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:
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.