In recent years there have been increased attempts to use mathematical models to understand the development of cognition (Anderson, 1980; Brainerd, Howe, & Desrochers, 1982; Wilkinson, 1982). In fact, in the current volume one chapter proposes a mathematical model for assessing children's developing rule use (Sophian, Larkin, & Kadane) and others exploit log-linear (Wellman, Fabricius, & Sophian) or Monte-Carlo (Heth & Cornell) modeling techniques. There is nothing particularly novel in these attempts; mathematical models have a classic place in psychological theorizing (Luce, Bush, & Galanter, 1963; Miller, 1964; Restle, 1971) and the expected gains from such endeavors are well known. These include most prominently (a) that such models require analytic specificity and thus encourage theoretical clarity and rigor, (b) that once formulated such models can generate new nonobvious predictions, and (c) that mathematical models enable the separation of response components that are difficult or impossible to distinguish otherwise-as in the separation of sensitivity from bias in signal detection models.