Solving inductive reasoning problems in mathematics: Not-so-trivial pursuit

This study investigated the cognitive processes involved in inductive reaso ning. Sixteen undergraduates solved quadratic function-finding problems and provided concurrent verbal protocols. Three fundamental areas of inductive activity were identified: Data Gathering, Pattern Finding, and Hypothesis Generation. These activities are evident in three different strategies that they used to successfully find functions. In all three strategies, Pattern Finding played a critical role not previously identified in the literature . In the most common strategy, celled the Pursuit strategy, participants cr eated new quantities from x and y, detected patterns in these quantities, a nd expressed these patterns in terms of x. These expressions were then buil t into full hypotheses. The processes involved in this strategy are instant iated in an ACT-based model that simulates both successful and unsuccessful performance. The protocols and the model suggest that numerical knowledge is essential to the detection of patterns and, therefore, to higher-order p roblem solving.