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Standard-Based Math Page 1 Running head: STANDARDS-BASED CURRICULA Standards-Based Mathematics Curricula Jonette Burns TET 763 – Applied Research in Education and Training University of South Dakota Standard-Based Math Page 2 Standards-Based Mathematics Curricula Introduction 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 Standards. 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? Standard-Based Math Page 3 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, Standard-Based Math Page 4 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 Standard-Based Math Page 5 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 Standard-Based Math Page 6 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 Standard-Based Math Page 7 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 Standard-Based Math Page 8 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). Conclusion 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. Recommendations 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 Standard-Based Math Page 9 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. Standard-Based Math Page 10 References 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 http://www.cambridecollege.edu/public/acadmemic/medu_con/math.cfm/ 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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