Center for Mathematics Education
An EDC project in the
Science and Mathematics Programs
(presentation slides) |
© Copyright 2004-2011 Education Development Center, Inc. (EDC)
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.