Placeholder structure and numerical computation

This symposium explores the role of placeholder structures—systems of words, non-linguistic symbols, or procedures—in the construction and manipulation of numerical concepts. The structure supplied by a placeholder system – like the count list in English – critically constrains the potential for creating and manipulating conceptual content. A great deal of empirical work has explored the role of placeholders in numerical cognition, in large part by investigating how children learn number word meanings when exposed to Arabic numerals and corresponding count routines (for review see Carey, 2009). One contribution of this work has been to suggest that learning a count list creates an important structure for constructing new numerical concepts. For example, learning to count is a critical precursor to acquiring large exact numerical concepts like “77”, and how such concepts are related (e.g., that 78 is greater than 77, by exactly one). According to some, this learning is guided by a semantic induction, whereby children realize that each successive numeral in the count list denotes a quantity of 1 more than the number that came before it. Beyond these studies, relatively little work has tested the role of placeholder structures outside the Arabic numeral system. As a result, little is known about the role that this particular structure plays in numerical development, and whether the use of alternative systems might result in different conceptual outcomes. Perhaps the best evidence that placeholder structures are critical to constructing numerical concepts comes from fieldwork in the Amazon, where studies of the Piraha and Munduruku have made clear that learning to count is important to acquiring at least some numerical concepts (Gordon, 2004; Frank et al, 200; Pica et al.). However, between the Piraha and English-speaking adults who use Arabic numerals lies a vast array of potential intermediate systems. At least some of these systems have been tested in nature by humans, and are used today. This symposium explores the role of placeholders systems to numerical development, the effects of structural variations, and how different modalities like gesture and vision are used to create alternatives to the Arabic numeral system, with different consequences for cognition. Michael C. Frank ([email protected]) Department of Psychology Stanford University