Foundations of Mathematical Understanding: Early Computational Ability with Nonsymbolic Quantities

Hilary Barth

Human adults, human infants, and many nonhuman animals share the ability to process numerical quantities nonlinguistically through the use of approximate representations of magnitude, a "number sense." Studies on nonsymbolic number processing in human adults (for example, estimating the approximate number of elements in a large group) have demonstrated remarkable parallels to comparative work in other species. Infant, animal, and human adult numerical abilities share such similar characteristics that many researchers have supposed that an evolutionarily continuous system of knowledge, present in many species, is responsible for the sense of number and forms the basis for the complex symbolic manipulation of number developed by humans alone. Nonsymbolic numerical processing is thought to be mediated by rough analog representations of magnitude, described metaphorically as number lines or vessels filled with liquid. Behavioral and neuroimaging studies in adults suggest that approximate numerical representations are not recruited only for nonsymbolic tasks. Judgments about exact symbolic quantities produce patterns of performance that exhibit the characteristic signatures of approximate number representations, suggesting that approximate numerical representations come into play automatically, even when tasks deal only with Arabic numerals. An important question remains unanswered: do approximate numerosity representations play a functional role in these symbolic operations? If the primitive number sense includes the capability to recruit nonsymbolic representations for computational purposes, there is great potential for educational application. In this project, I will continue my ongoing studies of number processing in adults in order to address some of the questions about how nonsymbolic abilities could serve as a building block of learned mathematics. I will also extend these studies to children, examining the early representational and computational abilities that accompany the number concept and its potential links to symbolic math learning. Advances in our understanding of nonsymbolic numerical abilities have broad implications for education; deeper knowledge of the conceptual roots of mathematics will lead to a better understanding of how early math learning works. Educational approaches based in universal nonsymbolic abilities have the further advantage of applicability to all human cultures, as these abilities arise before linguistic competence and culture-specific knowledge develop.

About Hilary Barth

Hilary Barth is a postdoctoral research fellow in the Department of Psychology at Harvard University. She received her Ph.D. in Cognitive Neuroscience from the Massachusetts Institute of Technology in 2002. Her graduate studies included work in visual perception and numerical cognition. Currently, she is conducting research on nonverbal number and quantity understanding in the Harvard Laboratory for Developmental Studies, working with Dr. Elizabeth Spelke. Dr. Barth is a participant in the OECD/CERI Learning Sciences and Brain Research initiative on numeracy. As a National Academy of Education/Spencer Foundation postdoctoral fellow, she will continue to pursue research in numerical and mathematical cognition.