Modeling Children's Understanding of Quantitative Relations in Texts: A Developmental Perspective

This article describes developmental models of word problem solving that are grounded in the notion of general developmental constraints of the mind. These models were constructed based on the assumption that differences in children's word problem-solving performance are due, at least in part, to developmental differences in their conceptual structures in the quantitative domain. Three levels of knowledge were identified and modeled. The simplest model represents quantitative relations as an ordered array of mental objects. The next level of the model represents numbers as objects of manipulations open two mental number lines that are coordinated in a tentative fashion. The most complex model represents numerical operations as objects of manipulations on two mental number lines that are well-coordinated with explicit, functional rules. These models were implemented as production systems. The accuracy of the predictions resulting from the simulations of the models was tested in an empirical study. Global tests of the models found a good fit of the data to the models. The results wee consistent with the theoretical analysis that the three levels of knowledge were internally coherent and qualitatively different from each other, and that the models could predict children's performance differences to a satisfactory degree.