Design Principles based on Research

Mathematics is a vibrant and broadly useful subject that can best be learned and understood as an active science of patterns. So ideas of experimentation, data analysis, and seeking and verifying patterns are pervasive in the CPMP curriculum.

Steen, L. A. (Ed.). (1990). On the shoulders of giants: New approaches to numeracy. Washington, D. C.: National Academies Press.

The curriculum uses problems as a context for developing student understanding of mathematics. The learning of mathematics is situated within the context of investigating and making sense out of rich applied problem situations.

Donovan, M.S. & Bransford, J.D. (2005) How Students Learn: History, Mathematics, and Science in the Classroom. National Academies Press.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-21.

Research suggests that deep understanding of mathematical ideas includes connections among related concepts and procedures, within mathematics and connections to the real world. For this reason, the curriculum was developed along interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics.

Donovan, M.S. & Bransford, J.D. (2005) How Students Learn: History, Mathematics, and Science in the Classroom. National Academies Press.

Skemp, R. R. (1987). The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.

Research suggests that classroom cultures of sense-making shape students' understanding of the nature of mathematics, as well as the ways in which they use mathematics. Thus, the curriculum is designed to support classrooms where students make sense of the mathematical concepts they are learning. This can be seen in the organization of the textbook and also in the specific questions asked of students. (See CPMP Classrooms.)

Resnick, L. B. (1987). Education and learning to think. Committee on Mathematics, Science and Technology Education, Commission on Behavioral and Social Sciences and Education. National Research Council. Washington, D.C.: National Academies Press.

The curriculum is written to promote the use of small-group collaborative learning in addition to teacher-led class discussion launching and summarizing investigative work. The notion of collaborative group work was inspired, in part, by the increasing use of project teams in business and industry.

It is also based on theories about the importance of social interaction in developing shared mathematical understandings and the role of communication in the construction of mathematical ideas.

There also is some evidence that small-group collaborative learning encourages a variety of social skills conducive to the learning styles of groups that are currently underrepresented in mathematics.

Cobb, P. (1995). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13-20.

Oakes, J. (1990). Opportunities, achievement, and choice: Women and minority students in science and mathematics. In C.B. Cozden (Ed.). Review of Research in Education, 16. Washington, D.C.: American Education Research Association.

Another principle underlying the process is that in any attempt to develop a new curriculum, each part of the curriculum should be justified on its own merits. In designing a particular course, we considered carefully the questions, "If this is the last mathematics students will have the opportunity to learn, is the most important mathematics included?" In that sense, the CPMP curriculum was developed from the ground up, as opposed to being exclusively driven by preparation for future course-taking (as has often be the case for mathematics curriculum development).

Schoen, H. L., & Hirsch, C. R. (2003). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, (110)2, 109-123.

The curriculum development also focused on mathematical habits of mind such as visual thinking, searching for and describing patterns, and making, checking and proving conjectures as a means of unifying the strands.

Donovan, M.S. & Bransford, J.D. (2005) How Students Learn: History, Mathematics, and Science in the Classroom. National Academies Press.

Research studies indicate that that students' operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. The results for both skill types were mixed when calculators were not part of assessment, but in all cases, calculator use did not hinder the development of mathematical skills. Students using calculators had better attitudes toward mathematics than their noncalculator counterparts.

Heid, K. M., (1997) The technological revolution and the reform of school mathematics, American Journal of Education. 106 5-61.

Ellington, A. J. (2003) A Meta-Analysis of the Effects of Calculators on Students' Achievement and Attitude Levels in Precollege Mathematics Classes, Journal for Research in Mathematics Education, 34(5).