Logic in Genetic Epistemology

This chapter explores Piaget’s use of formal logic to model children’s reasoning. This is related to, but not the same as, Piaget’s studies of the logic of children’s reasoning. The distinction lies between considering when and how children’s reasoning fits an existing expert model and how to describe the structure of the ways children draw inferences of various types. Logic occupies a large portion of Piaget’s writings, but has not been widely taken up in mathematics education research. This is because logic is less studied in mathematics education (with good reason) and because Piaget’s use of these models was particularly challenging to follow. This chapter tries to elucidate some of what Piaget did in this line of research, drawing particular attention to the role of task design and the subtle ways Piaget reformulates the logical models for the purpose of his modeling of student reasoning. This provides an opportunity to consider the role of expert models more generally in the work of studying student mathematics and to observe the pitfalls and challenges inevitably imposed by this kind of work. One reason I propose for logic’s marginal place in mathematics education research is the gap between student reasoning, which is usually contextual and content-specific, and the features of formal logical models, which are decontextualized and content general. This fundamental gap both increases the likelihood of miscommunicating with such models and for tension between the model and what is being modeled.