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Research Base
Research Influences on the Development of the CPMP Program
Development of the Core-Plus Mathematics Project (CPMP) curriculum, now
published as Contemporary Mathematics in Context, was informed by research
on teaching and learning and the NCTM Curriculum and Evaluation Standards.
There were several overriding design principles guiding the curriculum development process:
- 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).