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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, called the Pursuit strategy, participants created new quantities from x and y, detected patterns in these quantities, and expressed these patterns in terms of x. These expressions were then built into full hypotheses. The processes involved in this strategy are instantiated in an ACT\u2010based 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\u2010order problem solving.<\/jats:p>","DOI":"10.1207\/s15516709cog2402_3","type":"journal-article","created":{"date-parts":[[2005,8,6]],"date-time":"2005-08-06T01:38:47Z","timestamp":1123292327000},"page":"249-298","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Solving Inductive Reasoning Problems in Mathematics: Not\u2010so\u2010Trivial Pursuit"],"prefix":"10.1111","volume":"24","author":[{"given":"Lisa A.","family":"Haverty","sequence":"first","affiliation":[]},{"given":"Kenneth R.","family":"Koedinger","sequence":"additional","affiliation":[]},{"given":"David","family":"Klahr","sequence":"additional","affiliation":[]},{"given":"Martha W.","family":"Alibali","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2000,6]]},"reference":[{"key":"e_1_2_1_2_1","volume-title":"Rules of the mind.","author":"Anderson J. 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