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The vision for school mathematics described by the National Council of Teachers of Mathematics (NCTM) suggests a need for new approaches to the teaching and learning of mathematics, as well as new curriculum materials to support such change. This article discusses implications of the NCTM standards for mathematics curriculum and instruction and provides three examples of lessons from problem‐based curricula for various grade levels. These examples illustrate how the teaching of important mathematics through student exploration of interesting problems might unfold, and they highlight the differences between a problem‐based approach and more traditional approaches. Considerations for teaching through a problem‐based approach are raised, as well as reflections on the potential impact on student learning.
Harris et al. (2001) studied this question.