Instruction within a Classroom

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					                                            Standard-Based Math   Page 1


                Standards-Based Mathematics Curricula

                            Jonette Burns

         TET 763 – Applied Research in Education and Training

                      University of South Dakota
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                            Standards-Based Mathematics Curricula


       Reform mathematics has been an interesting topic facing school districts in education

today. There has been a great deal of discussion regarding children in the United States not

scoring comparable to students in other countries on high stakes tests. “American children have

more trouble learning math than any other subject” (Cambridge, 2005). Traditional

mathematics, teachers demonstrating an algorithm while students practice the concept by

completing a series of problems, has come under scrutiny. The National Council of Teachers of

Mathematics (NCTM) released the first Standards document in 1989 followed by a revised

document in 2000. The revision, Principles and Standards in School Mathematics, “emphasizes

the development of conceptual understanding and reasoning” (Goldsmith, 1999). The focus of

mathematics in education has moved from direct instruction, drill and practice toward more

“active student engagement with mathematical ideas through collaborative investigations, hands-

on explorations, the use of multiple representations, and discussion and writing” (Goldsmith,

1999). Students actively involved in building their own mathematical understanding is referred

to as constructivism. This approach helps students gain a deeper understanding of mathematical

concepts. Many new approaches to secondary school mathematics are based on the NCTM


Research Questions

   1. How does the achievement of students using Standards-based mathematics curriculum
      materials compare with students using traditional mathematics curricula?

   2. What are important factors that contribute to the effectiveness of teachers in
      implementing standards-based mathematics curriculum in their classrooms?
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The Research

       When researching standards-based mathematics, there were many articles that focused on

the topic. Some were written by a combination of the same people and each article coincided

with each other. Although I am aware articles exist that oppose standard-based mathematics, the

articles I located on ProQuest supported the topic. These articles provided comparative studies

and research to refute the opposition.

       The article written by Trafton (2001) discussed the origination of standards-based

mathematics curricula. Further, the article describes six central characteristics of standards-

based mathematics curriculum materials. The first characteristic is a focus on core mathematics

for all students which incorporates a range of important mathematics. The second characteristic

refers to coherence so that the core ideas of the subject are highlighted and cause students to see

it as an integrated whole. “Standards-based materials promote coherence through an initial focus

on big ideas, with an emphasis on connections and links to related mathematical ideas and

applications” (Trafton, 2001). The third characteristic is that the “increased sophistication in the

way mathematical ideas are treated, together with the coherent development of mathematical

ideas, helps students toward deeper understanding” (Trafton, 2001). In-depth learning of

mathematical concepts is more likely to occur when the curriculum concentrates a few big ideas

and their interconnections and when teachers encourage their students to engage in these ideas.

The fourth characteristic of standards-based mathematics is that they help students make sense of

the subject. Promoting sense-making occurs when students are allowed to “create and use their

own ways of thinking to solve problems and having them share their thinking with other students

and the teacher” (Trafton, 2001). The fifth characteristic of these materials is that they engage

students physically and intellectually through problems and tasks. Through the curricula,
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problems and tasks that raise students’ curiosity are posed. “When a task is intriguing and poses

a challenge students are more likely to pursue a solution and explanation” (Trafton, 2001). The

final characteristic of standards-based instructional materials is that they motivate learning. A

good example is shown in the relationship between the rate of walking and the distance covered

which demonstrates that the faster one walks, the greater the distance one covers. This is shown

by the steepness (slope) through a graph and table of values. Slope emerges from many real-life

applications such as the steepness of a set of stairs or the steepness of a wheelchair ramp. “The

use of applications to contextualize mathematical study is an important characteristic of

standards-based materials” (Trafton, 2001). Instructional materials represent efforts to capture

the vision and essential elements of the NCTM Standards.

       The next article conducted “a comparative study on the effects of the Core-Plus

Mathematics Project (CPMP) curriculum and more conventional curricula on growth of student

understanding, skill, and problem-solving ability in algebra” (Huntley, 2000). These changes

would include implementing curriculum that contains an extensive core of mathematics that is

useful to all students, an emphasis on student-centered instruction that engages students in

exploration through collaborative work, and assessment through various strategies. The Core-

Plus Mathematics Project was funded by the National Science Foundation in 1992 to construct a

3-year integrated mathematics curriculum for all students plus a 4th year course continuing the

preparation of students for college mathematics (Huntley, 2000). The CPMP curriculum is based

around the idea of making mathematics applicable to students. The topics within the curriculum

are intended to be accessible and engaging to all students, and lessons promote cooperative

learning.   They invited Course 3 teachers to participate in the comparative study of algebraic

reasoning. Six schools using CPMP accepted the invitation: two were in the Southeast, two in
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the Midwest, one in the South, and one in the Northwest. Following testing, the study examined

the mean scores between groups. The scores showed that the group using the Core-Plus

Mathematics scored higher on the administered test than students learning mathematics from a

traditional method. However, researchers determined a great deal of improvement needed in

algebraic reasoning, problem solving, and calculation.

       A third article discussed the top ten elements that must be in place to implement

standards-based mathematics curricula. In the transition class I recently took, I discovered that

the transition process is very difficult and one must go through the transition process to be

successful in a time of change. Change is difficult. According to Bay (1999), few kinds of

change are more challenging for teachers than changing the curriculum and the teaching

materials they use. Making a major curriculum change means facing new types of problems,

altered teaching methods, different forms of assessment, and questions from parents are likely to

increase. The first critical element of implementation is support from administration. Earlier

this year, our high school took an aggressive approach in investigating new mathematics

curricula. After we decided to research standards-based curricula, our principal fully supported

our decision and helped arrange for us to visit schools in Colorado that were implementing the

program for several years. Our department has expressed concern about having proper training

in the summer and during school to effectively implement the program. Again, our principal has

arranged three weeks of paid training and has ensured that we will have a math coach available

as an additional resource. This leads to the second critical element, opportunities to study. The

teachers in the article reported that “without the time to become really familiar with each of the

curricula and to discuss them with colleagues, they would not have developed the confidence to

try out a new curriculum at all” (Bay, 1999). The third critical element of implementation is
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sampling the curricula. This allows teachers to experiment with standards-based reform.

Sampling curricula permits teachers to adjust their teaching styles without being overwhelmed

by having to implement an entire program. The fourth element is interaction with experts. The

article states that teachers implementing a standards-based curriculum stress the “value of

observing a teacher using a standards-based curriculum in the classroom” (Bay, 1999). The

observation our math department conducted while in Colorado was very beneficial. We were

able to see the instructional methods and questioning techniques teachers used. Further, we

witnesses students taking ownership of various mathematics problems. One of the weeks

designated for training this summer will be held in Kalamazoo, Michigan. This is the

headquarters for the Core-Plus curriculum, which we adopted for next year. Therefore, we will

receive training from those who developed the curriculum and have experience teaching from it.

The sixth critical element of implementation is collaboration with colleagues. The article stated

that collaboration is critical to teachers because they need to learn what units others are using,

how they pace activities and units, how they manage their classroom, and how they handle

grading. Collaboration is probably the most critical feature in enabling change. For next year,

we will be implementing Course I for all incoming freshman. Each year we will implement

another course until all four courses are fully implemented. Our principal has ensured that all

teachers in the math department, with the exception of one, will teach at least one section of the

first course. He will also try to make sure that two teachers have common planning time. The

seventh critical element of implementation is incorporating new assessments. The article stated

that “teachers find that they have to invest a great deal of time in just becoming familiar with the

new forms of assessment” (Bay, 1999). In our math department, this is also a concern. I am

hoping that the training will provide suggestions and remedies so we are not spending hours on
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assessment techniques. The eighth critical element is communicating with parents. “To help

parents see that mathematics is much more than formulas and procedures, it is important to share

the positive outcomes of such interaction” (Bay-Williams, 2003). The article stated that

“engaging parents in a mathematics project or lesson from the new curriculum” (Bay, 1999) can

be a successful outcome of parent meetings. The ninth critical element of implementation is

helping students adjust. “It takes time for students to realize that these standards-based

mathematics curricula include a great deal of mathematics in addition to computation” (Bay,

2000). The elementary and middle school in our district is currently implementing standards-

based mathematics. Through the sixth grade, teachers have commented that students love the

mathematics and their understanding of mathematical concepts seems to be deeper than in

previous years. The seventh and eighth grade teachers both agree that this year has almost been

a train wreck. It has been very difficult to get students to do mathematics in a different manner.

Although our math department thought next year should be an easy transition due to the fact that

students will have a year of the standards-based math, we now realize that it will be crucial that

we help students to continue to adjust. The final critical element of implementation of standards-

based curricula is planning for transition. In the high school, we will wonder what skills and

concepts students should have when they begin their freshman year of Course I. Meeting with

the middle school to discuss plans for articulation across the grades would be the next step we

need to take. Supporting the implementation of standards-based mathematics curricula is crucial.

The ten elements in this article provide a useful picture of what is involved in supporting the

change to standards-based mathematics at any level.

       Another article provided a study that compared mathematics achievement of eighth

graders in three school districts in Missouri using standards-based mathematics with students
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who had similar prior mathematics achievement and family income levels in other districts.

“Achievement was measured using the mathematics portion of the Missouri Assessment

Program administered to all 8th graders in the state” (Reys, 2003). Significant differences in

achievement were identified where all of the significant differences reflected higher achievement

of students using standards-based materials. Students in each of the three districts using

standards-based materials “score higher in two content areas (data analysis and algebra), and

these differences were significant (Reys, 2003).


       In conclusion, there is considerable support for reform in traditional mathematics classes.

The articles agree that standards-based mathematics pushes students to think and discover how to

solve problems. A more rigorous environment is needed to allow students to develop skills and

conceptual depth. Curriculum must enable students to make sense of mathematics and to

recognize and value the power of their own mathematical thinking. The initial implementation

and notion of change will be difficult for teachers and students. However, if administration and

teachers carefully research, plan, develop on-going professional development opportunities, and

prepare for transition, students will develop a deeper and richer king of mathematical learning

for students.


       Throughout my master’s program, I have researched the topic of standards-based

mathematics quite a bit. It has interested me because our math department will be implementing

the Core-Plus curriculum next year. I have found an extensive amount of research dealing with

elementary and middle school students, but little on high school students. Quite a bit of this

research can be adapted to the high school, but further research at the high school level would be
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beneficial. For example, I think it would be interesting to research high school students who

have been taught mathematics from the traditional model as well as from the standards-based

model and compare their college entrance exam scores. Another recommendation is researching

the same type of students as they enter college. My curiosity stems from the fact that many

colleges remain traditional in their style of teaching. I am curious how high school students who

learned mathematics traditional versus standards-based perform in college mathematics classes.

One constraint of this type of research would be ensuring that the sample size is similar in

achievement prior to testing.
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Bay, J. M., Reys, B. J., & Reys, R. E. (1999). The top 10 elements that must be in place to

       implement standards-based mathematics curricula. Retrieved March 25, 2007 from

       ProQuest database.

Bay-Williams, J. M., & Meyer, M. R. (2003). Help! Parents and standards-based mathematics.

       Retrieved March 20, 2007 from ProQuest database.

Cambridge College. (2002). Mathematics Specialist.      Retrieved November, 1, 2005 from

Goldsmith, L. T., & Mark, J. (1999). What is a standards-based mathematics curriculum?

       Retrieved March 25, 2007 from ProQuest database.

Huntley, M. A. (2000). Effects of standards-based mathematics education: A student of the

       core-plus mathematics project algebra and functions strand. Retrieved February 26,

       2007 from ProQuest database.

Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of

       standards-based middle grades mathematics curriculum materials on student

       achievement. Retrieved February 18, 2007 from ProQuest database.

Trafton, P. R., Reys, B. J., & Wasman, D. G. (2001). Standards-based mathematics curriculum

       materials: A phrase in search of a definition. Retrieved from March 25, 2007 from

       ProQuest database.

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