Proof construction: adolescent development from inductive to deductive problem-solving strategies.

ABSTRACT

Inductive and deductive approaches to the construction of problem-solving proofs were examined using a task that requires the discovery of a geometrical figure hidden behind a series of covers. It was proposed that during adolescence, with the acquisition of a formal reasoning competence (as measured by Overton's [1990] version of Wason's selection task), there would be a transition from inductive to deductive proof construction strategies. One hundred adolescents were assessed on both the problem-solving proof task and the reasoning competence is associated with taking a deductive approach to proof construction. Formal reasoners tend to construct a proof based on the use of a falsification strategy as demonstrated by their search for disconfirming instances. A nonformal level of competence on the other hand is associated with inductive approaches. In this situation nonformal subjects tend to employ a verification strategy as demonstrated by the generation of redundant information. Results support the hypothesis that there is a cognitive developmental progression from an inductive approach to the construction of proofs to a deductive approach.