Learning through problem-solving: a constructivist approach to second grade mathematics

Abstract

At the risk of over-simplification, an immediate implication of constructivism is that mathematics, including the so-called basics such as arithmetical computation, should be taught through problem-solving. This does not mean that the instructional activities necessarily emphasize what are traditionally considered to be problems-stereotypical textbook word problems. In fact, the general notion that problems can be given ready-made to students is highly questionable. Instead, teaching through problem-solving acknowledges that problems arise for students as they attempt to achieve their goals in the classroom. The approach respects that students are the best judges of what they find problematic and encourages them to construct solutions that they findacceptable given their current ways of knowing. The situations that children find problematic take a variety of forms and can include resolving obstacles or contradictions that arise when they use their current concepts and procedures, accounting for a surprising outcome (particularly when two alternative procedures lead to the same result), verbalizing their mathematical thinking, explaining or justifying a solution, resolving conflicting points of view, and constructing a consensual domain in which to talk about mathematics with others. As these examples make clear, genuine mathematical problems can arise from classroom social interactions as well as from solo attempts to complete the instructional activities.