Continuous Issues in Numerical Cognition

How Many or How Much

Avishai Henik

• Publisher: Academic Press
• Year: 2016
• Print ISBN: 9780128016374
• eBook ISBN: 9780128017937
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Continuous Issues in Numerical Cognition: How Many or How Much re-examines the widely accepted view that there exists a core numerical system within human beings and an innate ability to perceive and count discrete quantities. This core knowledge involves the brain's intraparietal sulcus, and a deficiency in this region has traditionally been thought to be the basis for arithmetic disability. However, new research findings suggest this wide agreement needs to be examined carefully and that perception of sizes and other non-countable amounts may be the true precursors of numerical ability. This cutting-edge book examines the possibility that perception and evaluation of non-countable dimensions may be involved in the development of numerical cognition. Discussions of the above and related issues are important for the achievement of a comprehensive understanding of numerical cognition, its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. - Serves as an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse topic - Features chapters from leading researchers in the field - Includes an overview of the multiple disciplines that comprise numerical cognition and discusses the measures that can be used in analysis - Introduces novel ideas that connect non-countable continuous variables to numerical cognition

Section I

Development

Chapter 1: Development of Quantitative Thinking Across Correlated Dimensions

Chapter 2: Link Between Numbers and Spatial Extent From Birth to Adulthood

Chapter 3: Catching Math Problems Early: Findings From the Number Sense Intervention Project

Chapter 4: Contextual Sensitivity and the Large Number Word Bias: When Is Bigger Really More?

Chapter 5: Learning, Aging, and the Number Brain

Chapter 6: Development of Counting Ability: An Evolutionary Computation Point of View

Chapter 1

Development of Quantitative Thinking Across Correlated Dimensions

Kelly S. Mix^*

Susan C. Levine^**

Nora S. Newcombe^†
* Michigan State University, East Lansing, MI, United States of America
^** University of Chicago, Chicago, IL, United States of America
^† Temple University, Philadelphia, PA, United States of America

Abstract

This chapter provides an overview of research related to the proposal that human quantification originates in a generalized magnitude system. We review research related to both looking time methods and visual perception to determine what stimulus dimensions might be included in such a system. Then we relate this literature to the research on quantification in infancy and early childhood. We consider various mechanisms by which a generalized magnitude system might become differentiated into separate quantitative dimensions, such as perceptual redundancy, emergence of object concepts, and the possible effects of language, including object names and counting. Finally, we identify mechanisms by which these dimensions become coordinated into a coherent quantitative system, focusing primarily on the impact of unitizing and spatial scaling, and their relation to several challenges in mathematical development, including measurement, proportional reasoning, and understanding fractions.

Keywords

cognition

development

space

number

infancy

early childhood

looking time

visual perception

quantification

generalized magnitude system

measurement

Outline

1.1 The Use of Looking Time to Measure Infant Quantification

1.1.1 Early Work on Infant Perception: The Advent of Looking Time Measures

1.1.2 Studies of Infant Number

1.2 Generalized Over What?

1.3 Mechanisms of Differentiation

1.3.1 Redundant Cues

1.3.2 Unitization

1.3.3 Selective Attention

1.4 Mechanisms of Reintegration

1.4.1 Proportional Scaling and Spatial Division

1.4.2 Symbolic Representation

1.5 Conclusions

References

The origins of human quantification have been the subject of intense study for decades. Methodological advances in the 1960s allowed researchers to ask what perceptual information infants notice, and this led to a proliferation of research on numerical sensitivity. Based on initial evidence, there were strong claims about innate capacities for number and these claims defined the research agenda for many years. However, the basis for these claims has not gone unchallenged. Some investigators have questioned whether infants’ quantitative responses are based on number at all, or rather, a host of correlated, nonnumerical percepts, such as contour length (eg, Mix, Huttenlocher, & Levine, 2002a).

Indeed, recent findings have led to a novel proposal—that human quantification is rooted in a generalized magnitude system that integrates these various perceptual streams into a unified representation and only later becomes differentiated into separate signals (Cantrell & Smith, 2013; Newcombe, Levine, & Mix, 2015). This st...

Table of contents

• Cover
• Title page
• Table of Contents
• Copyright
• Dedication
• List of Contributors
• Acknowledgments
• Introduction
• Section I: Development
• Section II: Animal studies
• Section III: Processes and mechanisms
• Section IV: Models
• Subject Index