Excerpt: Many educators base recommendations for teaching mathematics on “constructivist” thinking. However, they often misunderstand constructivism, so their recommendations may be incorrect or inappropriate. We need to examine what constructivism is and is not, what myths have grown up around constructivism, and what characteristics define it.

Excerpt: Radical changes have been advocated in recent reports on mathematics education, such as NCTM’s Curricu- lum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics 1989) and Everybody Counts (MSEB and National Research Council 1989). Unfortunately, many educators are fo- cusing on alterations in content rather than the reports’ recommendations for fundamental changes in instruc- tional practices. Many of these instructional changes can best be understood from a constructivist perspec- tive. Although references to constructivist approaches are pervasive, practical descriptions of such approaches have not been readily accessible. Therefore, to promote dialogue about instructional change, each “Research into Practice” column this year will illustrate how a constructivist approach to teaching might be taken for a specific topic in mathematics.