A productive way to think about imagistic mental models of physical systems is as though they were sources of quasi‐empirical evidence. People depict or imagine events at those points in time when they would experiment with the world if possible. Moreover, just as they would do when observing the world, people induce patterns of behavior from the results depicted in their imaginations. These resulting patterns of behavior can then be cast into symbolic rules to simplify thinking about future problems and (...) to reveal higher order relationships. Using simple gear problems, three experiments explored the occasions of use for, and the inductive transitions between, depictive models and number‐based rules. The first two experiments used the convergent evidence of problem‐solving latencies, hand motions, referential language and error data to document the initial use of a model, the induction of rules from the modeling results, and the fallback to a model when a rule fails. The third experiment explored the intermediate representations that facilitate the induction of rules from depictive models. The strengths and weaknesses of depictive modeling and more analytic systems of reasoning are delineated to motivate the reasons for these transitions. (shrink)

The interactivist approach to development generates a framework of types of constraints on what can be constructed. The four constraint types are based on: (1) what the constructed systems are about; (2) the representational relationship itself; (3) the nature of the systems being constructed; and (4) the process of construction itself. We give illustrations of each constraint type. Any developmental theory needs to acknowledge all four types of constraint; however, some current theories conflate different types of constraint, or rely on (...) a single constraint type to explicate development. Such theories will be inherently unable to explain important aspects of development. (shrink)