Date: Sept 30, 2020 03:00pm -4:30pm
Title: The Predicament of Quantity”: Analog Magnitudes and the Emergence of Number
Speaker: John Opfer:
Bio: John Opfer (Ph.D., 2000, Michigan) is a Professor of Psychology at The Ohio State University. His research concerns the role of relational reasoning in conceptual development, especially concepts from science and mathematics.
Prior to the 19th C., mathematics was considered to be the “science of quantity.” As a way of ensuring that mathematics hadn’t lost its grip on reality and as a way of approximating indirect measurements, this geometrical approach had its virtues. However, 19th C. mathematicians began to wonder if the geometrical approach had hit its limits. In this post-“science of quantity” era, scholars also began to wonder about the ontogeny of number and speculated that the representation of quantity was inadequate for even the precursors of direct measurement. But what exactly are the limits of the representation of non-symbolic quantity? How far can this representation take the developing child? Are these limits transcended just if children learn a symbolic code for numbers? In this talk, I examine evidence suggesting that (1) the limits of the analog magnitude system are real but grossly overstated and apply to perception of symbols too, (2) a series of visuo-spatial transformations (normalization, concatenation, and alignment) can be made to convert the cardinality of a set so that it can be compared to another cardinality as quickly and accurately as the comparison of two symbolic numbers. These results suggest that perception of quantity can play a much more supportive role in the ontogeny of number than is suggested by set-theoretic considerations.