Human thinking is supported by foundational abilities that we share with other creatures; but humans are unique in that we also construct astoundingly complex, conscious, symbolically mediated representational systems that support and enhance our cognition (e.g., spoken language, formal mathematics). All humans use representational systems, but individuals differ radically in their degree of sophistication in using them—for example, whereas some people deploy mathematics to design bridges and compute interplanetary distances, others struggle to compute a restaurant tip. Where do these individual differences come from, and how can deficits in such abilities be addressed so as to give all people access to more powerful cognitive tools?
In my work I test the premise that studying human mathematical thinking will yield answers to both of these questions. I have found that individual differences in people’s math abilities are linked to individual differences in the precision of an evolutionarily ancient Approximate Number System (ANS). That is, the same primitive conceptual system that allows fish to estimate the number of conspecifics in a nearby shoal, and rats to estimate the number of key presses in a laboratory cage, also supports humans’ ability to reason mathematically using formal systems for expressing quantity. Further, I have recently found that improving children’s ANS also improves their school math performance.
Surprisingly, nothing is yet known about the origins of these individual differences in approximate number representations—neither their beginning in our genes nor their responsivity to accumulated experiences. While I have found that the ANS improves dramatically during our school-age years, the best practices for interventions to improve ANS functioning remain a mystery. Because it is shared across all people, is measureable at birth, improves with practice, and supports better school math performance, the ANS offers a crucial test case for understanding the interplay between the biological and experiential factors that allow human cognition to emerge.
In its more extreme forms, this type of “nature versus nurture” polemic has rightly been criticized for being too sparse to serve as a foundation for productive research. We must seek to understand biology and learning as dynamic processes, not deterministic ones. My project takes a two-pronged approach. First, quantifying numerical approximation abilities among people of differing degrees of biological relatedness will reveal the extent to which individual differences in the Approximate Number System are heritable. Second, large-scale interventions designed to improve children’s non-symbolic numerical intuitions will reveal the extent to which the ANS is malleable, and can be sharpened with experience, in different populations with very different histories of formal educational exposure. These then are two windows onto a continuum–they can allow us to characterize the ways in which genes and experience intertwine to give rise to different mathematical abilities. This research has the potential for profound implications–both for educational practice, and for the basic science of understanding human cognition.