Center for Mathematics Education

An EDC project in the

Science and Mathematics Programs

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CME Principles

Our work is based on a set of core assumptions and principles that have evolved from our collective experience.

  • Fostering mathematical habits of mind
  • Developing mathematical talent
  • Making things “harder” to make them easier
  • Presenting mathematics as a discipline
  • Using technology to sharpen, not to replace, thinking
  • Keeing the classroom central

Fostering mathematical habits of mind
Mathematics is as much a set of ways of thinking - an evolving set of methods and habits of mind - as it is a body of results that have, over the centuries, been derived from those ways of thinking. Students who wish to advance in science or mathematics need a strong background in many of the results. But all students, those who may someday choose advanced mathematics and those who will not, need the habits of mind that mathematics hones and refines. They need to understand how mathematical results are created, and they need to be able to create results of their own. These ways of thinking must, therefore, be made an explicit part of curriculum, professional development, and research.

Developing mathematical talent
Except at the very extremes, talent is made, not found. We believe that the vast majority of students and teachers have the capacity to think in ways that are characteristically mathematical and to understand sophisticated mathematical ideas. But aptitude rarely blooms by itself. High achievement requires opportunities to develop that aptitude, through good content organization and high quality teaching.

Making things “harder” to make them easier
How can we hold such optimistic and ambitious views and even contemplate adding to the curriculum when history shows kids are still having trouble with the percents, fractions, and other basics? Attempts to simplify mathematics have often taken the form of breaking it down into "digestible" pieces, but we've repeatedly seen that when the connective tissue of genuine mathematical reasoning, habits of mind, and crosscutting ideas is taught well, the higher fidelity picture of mathematics eases learning for all students, not just the most advanced ones. Real mathematics becomes a comprehensible whole rather than an idiosyncratic collection of seemingly unrelated pieces, and mathematical thinking becomes a refinement of and an extension to natural thinking rather than a departure from it.

Presenting mathematics as a discipline
CME projects aim to close the gap between mathematics as a discipline and mathematics as a school subject. We want students to experience the thrill of solving problems and building theories, to understand the history of ideas behind the evolution of mathematical disciplines, and to appreciate the standards of rigor that are central to mathematical culture.

Using technology to sharpen, not to replace, thinking
We view technology as a tool for building new ideas and as a medium for developing mathematical habits of mind. Many mathematical phenomena do not have faithful physical counterparts, but do have computational ones. By performing actual experiments through building computational models of mathematical structures and objects, students can develop their abilities to perform comparable thought experiments.

Keeping the classroom central
High quality mathematics for all must be faithful to mathematics, must serve those who go on in mathematics and those who do not, and must work in real classrooms. Our work is grounded in the daily interaction among teachers and students through professional development, field tests, educational studies, focus groups with teachers and students, reviews of education research, and a regular presence in schools.