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.