Collaborative Research: Origins of Recursive Mathematical Knowledge in Childhood

University Of California-San Diego, La Jolla CA

Investigators

Abstract

This project will investigate how children between the ages of 3 and 7 years learn about the rules that govern counting. The main goal of this project is to examine how the verbal structure of counting in different languages affects children's ability to learn core math concepts like recursion and infinity. Therefore, the work will have a broad impact on understanding how the structure of symbolic systems taught to children affect their ability to learn core STEM concepts. The project will foster interdisciplinary research, and will create a collaborative bridge between the University of California-San Diego, a PhD granting university, and Skidmore College, where research is conducted as part of undergraduate training. This will promote new forms of training on both campuses, spanning Psychology, Cognitive Science, Linguistics, and Education. Researchers will examine how the structure of the verbal count list - which differs across languages - affects how children learn core mathematical concepts. To accomplish this, researchers will assess how high children can count, and assess the ability of children to generate the next number in a sequence of numbers when not counting. These two assessments will allow the researchers to determine whether children have acquired a recursive +1 rule (the "successor function"). Researchers will test whether learning this recursive rule leads children to infer that numbers are infinite. Finally, using similar methods, the researchers will examine whether learning that numbers are infinite might lead children to infer that other domains, like space and time, are also infinite. Therefore, the researchers will determine how learning a concrete system of counting rules might lead children to learn about abstract entities (such as infinity) that can never be directly experienced. Using simple behavioral methods, the project addresses a central property of mathematics education with important implications for educational practices in mathematics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.