Expanding the Equation: Learning Mathematics through Teaching in New Ways. Research Report 95-1.

Over the past decade, various reports have identified serious deficiencies in mathematics education in the United States (Mathematical Sciences Education Board, 1989 &1990; McKnight, et al., 1987, National Commission on Excellence in Education, 1983). The National Council of Teachers of Mathematics (NCTM) responded to calls for reform with the publication of the Curriculum and Evaluation Standards (1989) and the Professional Standards for Teaching Mathematics (1991). In these documents the NCTM presents a vision of mathematics education grounded in three areas: cognitive psychology, philosophy of mathematics, and how mathematicians do mathematics. In the classrooms the Standards describe, teachers are: • Selecting mathematical tasks to engage students’ interests and intellect;

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