University of Calgary
UofC Navigation

Abstract: Barner

Natural Language & Number

Over cultural history humans have developed rich symbolic representations that encode number, culminating in formal mathematics. In this talk I will discuss the cognitive origins of this human capacity for symbolic number representation by taking a developmental approach. In particular, I will focus on the role of natural language in the acquisition of the positive integers. I will argue that children's first number words, "one", "two", and "three" are acquired much like grammatical markers of number, akin to singular, dual, and trial. In support of this, I will present evidence that singular and dual marking selectively speed the acquisition of the numbers "one" and "two" cross-linguistically. Following on this, I will argue that the real domain-specific cultural innovation that led to the development of mathematics was not representing number per se, but instead the creation of the verbal count list, which grew out of ancient one-to-one tally systems. As part of this argument, I will present evidence from bilingual learners who are exposed simultaneously to two counting systems, and will show that learning the counting procedures in one language transfers to the other, whereas the meanings of small number words - i.e., one, two, three - does not. Small number words are represented as language-specific, whereas counting procedures are language-general. Also, I will show how learning the counting procedure sets up learning of higher order mathematical concepts like the successor function and the concept of infinity.