

Design Principles based on Research
Research Influences on the Development of the CPMP Program
Development of the CorePlus Mathematics Project (CPMP) curriculum 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), 1221.

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 sensemaking 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 smallgroup collaborative
learning in addition to teacherled 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 smallgroup 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), 1320.
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 coursetaking (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, 109123.

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 problemsolving 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
561.
Ellington, A. J. (2003) A MetaAnalysis of the Effects of Calculators
on Students' Achievement and Attitude Levels in Precollege Mathematics
Classes, Journal for Research in Mathematics Education, 34(5).
