Mathematics is often viewed as a highly symbolic domain in which the manipulation of symbolic expressions occurs according to structure-­‐sensitive rules.  Yet, mathematicians often describe mathematical ideas using visuospatial intuitions, and mathematics learners have great difficulty mastering the symbolic rules for manipulating mathematical expressions. An alternative view grounds mathematical cognition in terms of innate, intuitive systems; yet it is now clear that experience strongly shapes mathematical intuitions.  I propose an alternative to both approaches, based on the following ideas:  First, mathematics arises from cultural and technological developments, not intrinsic characteristics of mind, and its acquisition is largely a consequence of experience.  Second, mathematics is primarily a matter, not of manipulating symbolic expressions, but of mapping them onto their meaning in structured, human-­‐constructed, reference domains, including the number line, the Cartesian plane, and the unit circle. Third, the process of learning the reference domains and the mappings onto them is the product, not of sudden insight or rule discovery but of the gradual shaping of habits of mind – a process that occurs through experience-­‐dependent learning in multi-‐layer neural networks. My talk will argue for this approach and consider steps my lab is taking toward a framework for mathematical cognition based on these ideas.

This talk is sponsored by CMU, Department of Psychology, 100th Anniversary Colloq. Series.  

All lectures are open to the public.  For more information, call 412-268-3151.