Reflections on the Power of Genetic Epistemology by the Modern Cognitive Psychologist

In this chapter, we reflect on what this volume’s chapters convey about the power of leveraging Piaget’s genetic epistemology (GE) to provide insight into mathematical cognition, when viewed from the perspective of cognitive psychologists. We first reflect on the perhaps counterintuitive notion that the GE approach stands to make important contributions to cognitive psychologists’ measurement approaches, due to its concern for construct validity. Next, we discuss two constructs – fraction schemes and the figurative operative distinction – that, if imported from GE, might directly enhance psychological studies of mathematical cognition in the immediate near term. After making the case for how GE might contribute to cognitive psychology, we turn to consider how insights from modern cognitive psychology might motivate productive updates to GE perspectives. In particular, we argue that GE approaches would be more powerful if updated to include an explicit theory of memory and to include more probabilistic, emergentist conceptions of cognition. Finally, we conclude with a few open questions about how some of the central constructs of the GE approach might evolve if the perceived distance between perception and higher-order thought were reconceptualized to allow for much stronger links between the two.