Investigating Approximate Number System Computation in Children

Trustees Of Boston University, Boston

Investigators

Abstract

This project investigates children's capacity for arithmetic computation without symbols or formal notation, before they encounter formal mathematics training in school. The Approximate Number System (ANS), a cognitive system which is operational from early infancy onward, allows humans to approximately quantify sets of items without language or symbols. Research suggests that the ANS could potentially support arithmetic operations, such as addition and subtraction, and that the ANS could therefore serve as a bridge to learning formal mathematics. However, the arithmetic capacity of the ANS, and how this capacity develops, is not well understood. This project fills that knowledge gap by systematically examining the computational capacity of the ANS using a series of experiments designed to assess young children before they learn the formal rules of arithmetic in school. The project addresses theoretical debates about the early cognitive architecture of the ANS and its role in arithmetic computation. The project will identify potential ways that educators could leverage children's pre-symbolic mathematical intuitions in order to help them learn formal mathematics. This has implications for STEM (Science, Technology, Engineering, and Mathematics) education. This project will examine the degree to which computations performed over ANS representations parallel true arithmetic computations. The development of the computational capacity of the ANS will be examined. Symbolic arithmetic computation obeys a set of functional rules. For example, the result of an arithmetic computation like 5+6 is a new, independent quantity that is just as precise as the quantities it was derived from, and which can be manipulated and used in further computations. These functional rules make symbolic arithmetic computation both powerful and flexible. This project aims to identify the functional rules of non-symbolic arithmetic with the ANS. In a series of experiments, four to six year-old children will be asked to solve non-symbolic problems with unknown addends (e.g., 5+__=11). This task requires children to perform arithmetic-like computation, holding two separate ANS representations in mind (e.g. approximately five and approximately 11) and performing a computation over them (e.g. subtracting approximately five from approximately 11) to derive a solution. Each experiment is aimed at examining different components of the functional rules of non-symbolic arithmetic, including the representational structure and precision of the solutions to ANS computations and the extent to which these solutions can be used in further computations. Additional measures of working memory capacity, symbolic math performance, and ANS representational precision are used to elucidate contributions of these cognitive systems to the computational capacity and development of the ANS. Data will be analyzed using a combination of traditional null hypothesis significance testing, Bayes factor analysis, and logistic regression. The project will therefore compliment what is known about the representational structure of the ANS by shedding light on its computational architecture and the development of this architecture in early childhood. 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.