New School
Mathematics Curriculum Recommendations
Prepared by Denise K. Henry May, 2009
Henry/ED 795A Spring 2009: Product Report
1
Table of Contents
Executive Summary .......................................................................................................................3 Introduction ..................................................................................................................................4 School Accountability ....................................................................................................................4 Opportunity ..................................................................................................................................5
Analyses
Performance Analysis ............................................................................... 6 Cause Analysis ...................................................................................... 8 Needs Analysis ...................................................................................... 8 Environmental Scan ................................................................................ 10 Relevant Literature ...................................................................................................................... 12 Curriculum Pilot .......................................................................................................................... 13 Recommendation......................................................................................................................... 15 Limitations ................................................................................................................................. 15 Competency Development ............................................................................................................ 16 References .......................................................................................... 18
Appendices
Appendix A Survey Responses .................................................................... 19 Appendix B Observation Form..................................................................... 28 Appendix C Contract ................................................................................................................ 29 Appendix D Project Timeline .................................................................................................... 32
Henry/ED 795A Spring 2009: Product Report
2
Executive Summary
New School is a Community Day School located in Watsonville, California. The school’s faculty of 4 credentialed teachers delivers instruction to approximately 70 students in the Pajaro Valley Unified School District. New School’s student body possesses characteristics that place them in a high-risk category for academic failure: substance abuse, mental and physical abuse, gang affiliation, truancy, and defiance of authority. Most students lack proficiency with the English Language. High school students in the school’s district earn approximately 55 credits toward graduation each year. On average, New School students are deficient at least 55 credits for their grade level. The school launched 15 years ago in response to escalating gang violence in Watsonville. The founding principal developed a program centered on socio-emotional support for youth; academic instruction was regarded as a secondary need for the students. Curricula did not align directly with California content standards for high school students. Individual or group counseling and community building activities consumed most of the school day. American schools experienced increased accountability during the Bush administration with the passage of the No Child Left Behind Act (NCLB) in 2001.The Act requires states to assess basic skills to be given to all students in certain grades, if those states are to receive federal funding for schools. Many states across the country implemented high school exit examinations in response to legislation. California’s graduating class of 2006 was the first in the state required to achieve a passing score the California High School Exit Examination (CAHSEE) prior to being awarded a high school diploma. New School would soon feel the pressure imposed by NCLB to prepare students for standardized testing and exit examinations. The 2008-2009 school year is one of great transition for New School. The School’s founding principal announced his retirement and vacated his position during winter break. A substitute principal filled the position for two months until a permanent administrator joined the staff in February. Two months prior to the end of the year the assistant superintendent, to whom the principal directly reports, announced her retirement. The change in key administrative staff members provided the opportunity to examine the effectiveness of New School’s ability to meet district, state, and federal accountability measures for student achievement. The new principal requested that I analyze the effectiveness of the current mathematics curriculum then make recommendations to boost student achievement if necessary. This report contains an analysis of New School’s student performance in mathematics for the last three school years, reviews the current curricular resources, examines math classes at alternative schools in the same district, and makes specific curricular and pedagogical recommendations for New School.
Henry/ED 795A Spring 2009: Product Report
3
Introduction
New School, a Community Day High School located in Watsonville, California, is in the process of redefining its goals for students. The school, founded to offer intensive socio-emotional support and an accelerated credit recovery program, has grown from 20 students to 70 students over the last 15 years. For many years academic instruction took a back seat to counseling and therapeutic interventions. In January 2009, the founding principal retired. The new leadership determines it necessary to align academic instruction with high school content standards. In conjunction with this decision, the school’s new administration requested my assistance to revitalize the mathematics curriculum. This report centers on mathematics curriculum and classroom supports for the high-risk students attending New School. It is necessary to obtain a clear picture of the school and its population prior to making curricular recommendations. New School, the sole Community Day School (CDS) in the Pajaro Valley Unified School District (PVUSD), is unique among the districts alternative. In a sense, a CDS functions like a small business; it receives funding directly from the state and contracts PVUSD for business services and credentialed staffing needs. The principal hires non-credentialed instructors for elective classes and counselors herself. The autonomy offered through the CDS allows New School to offer unique experiences to students such as a class that counts toward Fine Art credit facilitated by an art therapist. Another major difference between a CDS and an alternative school is the number of hours CDS students are required to attend each day. CDS students are required to attend 360 instructional minutes per day; alternative school students often attend only 240. New School students are not “at-risk” of dropping out of school; they are “high-risk” students who require intensive support to complete high school. Many are classified as English Language Learners (ELL). Additionally, the students are far behind their graduating class’ expectations for earned credits. Some are under expulsion contracts, on probation, struggle with substance abuse, or experience gangrelated violence daily. Curriculum addressing foundational learning gaps and pedagogy that develops study skills in an exceptionally supportive environment is critical to the academic success of New School students. Varieties of analyses are necessary to zero in on curricular elements that support the high-risk students attending New School.
School Accountability
Curricular elements affect several stakeholders. Students and teachers feel the daily effects while administrators and district personnel may focus on the curriculum only during the creation of reports that communicate student achievement. Although each stakeholder’s measure of student achievement differs, Henry/ED 795A Spring 2009: Product Report
4
all stakeholders ultimately must meet achievement standards outlined in the federal No Child Left Behind (NCLB) legislation. NCLB legislation requires 100% of students attending publically funded schools to meet state standards in English language arts and mathematics by the year 2014. Each year, schools are evaluated on their ability to make “adequate yearly progress” (AYP) toward meeting that goal. New School will meet AYP if: At least 23.7% and 23% of student’s California High School Exit Examination (CAHSEE) scores fall in the “proficient” range in mathematics and English Language Arts respectively. At least 95% of enrolled students take designated state tests. Graduation rates rise to 82.9% or above. If the school falls into “Program Improvement” (PI) status, then graduation rates must rise .01 or .02 for fist and second-year PI status respectively. Academic Performance Index (API) growth is at least 590 or shows at least one point growth at the time of reporting. API uses student’s California Standardized Test (CST) and CAHSEE results to calculate learning gains. PVUSD communicates three goals that directly relate to curriculum: 1. All students will meet or exceed API growth targets and expectations for AYP.
2. All curriculums will be standards-based, designed in collaboration with teachers, consistent across the district, designed to produce results that will challenge each student at his or her academic level. 3. Implement procedures to ensure that all students of the class of 2008 will have passed the CAHSEE, including appropriate early alters to students and their parents, intervention steps, and documentation of services offered and those accepted. New School’s School Accountability Report Card (SARC) includes AYP and API data. In the last two school years, 2006-2007 and 2007-2008, the school did not meet AYP goals. Clearly, a mathematics curriculum aligned to federal and district expectations and outcomes are a necessity for New School. It is not clear whether New School will fall into program improvement status once this year’s test standardized results are published.
Opportunity
In August 2008, the first math teacher credentialed in mathematics joined the faculty. New School’s founding principal and his supervisor at the district announced their retirements effective December 2008 and June 2009 respectively. The change in teaching and administrative staff brings a shift in the focus of the school from a “social and emotional problems first, academics second” to place equal emphasis on academic performance and student’s non-academic issues. The new leadership and current faculty are Henry/ED 795A Spring 2009: Product Report 5
working together to redefine the school’s mission and vision. The academic program’s curriculum and resources for the 2009-2010 school year are under review as well. The new principal requests a recommendation for curricular elements and classroom supports appropriate for New School mathematics courses. It is important to note that replacing a familiar curriculum with an entirely new one can be met with resistance from teachers or administrators. As a school’s culture evolves, individuals who invest time and energy to develop processes, procedures, and curricula may feel a personal connection to existing elements. The new staff holds no emotional connection to the current curriculum and is clearly focused on supporting student’s content mastery of high school level concepts and the achievement of a passing score on the CAHSEE.
Analyses
A performance analysis revealed the disparity between district, state, and federal student expectations and student performance. A cause analysis identifies specific constraints imposed on learning by current teaching practices, the school environment, and current curriculum. Resources students require to meet expectations emerged through needs analysis.
Type of Analysis
Performance
Issues to Explore
Student expectations vs. Student performance
Outcomes
Supports curriculum and pedagogy recommendations Delineates environmental issues from student issues then recommends the type of curriculum necessary
Cause
Constraints to student achievement
Environmental Scan
Mathematics instruction at other sites
Curricular alignment with parallel sites & best practices to mirror at new school
Performance Analysis Academic intervention was not a focus for New School in previous years and the school did not track student’s academic growth internally. The only achievement data in existence is the standardized test scores published by the district and state. California student’s standardized tests scores fall on a continuum ranging from “Far Below Basic” to “Advanced”. The percentage of New School student scores falling below “Proficient” for the past three school years appear in the table below. Henry/ED 795A Spring 2009: Product Report 6
2005-2006
Test Below/Far Below Basic 50% Basic
2006-2007
Below/Far Below Basic NT* Basic
2007-2008
Below/Far Below Basic 100% Basic
Alg. 1, Grade 9
50%
NT*
0%
Alg. 1, Grade 10
67%
33%
NT*
NT*
50%
50%
Alg. 1, Grade 11
NT*
NT*
50%
50%
100%
0%
General Math, Grade 9 Geometry
100% NT*
0% NT*
67% 100%
33% 0%
71% NT*
29% NT*
* NT = Not tested this reporting year.
Each year since 2006, at least 50% of students do not demonstrate proficiency on standardized tests. A noteworthy effect on standardized testing is student motivation. The test proctor reports mixed effort among students during the test. Some appear to “take the test seriously”, while others fill in bubbles without attempting the questions. The analysis of achievement data does not delve into the effect of student motivation on reported scores.
Henry/ED 795A Spring 2009: Product Report
7
Cause Analysis Several factors influence student’s mathematics achievement at New School. The cause analysis delineates personal and environmental factors.
Skills Learning Strategies
Students lack skills to organize learning: Organization Metacognition Note-taking Self-review Self-regulating behaviors underdeveloped
Knowledge Prior Knowledge
Far, wide, and varying knowledge gaps: Basic computational skills Concepts do not “connect” to each other Language barriers
Motivation Desire to Learn
Learning is not a priority: Undervalued and/or unsupported at home Little to no peer value Effort to learn viewed as a “hassle”
Environment School & Classroom
Environment in transition: Credit and grade procedure in development historical lack of academic focus Achievement not tied to credit granting structure
Needs Analysis Mathematics course typically organize around a set of standards encompassing the district and state learning expectations for students. In 2004, New School’s previous administrator felt the students were better served through a set of teacher-developed curriculum maps. The maps delineated basic skills, starting at 2nd grade level. The map did not align content to California content standards or high school level textbooks. The administrator selected the manipulatives-based curriculum, Moving with Math, which aligns with the teacher-developed content map. In my role as math teacher at New School, I examined the Moving with Math curriculum at the beginning of the school year and found it insufficient for student needs. First, the student to text ratio is not 1:1 as mandated by the California Department of Education. The texts cover content from elementary grades through 7th grade. Omitting 8th grade material from the curriculum neglects pre-algebra concept development. The texts themselves are also problematic. Moving with Math neglects the development of math vocabulary, a critical feature of math texts, especially for implementation with English language learners. Finally, the texts, printed in black and white, display graphics aimed at an elementary school-age audience.
Henry/ED 795A Spring 2009: Product Report
8
New School’s previous math teachers did not hold mathematics credentials and had not completed training specific to mathematics instruction. Former teachers could not be located for interview, and no information is available at the school to speak to their implementation strategies. The sole measures of student data available, published test scores, indicate that the Moving with Math curriculum does not support standardized test achievement. It is certain that New School’s learning expectations and curricular resources neglected alignment with the standards that measure the high school student performance.
Henry/ED 795A Spring 2009: Product Report
9
Environmental Scan Under previous leadership, New School’s faculty spent many years working in instructional isolation from their colleagues across the district. The newly hired principal requested an exploration of alternative sites within the district and Community Day Schools in her personal network to “get a feel for what they are doing.” Several math teachers in the state of California representing different alternative educational settings completed a survey and participated in personal interviews in May 2009. See Appendix A for delineated survey responses.
Focus Area Average number of years teaching math in an alternative setting Content taught Quarter 1 Moving with Math 78% Geometry 67% Algebra 1 Quarter 2 Algebra 1 and Geometry 56% CAHSEE prep 44% Grade 6 - 9 content Quarter 3 & 4 Algebra 1 and Pre-Algebra 33% Grade K – 5 content 5 4 New School Survey Respondents
Curriculum resources
Moving with Math
89% use mainstream high school textbooks (Glencoe, Prentice Hall, etc.)
UCLA Algebra Readiness
Geometry and Algebra 1 Implementation strategies Blend of whole class instruction and small group instruction 44% facilitate individualized learning No individual learning plans developed Student demographics 72% Classified as ELL plans 17% Classified as ELL 67% provide whole class instruction
50% + Performing below grade level
42% Performing below grade level
Assessment and grading practices are of interest as New School works to establish new credit granting procedures in classrooms. Similarities emerge among the instruments teachers use to assess learning gains and the products used to assign a grade to students. An overwhelming majority, 88%, rely
Henry/ED 795A Spring 2009: Product Report
10
on self-developed instruments. The next highest reported assessment indicators are daily assignments (55%) and informal observations (33%). Teacher’s grade calculations affect the rate at which credits accumulate. Grading trends emerging from the survey yield the following: Nearly every respondent includes summative assessments, classwork, and homework in his or her final grade calculation Each teachers calculate grades as a weighted average
Attendance, Portfolio, and Projects
16%
Summative Classwork Assessment
16%
52%
Average Weighted
Homework 16%
Grade Calculation
New School’s principal scheduled observations of math classes at two alternative schools in the district. Both teachers submitted a survey, prompting me to focus qualitative data collection (see Appendix B). The observation focused on gleaning best practices from the teachers that may increase motivation and learning among New School students. The first school, Academic Vocational Charter Institute (AVCI), is a charter school with a population similar to New Schools. The teacher participates in a consortium of math teachers working to develop peer-evaluated instructional content. He implements researched-based instructional strategies proven effective with non-traditional students. I observed a Geometry and an Algebra 1 class. I left with the overall impression that the learning environment contributes to student learning.
Henry/ED 795A Spring 2009: Product Report
11
Key points from the AVCI observation: Student materials are maintained in a portfolio that students leave in the classroom Curricular elements are pulled from high-school level textbooks and released standardized test questions. Books are not issued to students. The majority of instructional time is devoted to whole-class, guided practice No homework is assigned Summative assessments are multiple choice response tests. The teacher eliminates two of the four answer choices on the instrument by crossing out two answer choices The teacher strives to build community and develop characteristics leading to academic and personal success The second visit was to Renaissance High School (RHS). New School’s founding principal taught at RHS for several years. He mirrored RHS’s organizational and instructional procedures when he designed New School. Teachers at both schools are required to develop and maintain academic plans, track credits earned, and manage discipline for a group of students. The teacher shared displeasure with the additional roles and felt they detract from his focus on classroom instruction.
Key points from the AVCI observation: Small class size, no more than 15 students per class The curriculums, Moving with Math, supplemented by copious amounts of teacher created “packets” provide worked examples for key concepts. Instruction is delivered as a blend of whole-group and individualized learning plans Computer-based instruction is used to address individual learning gaps, however, students worked only 10 minutes in the program.
Relevant Literature
Research by Gamoran, Porter, Smithson and White (1997) examines the achievement of students enrolled in California’s Math A course. Math A, viewed as a transitional course, bridges middle school and high school content. The authors find that low-income, low-achieving youth make moderate learning gains in transitional courses. Gamoran et al. (1997) report that students make the largest learning gains when exposed to rigorous mathematical content using a range of cognitive strategies. Their findings support the selection and implementation of math curriculum that is both transitional and rigorous. Henry/ED 795A Spring 2009: Product Report
12
A particularly relevant theory applicable to increasing student achievement is Cognitive Load Theory, Clark, Nguyen, and Sweller (2006) offer several principles that offer guidance in the review of an appropriate curriculum for New School students. Following is a checklist to evaluate curricular resources based on cognitive load principles.
Factor
Prior Knowledge
Relevance to New School
Few New School students demonstrate proficiency with concepts and possess little content-specific prior knowledge.
Curricular Element
Provide worked and faded examples, directive lesson design, and concise text. Present formulas, theorems, and postulates separately from worked and faded examples.
Content Complexity
Math proves to be a complex subject area for most students.
Extraneous Load
Many texts increase extraneous load in an attempt to make math more interesting to students.
Use diagrams in place of text when possible. Cuing is used to draw attention to important information, scaffold and chunk lessons, pace lessons according to learner’s readiness.
Content Transfer
Far transfer is required to achieve a passing score on standardized tests and the CAHSEE.
Provide step-by-step completion problem examples, present diverse examples and “what if” scenarios to extend thought beyond current case, develop metacognition, provide sufficient learning time.
Curriculum Pilot
After careful review of New School student’s unique needs, thoughtful consideration of other alternative high school math teacher’s resources and strategies, and review of relevant literature, a clear picture of the types of resources and pedagogical supports emerged. The process to locate curricular resources began. New School’s principal arranged a meeting with the district’s Mathematics Coordinator who has extensive knowledge of approved resources. New School’s principal, and I explained curricular features we desired. The district coordinator offered to provide a resource developed by the University of California, Los Angeles (UCLA) that would serve as a transitional resource. The Math Coordinator Henry/ED 795A Spring 2009: Product Report
13
communicated promising information about the curriculum; weekly, UCLA offers weekly (online) trainings, pilot schools report boosts in test scores, and a surplus of free materials are on hand. After review of a curriculum sample, we decided to pilot the materials with three classes at New School. In January 2009 I located a set of discarded McDougal Little Algebra 1 textbooks at the school. I requested and received student workbooks and a CD Rom containing printable supplementary resources to use in an Algebra 1 course pilot. The consumable workbooks scaffold learning and provide vocabulary practice. Supplementary resources offer numerous printable worksheets and assessments, both formative and summative. The principal and I decided to continue piloting through the fourth quarter with the cohort of students. I am in the 5th week of the UCLA pilot and the 15th week of the Algebra 1 pilot. I am pleased with both the UCLA and McDougal Little curriculum resources. Both publishers’ materials scaffold lessons, provide each student with their own consumable resources, and include vocabulary development. I am familiar with the traditional structure of the McDougal Little resources, no implementation support is required. The format of the UCLA course is new. The online training and teacher resources are sufficient to support a smooth implementation. Additionally, the online trainings provide a valuable opportunity to collaborate with other math teachers, an opportunity that does not exist at New School. New school students did not contribute to data collection surrounding their perspective on the pilot curriculums due to issues associated with data collection from minors in a public school setting. Observations of students working through the UCLA lessons in class yield a positive impression of the resources. Students who once complained that they “need to learn second grade math” are working through content several grade levels above their perceived capabilities. Students engage with the content in class, ask thoughtful questions, and display positive affect while working. When asked if students communicate their feelings surrounding the UCLA curriculum, the principal reports fewer student complaints about the complexity of the math content. The students are not aware that that the complexity is greater in the UCLA curriculum than the Moving with Math curriculum because the UCLA curriculum’s design adheres instructional design and learning theories that offer greater cognitive supports. Observations of students working through the McDougal Little are promising. Students are exposed to the same level of rigor offered in a traditional high school, however, the pacing is decelerated. Students exhibit a “stick with it” attitude toward the work, participate in academic discussion with peers, and submit completed assignments. I supplement lessons with online manipulatives, poster projects, and games. Students who were one thought “incapable of learning algebra” are making progress in the course.
Henry/ED 795A Spring 2009: Product Report
14
The principal observed one lesson implementation for each publisher’s curriculum. Feedback on the Algebra 1 curriculum was positive, however, she has not provided specific feedback from the UCLA curriculum observation to date.
Recommendation
The recommendations in this report derive from analyses, online survey, interviews and observations, informal pilot of curriculum, and New School’s emerging vision for student success. The recommendations focus on the instruction of students in a transitional math course and Algebra 1. I recommend that New School implement the UCLA Intro to Algebra and McDougal Little Algebra 1curriculum in the 2009-2010 school year. New School’s math teacher should provide a placement test for the courses and develop a pacing guide prior to implementation. New School will develop revised grading policies and credit granting procedures, which further support implementation efforts. The UCLA curriculum will require implementation support, best provided through weekly online trainings. An experienced math teacher should be familiar with the format of the Algebra 1 resources, thus eliminating the need for implementation support with this course. It is imperative for the math teacher to implement methods to monitor student progress rather than relying on standardized test outcomes to determine student skill levels. Longitudinal data collection is necessary to determine the effect of either curriculum on students’ standardized test scores. I also recommend that New School develop its own set of teaching best practices that are both subject specific and applicable in every classroom. New School should also continue to employ math teachers who hold credentials in their subject area. The math teacher should seek opportunities to network and collaborate with other math teachers in the district and beyond its boundaries.
Limitations
Considerable limitations of this project are the lack of internal student achievement data, limited comparative data available from Community Day Schools in California, and the organizational uncertainty of New School itself. New School’s lack of student achievement data leaves one to rely on published data to analyze student’s learning gains. California does not publish CAHSEE scores for schools if the number of test-takers is lower than 50 to maintain student confidentiality. The number of test-takers is always less than 50 at New School. Given the importance of CAHSEE preparation for the students attending New School, the curriculum exploration should continue so that an appropriate exam prep curriculum can be found. Henry/ED 795A Spring 2009: Product Report 15
Additionally, the data collected through survey and interview does not completely align with the implementing site. The sample population, provided by the principal, is not entirely comprised of Community Day Schools. The classroom observations, arranged on short notice by the principal, lacked a specific plan for data collection. As mentioned earlier, New School is reorganizing process and procedures while working to define a vision and goal for the school. It is difficult to recommend curricular supports in the absence of a clear understanding of the school. Extremely problematic is the looming question of whether or not to return students to traditional settings after students recover a sufficient number of credits. It is impossible to articulate a full mathematics curriculum for the school at this time. Another limitation is the lack of time to complete and evaluate curriculum pilots. No quantitative data will emerge prior to delivery of this report. A full evaluation of the effectiveness of a particular curricular element, i.e. pedagogy or texts, requires longitudinal evaluation since learning gains are best represented as trends vs. discrete moments in time. Teaching strategies that best support New School’s population require further, formal investigation. Finally, I am both the math teacher and the consultant in this project. Although I strive to maintain objectivity in my review of the school and its processes, my personal feelings may affect the level of neutrality in my reporting. I am an experienced math teacher in alternative settings and made every effort to ensure that my recommendations are based on my education, training, and knowledge gained in recent graduate coursework rather than personal experiences.
Competency Development
This project offered several opportunities to develop competency in the development and evaluation of products that enhance student performance and learning in mathematics. Core competencies in terms of the Educational Technology Department’s expectations evident in this project are: Values Pragmatism o Recommendations in the report are realistic for New School Data-based decision making o Data collection and analysis informed the recommendation Eclecticism o Numerous sources inform the curriculum recommendation Commitment to Learning o Project alignment with my personal quest to improve mathematics instruction for highrisk and at-risk students using research and data to guide efforts Skills
Henry/ED 795A Spring 2009: Product Report
16
Technical o Employed online data collection Cognitive o Analyzed and synthesized data o Inductive (observational) and deductive (data-based) reasoning inform curriculum selection Interpersonal Communication o Written - Held weekly meeting with principal via email o Oral – Communicated with colleagues during interview Intrapersonal Communication o Identified personal weakness which may affect reporting Knowledge Principles, Theories, and Models o Applied cognitive load theory to curriculum selection o Garnered best practice models from classrooms which may be implemented at New School Processes o Gained an incredible amount of knowledge into the curriculum selection and adoption process at schools in my district o Developed skills necessary to apply research-based criteria to curriculum adoptions Systems o Gained a deeper understanding of the high school system in my district
Henry/ED 795A Spring 2009: Product Report
17
References
Clark, R.C, Nguyen, F., & Sweller, J. (2006). Efficiency in Learning, Evidence –Based Guidelines to Manage Cognitive Load. San Francisco: Pfeiffer.
Gamoran, A, Porter, A.C., Smithson, J. & White, P.A. (1997). Upgrading High School Mathematics Instruction: Improving Learning Opportunities for Low-Achieving, Low-Income Youth. American Educational Research Association., Retrieved on April 19, 2009, from American Educational Research Association.
Pajaro Valley Unified School District. (n.d.) New School Facts and Accountability Information. Retrieved April 17, 2000, from http://pajarovalley.schoolwisepress.com/home/site.aspx?entity=24121&year=2008&locale=en-US
San Diego Unified School District. (2006). San Diego Unified School District Fact Sheet. Retrieved April 17, 2009, from http://www.sandi.net/comm/factsheets/ayp.pdf.
Henry/ED 795A Spring 2009: Product Report
18
Appendix A Survey Responses
Textbook Grade K - 5 Grade 6 - 9 Glencoe Algebra Concepts and Applications CAHSEE Preparation Algebra 1 Geometry Other (please specify)
Unknown
Glencoe Algebra I
Glencoe Geometry
Glencoe
Glencoe
Glencoe PreAlgebra
Glencoe Geometry Glencoe Algebra II and Houghton Mifflin Precalculus
Glencoe Geometry Glencoe Geometry, Glencoe Geometry: Concepts and Applications Glencoe, AGS, Teaching Textbook Moving with Math, Glencoe study Guide and Intervention
Precalculus with limits: a graphing approache by Houghlin Mifflen
No Text
Prentice Hall Math
Princeton Review
Moving with Math other supplemental other supplemental
Ca review
Other
Other
California Algebra I, published by CGP Education, Copyrighted 2007
Glencoe Geometry, published by Glencoe, Copyrighted around 1998
Henry/ED 795A Spring 2009: Product Report
19
Instructional Software Grade K - 5 Accelerated Math Algebra 1 Accelerated Math Geometry Accelerated Math Other/Additional Software
Software + and Open-Ended Response
Accelerated Math Weak: Problems are often too hard, objectives do not follow standards, takes much class time, Strong: direct feedback for students, homework has to get done, students work harder. My middle school students are required to complete 30 minutes of Compass Learning math content work each week.
Accelerated Math
Accelerated Math
Compass Learning
Nutshell Math
Strength is that it is directly aligned with Glencoe.
none
not applicable
I use online math tutorial with Prentice Hall. I also use Teaching Textbook.
I like the online Prentice Hall whiteboard tutorials. I wish they went into more topics.
Plato
The strengths are readability and prescriptions. The weakness is the time allocated each day is limited. It is not a quick learning tool. Sometimes it could be hard to follow Too hard Doesn't give too much practice
Plato
Henry/ED 795A Spring 2009: Product Report
I had used Accelerated Math Enterprise, but it turned out all educational research that was written about it was for the stand alone (old) version. Since that was replaced by the current version that is a part of Renaissance Place, it is virtually useles
20
Technology Teachers Rely Upon and the Frequency of Use
Student Computers Integral to everyday practice Student Computers Fundamentally part of my everyday practice Student Computers Generally part of my everyday practice Student Computers Not part of my everyday practice
X X X X X X X X 5
0
0
3
Digital/LCD Projector Integral to everyday practice
Digital/LCD Projector Digital/LCD Projector Digital/LCD Projector Fundamentally part Generally part of my Not part of my of my everyday everyday practice everyday practice practice
X X X X X X 1 5
0
X 1
Printer Integral to everyday practice
X X
Printer Fundamentally part of my everyday practice
Printer Generally part of my everyday practice
Printer Not part of my everyday practice
X X X X X 2 1 0
X 5
Henry/ED 795A Spring 2009: Product Report
21
Student Hand-Held Response System Integral to everyday practice
Student Hand-Held Response System Fundamentally part of my everyday practice
Student Hand-Held Response System Generally part of my everyday practice
Student Hand-Held Response System Not part of my everyday practice
0
0
0
X X X X X X X X X 9
Henry/ED 795A Spring 2009: Product Report
22
Document Camera Integral to everyday practice
Document Camera Fundamentally part of my everyday practice
Document Camera Generally part of my everyday practice
Document Camera Not part of my everyday practice
X X X X X X X 7
0
0
0
Interactive Whiteboard Integral to everyday practice
Interactive Whiteboard Fundamentally part of my everyday practice
Interactive Whiteboard Generally part of my everyday practice
Interactive Whiteboard Not part of my everyday practice
X X X X X X 4
1
0
1
Scanner Integral to everyday practice
Scanner Fundamentally part of my everyday practice
Scanner Generally part of my everyday practice
Scanner Not part of my everyday practice
X X X X X X X 5
1
0
1
Henry/ED 795A Spring 2009: Product Report
23
How is your class organized for learning? Check the two or three options that best depict your situation. Individual Learning Plans (Students Working Independently on Different Assignments Simultaneously)
Whole-Class Instruction (Traditional Class Arrangement)
Blend of Whole Class and Individualized Learning Plans
Blend of Whole Class Instruction, Computer-Based Individualized Instruction Learning Plans & Computer-Based Instruction
Other (please specify)
X
X
X
X X X X X Class blog to discuss math when we are not in the classroom.
X
X
X
X
X
X
X
X
X
X 6
4
4
1
3
Henry/ED 795A Spring 2009: Product Report
24
Please describe the typical sequence of instructional events in your classroom.
ELL accomodation strategies
Open-Ended Response
Open-Ended Response
Warm-Up, homework review, lesson lecture, practice problems, more homework. Review, going over homework, teaching new material, students practice new material on the board, assign homework. WHole class opener, small group work for the rest of the period.
This is a non-issue. use of dictionary, translating into Spanish, help from other students.
Whole class completes an opener, then students receive an overview of the topic. Students then choose either independent work or a more detailed guided practice session. Finally, all students work on individual assignments for the remainder of class. not applicable I teach the remedial high school math classes - at least oversee them. I'd have to say that about 50% pass my math Completely independent learning with classes. I have many low one to one tutoring. achieving students. SADAI practices are used. There are word walls. Student are dynamically grouped. Tablet marker boards have been most helpful. Math dictionaries and There is a whole class assignment each glossaries as well as day. Then the students work on daily notes are also individualized packets for areas of provided to each growth that are needed. Some students student. Students also utilize the computer software. write in a math jou SADAIE methods, differentiated instruction. Use a lot of visual cues. 1) a warm-up I call REM, where students 3-5 cues is best. For write down what I think are the correct example, verbally, hand preconceptions necessary to the success gestures, writing on the of the lesson. 2) students take notes board, and close-up 3) students do guided practice inspection of work. Every day is different depending on students' needs and mastery.
Henry/ED 795A Spring 2009: Product Report
25
On which instruments do you rely to assess your student's learning gains? Rank choices from most often (1) to leas often (7) used. Most often used (1) Hard copy assessments from publishers Hard copy teacher-developed assessments Software or online assessments from publishers Software or online teacherdeveloped assessments Student portfolios Daily assignments My own, informal observations Least Often Used (7)
2
3
4
5
6
Response Count
20.0% 44.4% 0.0% 0.0% 20.0% 28.6% 0.0%
0.0% 22.2% 0.0% 14.3% 0.0% 28.6% 33.3%
20.0% 22.2% 20.0% 0.0% 0.0% 14.3% 16.7%
20.0% 0.0% 20.0% 0.0% 20.0% 14.3% 16.7%
20.0% 0.0% 40.0% 14.3% 20.0% 14.3% 0.0%
0.0% 11.1% 20.0% 42.9% 0.0% 0.0% 16.7%
20.0% 0.0% 0.0% 28.6% 40.0% 0.0% 16.7%
5 9 5 7 5 7 6
Henry/ED 795A Spring 2009: Product Report
26
Which of the choices below contribute to the credit students earn in your math class? Attendance 0% Classwork 10% 20% 15% 0% 10% 25% 25% 25% 14% Homework 10% 30% 30% 25% 40% 30% 15% 0% 20% Summative Assessments 80% 50% 50% 75% 50% 50% 15% 25% 44% Projects Portfolios Other
5% 0% 0% 70% 25% 3% 20% 25% 5% 5% 9%
0%
Average
10% 10% 25% 5%
Henry/ED 795A Spring 2009: Product Report
27
Appendix B Observation Form
Teacher _______________________________ Date:____________________ School________________________________ Flow of class
What did the teacher do?
What did the students do?
Review student work
Behavior management
Classroom arrangement
Notes
Henry/ED 795A Spring 2009: Product Report
28
Appendix C Contract
New School Mathematics Curriculum Recommendation
Consulting Contract February 2009
OVERVIEW
The following document establishes a contract between, New School, the client, and Denise K. Henry, the consultant. This contract includes information on the consultant’s strategy leading to mathematics curriculum recommendations. This project is to be completed as partial fulfillment for San Diego State University’s graduate class, “Seminar in Educational Technology.” This document contains the project summary and goals, services and methods offered to complete the project, and deliverables created throughout the duration of the project.
PARTIES
Denise K. Henry, the consultant, will provide the services and deliverables described below for New School, the client, represented by Victoria Sorensen, principal.
PROJECT SUMMARY & GOALS
The consultant will recommend a research-based mathematics curriculum to support the nontraditional needs of a New School student. The curriculum will: Allow for chunking into discrete units of study Addresses student learning gaps in foundational skills Accommodate students in multi grade-level classrooms Capitalize on digital technologies to supplement learning Support ELL students Meet Williams case criteria Henry/ED 795A Spring 2009: Product Report
29
SERVICES & METHODS
The consultant will perform the following tasks: Review literature relevant to at-risk high school student s’ achievement in mathematics Conduct a Performance Analysis to examine strengths and weaknesses in current curriculum and its implementation Conduct a Cause Analysis to identify performance constraints in knowledge, the environment, and incentives to succeed Conduct an Environmental Scan to garner insight into implementation at other sites Furthermore, the client and consultant agree that weekly meetings be held via telephone, or in person at a location to be confirmed via email.
DELIVERABLES
The consultant will provide New School with the following materials: Analysis: This will include a review of current literature on at-risk populations’ achievement in mathematics. Design Document: This will include specific curriculum resources, teaching strategies, and environmental supports to increase achievement.
ROLES
The consultant’s responsibilities are as follows: Maintain proactive and open communication to ensure a positive outcome, Schedule meetings and distribute agendas and follow-up meeting minutes, Seek approval from Victoria Sorensen for all final decisions, and Adhere to the confidentiality agreement as stated later in this document. The client’s responsibilities are as follows: Maintain communication by delivering materials and approvals in a timely manner.
Henry/ED 795A Spring 2009: Product Report
30
Ensure Pajaro Valley Unified Schools staff members are willing to assist the consultant in achieving the goals outlined in this contract. Provide access to people and information necessary to complete the defined deliverables.
TIMEFRAME
The consultant will follow a timeline including milestone dates based on the length of the semester (January 22, 2009 – May 20, 2009) and the academic requirement of 75 hours of work. The following is a tentative schedule for transfer of deliverables: Week of April 13, 2009: Week of May 20, 2009: Analysis Design Document Outlining Curriculum Recommendations
CONFIDENTIALITY & RIGHTS
The consultant understands the requirement that student data remain confidential and guarantees that all information collected will be kept confidential.
STATEMENT OF AGREEMENT
We, the undersigned, do hereby agree to the terms and conditions as outlined in the preceding document. As representatives, we agree to abide by these terms and conditions.
Both parties enter into this agreement on February 23, 2006.
Client:
Consultant:
Victoria Sorensen Victoria Sorensen, Principal New School
Denise K. Henry Denise K. Henry, Consultant COMETeer Creations
Henry/ED 795A Spring 2009: Product Report
31
Appendix D Project Timeline
Henry/ED 795A Spring 2009: Product Report
32