Construct Knowledge and Mathematical Concepts

Since the mid-1980s, constructivism has played a major role in
mathematics education, and constructivist approaches to learning -
which are supported in the two NCTM *Standards* documents -
are beginning to influence the teaching of mathematics. Two
hallmarks of the constructivist position (Van de Walle, 1995) help
guide effective mathematics teaching and learning. First,
constructing knowledge is a highly active endeavor on the part of
the learner (Baroody, 1987). Constructing and understanding a new
idea involves making connections between old ideas and new ideas.
Teachers might help make this connection by asking reflective questions such as the
following:

- How does this idea fit with what you already know?
- In what ways is this problem like other problems/situations
you've experienced?
- What is it about this problem that reminds you of yesterday's problem? (Cook & Rasmussen, 1991)

Constructing knowledge requires reflective thought.

Second, networks or "cognitive schemas" that exist in the learner's mind are the principal determining factors for how an idea will be constructed. These networks are the product of both constructing knowledge and developing mathematical concepts.

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