Sources of Mathematical Thinking

Harvard University, Cambridge MA

Investigators

Abstract

The proposed project continues current work to examine non-human primates, children, and adults and investigate the foundations of mathematical thinking. Past research has converged on the identification of three 'building-block systems' on which mathematical thinking is based: 'exact small number system,' 'approximate large number system,' and the quantification and counting functions of natural language. The proposed studies continue to investigate these three systems in non-human primates, children, and adults through a variety of primate and developmental research techniques (e.g., studies that investigate what stimuli primates or infants can discriminate through measures of attention, gaze, and so on.). The proposed research is a strong program of four strands of research that investigate each of these foundational systems: (1) number representation in monkeys, (2) number representation in preschool children (e.g., examining learning first number words), (3) number representation in adult humans (using mental addition, multiplication etc. to examine the capabilities of the approximate large number and exact small number systems without symbolic manipulation), and (4) mapping between linguistic and number systems in children learning formal mathematics. The studies are well designed and exciting in the attempt to pull together primate and developmental research to construct a model of the foundational systems on which mathematical reasoning is based. What are the broader impacts of the proposed activity? In general, the studies have the potential to provide important contributions to the foundational theories that underlie mathematical thinking. The synergy between the primate, infant, and preschool developmental research has been exploited in past work to advance the state of understanding of the basic cognitive mechanisms on which mathematical thinking is built. The fourth strand of research attempts to make the connection to education, looking at how the formal symbolic mathematics taught in school brings together the three systems in these studies.