Since the National Council of Teachers of Mathematics released its Standards in 1989, reform of mathematics curriculum to increase students’ understanding of mathematical concepts has been a major issue of discussion. Most agree on the goal; however, fierce debates have arisen about the best instructional methods to reach those goals. Some have stressed discussion of problem-solving strategies and the emergence of mathematical discussion between students as the most critical elements in mathematics reform. [Page 309]Others have feared that by minimizing the teaching of arithmetic computation and simple word problems, many students—especially those with learning disabilities, individuals with psychological processing or learning difficulties, and other learning problems—would never develop conceptual understanding.

In 2001, the National Research Council issued a report on lessons learned from experimental, development, and ...