Developmental patterns in proportional reasoning

摘要: The editors of this book asked the contributors to answer three basic questions about cognitive development: what, how and why. We will attempt to answer these questions by a careful study of one famous case of cognitive development: Piaget's balance scale task for assessing proportional reasoning. In the past, we have investigated this task in various ways and we will take the present opportunity to summarize and integrate our main findings. We approach the study of cognitive development from a methodological point of view. In each of the forthcoming sections, we apply a new technique in order to get a new perspective on the developmental process. We first shortly discuss the background of research on the balance scale task. In the second section we attempt to resolve the criticism of Siegler's (1981) rule theory, the main theory for balance scale reasoning, by introducing categorical latent structure models for rule assessment. In the third section we attempt to validate and extend this rule theory with response time (RT) measures. Using RTs allows the test of the rule theory in great detail and leads to a number of specifications and improvements of the theory. Fourth, we summarize our study of the transitions between the rules. Knowledge of these transitions is an important step in understanding the mechanisms involved in the development of proportional reasoning. We focus on a particular transition, from Rule I to Rule II, to investigate whether this transition is a genuine phase transition. Based on our results, we present a restricted overlapping waves model of proportional reasoning, in which some transitions are sudden and others are …