it important? (look for connections to real life) P: How did you learn it? 4. Did you do any (other) special projects or activities in the class? (if Yes) Tell me about them? P: (if they can‘t think of any) P: Did they go any where outside of the class? P: Were there any special speakers or guests? P: Did they talk with anyone outside of the class, like interviews or surveys? P: (Mention known projects from case study.) P: (if yes to any) What was that like? Why do you think Mr./Ms. X had you do that? What did you learn from that? Would you like to do something like that in another class (why or why not)? 5. Were there any parts of the class you would have changed if you could? P: How would you change them? P: Why? P: What about other kids in the class; what do you think they would say? 6. If friends of yours were thinking about taking this class from Mr./Ms. X next year, what advice would you give them? P: Would you tell them to take it? Why or why not? P: What would tell them about the class? P: What advice would you give them about getting the most out of the class/doing well? Figure 3: CTL focus group interview protocol 40 Table 1: Student Survey Adjusted* Frequency Table, with means Principle Q # Teacher Gr., Subject ! ! ! Response Freq. ! ! N µ µ all classes NA * 1 2 3 4 5 1 Sarah 7th, Science 1 8 4 2 15 3.47 3.68 Active engagement * 7 Sarah 7th, Science 1 5 4 3 2 15 3.00 2.89 Multiple contexts 2 Sarah 7th, Science 8 7 15 2.93 3.16 Student collaboration 3 Sarah 7th, Science 1 2 4 5 2 1 14 2.71 3.43 4 Sarah 7th, Science 1 1 4 3 4 2 14 3.14 3.56 Real world connections *12 Sarah 7th, Science 3 4 6 2 15 3.47 3.54 Helping society 5 Sarah 7th, Science 1 3 8 1 2 15 3.00 3.41 Prior experience basis 6 Sarah 7th, Science 1 3 5 5 1 15 3.13 3.51 Adaptive teaching 8 Sarah 7th, Science 6 5 3 1 15 2.93 3.66 Meaningful assessment 9 Sarah 7th, Science 2 5 3 3 2 15 2.87 3.28 *10 Sarah 7th, Science 12 3 15 1.20 2.76 Critical problem solving 15 Sarah 7th, Science 1 4 6 1 3 15 3.07 3.59 Self-direction 11 Sarah 7th, Science 6 3 5 1 15 2.07 2.90 13 Sarah 7th, Science 2 4 6 3 15 3.67 3.98 *14 Sarah 7th, Science 1 1 7 2 4 15 3.47 3.57 Caring Community 16 Sarah 7th, Science 4 4 4 3 15 3.40 3.74 General-interest 17 Sarah 7th, Science 2 2 1 7 3 15 3.47 3.97 General-learning 18 Sarah 7th, Science 1 3 6 5 15 4.00 4.12 1 David HS, Engin'ring II 1 1 6 3 11 4.00 Active engagement * 7 David HS, Engin'ring II 1 2 2 5 1 11 3.27 Multiple contexts 2 David HS, Engin'ring II 1 5 5 11 4.27 Student collaboration 3 David HS, Engin'ring II 2 6 3 11 4.09
4 David HS, Engin'ring II 2 4 5 11 4.27 Real world connections *12 David HS, Engin'ring II 2 1 3 5 9 4.33 Helping society 5 David HS, Engin'ring II 2 6 3 11 4.09 Prior experience basis 6 David HS, Engin'ring II 2 5 4 11 4.18 Adaptive teaching 8 David HS, Engin'ring II 4 3 4 11 4.00 Meaningful assessment 9 David HS, Engin'ring II 1 1 2 6 1 11 3.45 *10 David HS, Engin'ring II 2 2 1 3 3 9 3.56 Critical problem solving 15 David HS, Engin'ring II 2 1 3 5 9 4.44 Self-direction 11 David HS, Engin'ring II 2 1 1 1 3 3 9 3.67 13 David HS, Engin'ring II 2 1 3 5 9 4.44 *14 David HS, Engin'ring II 2 1 3 5 9 3.89 Caring Community 16 David HS, Engin'ring II 2 2 1 2 4 9 3.89 General-interest 17 David HS, Engin'ring II 2 1 1 7 9 4.67 General-learning 18 David HS, Engin'ring II 2 1 3 5 9 4.33 * In this Table, response frequencies for Qs 7, 10, 12, & 14 have been reversed, so that (1) is now consistently the least favorable response, while (5) is the most favorable. 41 This was done to make question means more easily comparable. Table 1: Student Survey Adjusted* Frequency Table, with means (p.2) Principle Q # Teacher Gr., Subject ! ! ! Response Freq. ! ! N µ NA * 1 2 3 4 5 1 Julia 7th, Science 5 3 3 6 17 3.59 Active engagement * 7 Julia 7th, Science 7 5 3 1 1 17 2.06 Multiple contexts 2 Julia 7th, Science 1 4 2 4 6 17 3.59 Student collaboration 3 Julia 7th, Science 3 7 4 3 17 3.41 4 Julia 7th, Science 2 1 7 3 4 17 3.35 Real world connections *12 Julia 7th, Science 3 1 4 4 4 1 14 3.00 Helping society 5 Julia 7th, Science 3 1 7 6 17 3.94 Prior experience basis 6 Julia 7th, Science 1 3 5 3 5 17 3.47 Adaptive teaching 8 Julia 7th, Science 3 4 4 6 17 3.76 Meaningful assessment 9 Julia 7th, Science 5 3 4 5 17 3.53 *10 Julia 7th, Science 2 1 5 4 4 1 15 2.93 Critical problem solving 15 Julia 7th, Science 1 3 3 2 3 5 16 3.25 Self-direction 11 Julia 7th, Science 1 2 4 5 2 3 16 3.00 13 Julia 7th, Science 1 1 4 3 5 3 16 3.31 *14 Julia 7th, Science 1 7 2 2 2 3 16 2.50 Caring Community 16 Julia 7th, Science 2 1 1 3 4 6 15 3.87 General-interest 17 Julia 7th, Science 1 1 2 1 5 7 16 3.94 General-learning 18 Julia 7th, Science 1 2 3 4 7 16 4.00 1 Cindy HS, Food Fund. 1 1 1 6 5 3 16 3.50 Active engagement * 7 Cindy HS, Food Fund. 1 1 3 4 6 2 16 3.31 Multiple contexts 2 Cindy HS, Food Fund. 1 4 2 5 5 16 1.75 Student collaboration 3 Cindy HS, Food Fund. 1 2 4 6 4 16 3.75 4 Cindy HS, Food Fund. 1 1 1 2 4 8 16 4.06 Real world connections *12 Cindy HS, Food Fund. 1 1 4 4 7 16 4.06 Helping society 5 Cindy HS, Food Fund. 1 2 3 2 5 4 16 3.38 Prior experience basis 6 Cindy HS, Food Fund. 1 4 2 4 6 16 3.75 Adaptive teaching 8 Cindy HS, Food Fund. 1 3 5 5 3 16 3.50 Meaningful assessment 9 Cindy HS, Food Fund. 1 2 1 6 4 3 16 3.31 *10 Cindy HS, Food Fund. 1 2 8 6 17 3.12 Critical problem solving 15 Cindy HS, Food Fund. 1 1 5 8 2 17 3.53 Self-direction 11 Cindy HS, Food Fund. 2 2 9 3 1 17 2.94 13 Cindy HS, Food Fund. 1 1 3 6 6 16 4.06 *14 Cindy HS, Food Fund. 1 1 9 1 5 17 3.47 Caring Community 16 Cindy HS, Food Fund. 1 2 4 4 6 17 3.71 General-interest 17 Cindy HS, Food Fund. 1 3 5 8 17 4.18 General-learning 18 Cindy HS, Food Fund. 1 5 2 9 17 4.12 * In this Table, response frequencies for Qs 7, 10, 12, & 14 have been reversed, so that (1) is now consistently the least favorable response, while (5) is the most favorable. 42 This was done to make question means more easily comparable. Table 1: Student Survey Adjusted* Frequency Table, with means (p.3)
Principle Q # Teacher Gr., Subject ! ! ! Response Freq. ! ! N µ NA * 1 2 3 4 5 1 Rhonda HS, Alg II (Hon) 2 5 12 5 24 3.83 Active engagement * 7 Rhonda HS, Alg II (Hon) 2 4 15 3 24 2.79 Multiple contexts 2 Rhonda HS, Alg II (Hon) 4 10 10 24 3.25 Student collaboration 3 Rhonda HS, Alg II (Hon) 7 7 9 1 24 3.17 4 Rhonda HS, Alg II (Hon) 1 2 7 8 2 4 23 2.96 Real world connections *12 Rhonda HS, Alg II (Hon) 1 10 6 6 1 24 2.83 Helping society 5 Rhonda HS, Alg II (Hon) 2 7 12 3 24 2.67 Prior experience basis 6 Rhonda HS, Alg II (Hon) 4 5 5 7 3 24 3.00 Adaptive teaching 8 Rhonda HS, Alg II (Hon) 1 3 13 7 24 4.08 Meaningful assessment 9 Rhonda HS, Alg II (Hon) 2 5 7 10 22 3.23 *10 Rhonda HS, Alg II (Hon) 1 4 13 6 24 3.00 Critical problem solving 15 Rhonda HS, Alg II (Hon) 1 1 8 9 5 24 3.67 Self-direction 11 Rhonda HS, Alg II (Hon) 2 5 12 5 24 2.83 13 Rhonda HS, Alg II (Hon) 3 8 13 24 4.42 *14 Rhonda HS, Alg II (Hon) 1 10 13 24 4.50 Caring Community 16 Rhonda HS, Alg II (Hon) 2 8 6 8 24 3.83 General-interest 17 Rhonda HS, Alg II (Hon) 2 2 5 10 5 24 3.58 General-learning 18 Rhonda HS, Alg II (Hon) 4 12 8 24 4.17 * In this Table, response frequencies for Qs 7, 10, 12, & 14 have been reversed, so that (1) is now consistently the least favorable response, while (5) is the most favorable. This was done to make question means more easily comparable. 43 Table 2: CTL-related characteristics of classes, as described by student focus groups Principle Sarah David Julia Cindy Rhonda ! ! (7th, Science) (HS, Eng. III) (7th, Science) (HS, Foods) (HS, Hon. Alg.II) Active engagement Some* Pervasive Some Pervasive Minor Multiple contexts Some Pervasive Pervasive Some Minor Student collaboration Minor Pervasive Pervasive Pervasive Minor Real world connections Some Pervasive Some Pervasive None Helping society None Some None Some None Prior experience basis Some Pervasive Some Minor None Adaptive teaching Some Pervasive Pervasive Some Pervasive Meaningful assessment None Pervasive Minor Some None Critical problemsolving Some Pervasive Some Pervasive Some Self-direction Minor Pervasive Pervasive Pervasive Some Caring Teacher** Minor Pervasive Pervasive Pervasive Pervasive * Descriptive ratings of each teachers' class in relation to the 11 CTL principles, based on compilation and analysis of all related focus group interview comments, were assigned as follows: None - Students describe no evidence of this characteristic in this class. Minor - Students describe only minor or occasional evidence of this characteristic in this class. Some - Students' describe one regular feature OR a major event or project evidencing this characteristic, but their descriptions do not indicate it is pervasive in this class. Pervasive - Students' descriptions indicate that this characteristic is pervasive in this class. ** This characteristic was altered in this analysis from "Caring Community" because focus groups discussed only caring or noncaring teacher behavior; no students discussed peer caring or hostility. 44 Examples of Focus Group Summary Descriptive Ratings In classes embodying the CTL principle of Meaningful assessment, learning is assessed in multiple meaningful contexts. According to the focus group interviews, this characteristic varied greatly among the five classes in this study. To illustrate the bases of the different summary descriptive ratings, each rating category is described below, followed by examples of the data that lay behind the assignment of that rating to the class(es) to which it is assigned. None - Students describe no evidence of this characteristic in this class.
Example - Rhonda's Algebra II class If we have a test or something she‘ll hand those back, like, if we had a test or quiz the previous day. (No other forms of assessment were mentioned.) Example - Sarah's Life Sciences class (Interviewer: What do you have to do on the quizzes?) Sometimes she‘ll give us fill in the blanks, half fill in the blank, and half the definition, and on the last one she made us do the whole definition. (No other forms of assessment were mentioned.) Minor - Students describe only minor or occasional evidence of this characteristic in this class. Example: Julia's Life Sciences class If you are failing, she‘ll give you some extra work or give you work back and you can redo em and she‘ll make copies and when you redo em she‘ll give you your grade and your grade goes up. We have to do facts sometimes, like we have to read, like, section three, then write 4 or 5 or 15 facts under a certain section and then answer the questions. . . . when the test comes, she gives you back the facts, then you can learn. . . . You can study for the test. . . . Sometimes it counts for a grade, and if you do it you get extra points, but if you don‘t do it then you get a zero. Some - Students' describe one regular feature OR a major event or project evidencing this characteristic, but their descriptions do not indicate it is pervasive in this class. Example - Cindy's Food Fundamentals class (Interviewer: Is that what your grade is based on, the quizzes, and the tests?) And the labs. (Interviewer: In the quizzes or tests, is there something you have to do in the lab, too; do you have to demonstrate anything?) Sometimes there‘s questions that pertain to the lab. Pervasive - Students' descriptions indicate that this characteristic is pervasive in this class. Example - David's Engineering III class 45 We just built a gumball machine, and that lasted a long time, because that was a major project. We build a prototype, and then built 5 like it. We had to have drawings, and then we cut out all of the wood, and we had to figure out how to put it all together, and make sure it worked. . . . (Interviewer: Then the test was, you had to mass-produce 5 in a class?) Right. (Interviewer: What are the requirements for the boat?) It couldn‘t be over eight feet long, and it had to hold at least one person, no motors or anything, and it had to go and turn around and come back. Nothing can be pre-manufactured, you had to produce it all yourself, from scratch, basically. . . . (Interviewer: So it was a race, too?) Yes. . . . We got third. Almost every project we‘ve done, we‘ve done a PowerPoint for it, and that just shows him what we learned. . . . The group does one, and we put how we came up with our design, our problems. What everyone did to help. The problems we faced, the tools we used. It‘s like you would get on a program that you would look up on the computer. Figure 4: Examples of Data Underlying Summary Descriptive Ratings of Classes, based on Focus Group Interviews Contextual Teaching & Learning
Contextual Teaching and Learning is... teaching traditional content through the use of problembased and context-based methods. It is engaging the student in meaningful and relevant learning experiences through the use of constructivist teaching and learning principles. Contextual Teaching and Learning... incorporates the best research in 'brain-based' learning, performance assessment and standards-based education. Contextual Teaching and Learning...incorporates multiple teaching strategies where the learner becomes a problem-solver, not an 'exercise-doer.' Contextual Teaching and Learning...helps students to make the connections between:
Knowing and Doing School life and Real life Knowledge and Application Content and Context
Separate subject matter domains
Email Mr. Seager Here!!
MAKING LEARNING MEANINGFUL AND FUN
The goals of contextual teaching and learning are to provide students with flexible knowledge that transfers from one problem to another and from one context to another. These goals will be achieved through contextual teaching and learning by embedding lessons within meaningful contexts. We believe this will result in deeper foundational knowledge. Also, learners will have a richer understanding of the problem and the ways to solve the problem. They will be able to independently use their knowledge to solve new and unfamiliar problems. They will take more responsibility for their own learning as they gain experience and knowledge. The importance of context in mathematics education is also emphasized in Principles and Standards for School Mathematics by The National Council of Teachers of Mathematics: "The opportunity for students to experience mathematics in a context is important. Mathematics is used in science, the social sciences, medicine, and commerce. The link between mathematics and science is not only through content but also through process. The processes and content of science can inspire an approach to solving problems that applies to the study of mathematics (NCTM, 2000, p. 65)." "The most important connection for early mathematics development is between the intuitive, informal mathematics that students have learned through their own experiences and the mathematics they are learning in school. All other connectionsÑbetween one mathematical concept and another, between different mathematics topics, between mathematics and other fields of knowledge, and between mathematics and everyday lifeÑare supported by the link between the students' informal experiences and more-formal mathematics. Students' abilities to experience mathematics as a meaningful endeavor that makes sense rests on these connections (NCTM, 2000, p. 65, p. 131)." "Instructional programs from prekindergarden through grade 12 should enable all students to— recognize and use connections among mathematical ideas;understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics (NCTM, 2000, p. 65, p. 199)." "Real-world contexts provide opportunities for students to connect what they are learning to their own environment. Students' experiences at home, at school, and in their community provide contexts for worthwhile mathematical tasks (NCTM, 2000, p. 65, p. 200)."
Although there exist no precise definition for Contextual Teaching & Learning, the following are among many interpretations: Definitions from UGA CTL Project Definitions/Reflections from our Students Definitions from other CTL Projects
Definitions from UGA CTL Project: Contextual
Teaching & Learning is ...
» CTL is instruction and learning that is meaningful. Typically that means that instruction is situated in context but for more advanced students meaningful learning can also be abstract and de-contextualized. » CTL is an approach/perspective to teaching and learning that recognizes and adresses the situated nature of knowledge. Through connections both in and out of classroom, a CTL approach aims at making experience relevant and meaningful to students by building knowledge that will have applications to lifelong learning. In general, CTL aims to build collaboration between the university/school and community in ways which are mutually beneficial. » CTL is opportunities for learning about how to link classroom experiences with the "real" working world. In university classes, CTL involved faculty connecting the control of courses with the future work experiences of the learners. By participating in university classes with a CTL orientation, prospective teachers should better understand how to help pupils make sense of what they are learning in the context of the working world. » CTL is connecting educational theoretical knowledge to community practical applications. » CTL is experiences that occur "in site" that tie education to careers-relevant and useful. » CTL is the integration of knowledge into real life applications. It is the translation of theoretically-based pedagogy into practice. It is the framework wherein which those who are learning are facilitated in their connecting what is learned to the real world. » CTL is a marriage between school-based teaching and learning and community-based teaching and learning. Students learn "in the filed" of their interest, often providing a service to the community during the learning experience. CTL promotes the development of knowledge and skills for success in the "real world". » CTL is education within a specific environment (e.g., business and industry). The purpose is to ground teaching and learning in a real world setting to assist the learner in making connections between lessons and life. » CTL is the process of relating classroom subjects with the real world. » CTL is providing a learning environment for teachers that integrates the activities of the community that the teaching takes place. » CTL is teaching and learning academic and life skills, information and knowledge and applications of that learning. » CTL is teaching and learning with a strong focus on practical applications and careers, one that combines theory and practice. » CTL attempts to bridge the gap between the academic disciplines and the real world experiences. It hopes to show students how teaching academics are used in their everyday
lives. » CTL is the building of communications between school learning and life outside of the classroom. » CTL is the process of using a variety of contexts, teaching methods/strategies, and student initiated learning. » CTL is a focus on the context of what we teach from the students' point of view. This involves the community and work context. CTL also focuses on aspects of text practice that allow students to learn better. These include appropriate teaching strategies, assessment strategies, etc. » CTL is concerned with providing educational experiences (for teacher ed. programs) based on concerns, problems, issues related to situations in the society, particularly related to business, industry, commerce and other areas of economic enterprise. » CTL is an attempt to adopt our instruction to better fit the learning needs and outcomes of business and industry. » CTL is the learning and teaching based on pedagogy that is grounded in real life. » CTL is an educational connection between and among disciplines, (ours) skills and the real world. It is bringing the work world into the classroom and taking the classroom into the world of work. Developing and using skills applicable in the real world. Providing students with opportunities to apply their knowledge. » CTL is I have no earthly idea. It probably has something to do with making real life experiences of our students connect with school experiences. » CTL is the process of placing learning within specific contexts so that the application of the skills and knowledge learned can occur more effectively and efficiently. » CTL is the educational philosophy which believes that students learning can be enhanced by connecting content into the context of the students' own lives and possible occupations. It also stresses that the classroom itself is a learning context and that this should be explicitly reorganized. » CTL is:
Using applications in the classroom (incorporating-can also be the basis for an instructional unit) Giving students opportunities to see where theories might be applied in job situations, in regular life outside the classroom Learning (as a teacher) what specific skills and techniques and activities might be beneficial for students pursuing jobs in certain areas. Making a subject relevant to spark interest.
» CTL is about creating environments and situations where both teaching and the related learning takes place. It should enrich learning, making connections between ideas. » CTL is: given some problem to solve or some task to complete-in some context. Acquire the concepts and skills necessary to solve the problem or complete task as you go along doing what you have to do. It is a circular relationship. Task --> Concept Skills -->Task » CTL is an approach to learning that is grounded in context, and connected to "real-world" situations. It provides opportunities for authentic assessment and individual reflection. » CTL is drawing on a diverse array of contexts to enrich and illustrate content. E.g. workplace, communities, environment, etc. » CTL is using the workplace or workplace experiences to promote education in the classroom. to top
Theoretical Roots of Contextual Teaching and Learning in Mathematics [Contextual teaching and learning represents a concept that involves connecting the content that students are learning with the context in which that content could be used. Connecting content with context is an important part of bringing meaning to the learning process. For that connection to take place, a variety of teaching approaches may be used. Over the years, a body of literature has emerged based on research and development on how people learn. The following teaching approaches include context as a critical component and are found in the literature on teaching and learning:
problem-based learning collaborative/cooperative learning project-based learning service learning work-based learning
"Contextual teaching and learning emphasizes higher-level thinking, knowledge transfer, collecting, analyzing, and synthesizing information and data from multiple sources and viewpoints" (Howey, 1998). Of critical importance is that the above approaches be used at the student's developmentally-appropriate level of learning, that the environment be established to support self-regulated learning, that culturally-relevant pedagogy be applied, that knowledge about multiple intelligences be considered, and that appropriate authentic assessment be included.]* *: This definition/explanation of Contextual Teaching and Learning is taken from CTL website at Bowling Green State University by Berns, R. .G. & Erickson, P. M. (2000). Problem-Based Learning
Problem-based learning is an instructional approach that uses real-world problems as a context for students to learn critical thinking and problem-solving skills, and to acquire knowledge of the essential concepts of a course.
PBL in Mathematics: What a Concept! How do we ensure that our students have the necessary skills to succeed in the workplace of the 21st century? We can't predict the future, but we will always have problems to solve. This session shares an innovative approach to teaching and evaluating problem solving and critical thinking skills in an arithmetic class. Problem Based Learning The NEW Applied Math Curriculum: A Change in Pedagogy. Center for Problem-Based Learning The Center for Problem-Based Learning (CPBL) was established by the Illinois Mathematics and Science Academy to engage in PBL research, information exchange, teacher training, and curriculum development in K-16 educational settings. Paper Title: Examining How Middle School Students Use Problem-Based Learning Software. Paper Problem-based, inquiry learning is a model of instruction that promotes critical thinking by presenting students with interesting and puzzling problems to solve. The problem solving process involves observing developing and testing predictions, collecting and organizing data and formulating concepts and explanations. The model works best when the problem presented promotes genuine inquiry and the materials used provides valuable instruction. It is important for students to experience the discovery of new knowledge, therefore the problem presented should be based on discoverable ideas. Ford Middle School This site links to other sites that provide information about using technology and problem-based Learning in the classroom. This list should be a starting place for information about problem-based learning. Also, this site includes examples of how teachers at Ford Middle School have integrated the use of technology and problem-based learning into the curriculum. Problem-Based Learning Design This site describes steps involved in designing problem-based Learning for the classroom.
back to top Collaborative/Cooperative Learning Collaborative/Cooperative learning is an instructional approach that uses small groups so that students work together to maximize their own and each other's learning.
Cooperative Learning In The Classroom: The Importance of a Collaborative Environment for Computer-Based Education Cooperative behavior of students playing an educational computer game was investigated. The combination of gender and whether one or two computers were present significantly affected the level of achievement as measured by the number of puzzles completed in the game. Female/Female pairs playing on two computers, on average, completed less puzzles than any other pairs in any other condition. Differences were also observed for gender pairs sharing control of the mouse while playing on a single computer. Male/Male pairs had a higher number and percentage of refusals to give up control of the mouse. Research on Cooperative Learning and Achievement: What We Know, What We Need to Know This research offers Four Major Theoretical Perspectives on Cooperative Learning and Achievement: Motivational Perspectives, Social Cohesion Perspectives, Cognitive Perspectives, Developmental Perspectives and Cognitive Elaboration Perspectives.
Project-based learning is a comprehensive approach to classroom learning designed to engage student investigation of authentic problems, including an in-depth study of a topic worth learning.
Project-Based Instruction in Mathematics for the Liberal Arts The purpose of this web site is to provide projects and resources for instructors and students who wish to teach and learn college mathematics or post-algebra high school mathematics via project-based instruction.
back to top Service Learning Service learning is an instructional method that combines community service with a structured school-based opportunity for reflection about that service, emphasizing the connections between service experiences and academic learning.
Community Based Learning CBL works with businesses and social service organizations to provide students with internships in the community as a part of their academic experience. CBL provides the opportunity for faculty interested in K-12 education to participate in school reform and curriculum development discussions. Community-Based Learning: A Foundation for Meaningful Educational Reform This topical synthesis summarizes what we have learned over the past 20 years about various community-based learning programs and describes how community-based learning can serve as an important contribution to educational reform in the future.
back to top Work-Based Learning Work-based learning is an instructional approach in which students use the context of the workplace to learn content of school-based courses and how that content is used in the workplace.
Work-Based Learning A report on educators in the workplace. This page consists of feedback on summer educator externships. The externships provided teachers an opportunity to see what is really happening in business/industry so they could then adjust their curriculum as necessary. In turn, this will help students to become more excited about career opportunities thus spurring more interest in job shadowing and then specific training to qualify for particular occupations of interest.
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The Department of Mathematics Education University of Georgia ©2001