Language and Culture in Mathematical Cognition

Daniel B. Berch, David C. Geary, Kathleen Mann Koepke

• Publisher: Academic Press
• Year: 2018
• Print ISBN: 9780128125748
• eBook ISBN: 9780128125755
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

Language and Culture in Mathematical Cognition, First Edition focuses on the role of linguistic and cultural factors in math cognition and development. It covers a wide range of topics, including analogical mapping in numerical development, arithmetic fact retrieval in the bilingual brain, cross-cultural comparisons of mathematics achievement, the shaping of numerical processing by number word construction, the influence of Head Start programs, the mathematical skills of children with specific language impairments, the role of culture and language in creating associations between number and space, and electrophysiological studies of linguistic traces in core knowledge at the neural level.- Includes cutting-edge findings, innovative measures, recent methodological advances and groundbreaking theoretical developments- Synthesizes research from various subdomains of math cognition research- Covers the full complement of research in mathematical thinking and learning- Informs researchers, scholars, educators, students and policymakers

Chapter 1

Introduction: Language and Culture in Mathematical Cognitive Development

Daniel B. Berch*; David C. Geary^†; Kathleen Mann Koepke^{‡ *} University of Virginia, Charlottesville, VA, United States
^† University of Missouri, Columbia, MO, United States
^‡ NICHD/CDBB, Rockville, MD, United States

Abstract

In this introductory chapter, we present a brief historical review of research on the roles of language and culture in mathematical cognition, and then provide readers with a useful framework for categorizing specific linguistic levels of influence on numerical processing (e.g., lexical, semantic, and syntactic). We then describe other considerations in studying linguistic influences on mathematical cognition, such as the neural substrates of verbal, language-based representations of numerical information and the impact of bilingualism on numerical processing. With respect to the role of cultural factors that influence mathematical cognition, we briefly review many of the classic studies on this topic, and then present some purported myths of cultural psychology as a framework for discussing specific kinds of cultural factors that could potentially influence mathematical learning and achievement. We conclude by discussing the complexities associated with disentangling linguistic and cultural influences on numerical processing and development.

Keywords

Lexical; Semantic; Syntactic; Phonological; SNARC effect; MARC effect; Approximate number system; Object tracking system; Analogical mapping; Linguistic transparency; Inversion; Transcoding; Intraparietal sulcus; Dyscalculia; Bilingualism

Introduction

The contributions of linguistic and cultural factors to the development and learning of numerical, arithmetic, and other mathematical concepts and skills are broad and varied, ranging from different types of linguistic influences to contrasting cultural beliefs about the relative importance of ability and effort in learning mathematics, to a traditional society whose language possesses only a limited numerical vocabulary. Indeed, the expansive collection of studies reviewed by the authors in this edited volume is a testament to the diversity of themes, critical issues, theoretical perspectives, research methods, and even the participants (e.g., dual-language learners, children with specific language impairments, and members of a remote indigenous population in New Guinea) that exemplify the fascinating and important spheres of linguistic and cultural influences on mathematical cognition.

In this introductory chapter, we begin by presenting a brief historical review of research on the roles of language and culture in mathematical cognition. Next, we provide readers with a useful framework for categorizing specific linguistic levels of influence on numerical processing (e.g., lexical, semantic, and syntactic), followed by a brief discussion of one of the major questions that has guided research on the role of language in numerical development. We then describe other considerations in studying linguistic influences on mathematical cognition, including the neural substrates of verbal, language-based representations of numerical information and the impact of bilingualism on mathematical thinking and learning.

With respect to the role of cultural factors that influence mathematical cognition, we begin by briefly reviewing many of the classic studies on this topic. Next, we present some purported myths of cultural psychology as a framework for discussing specific kinds of cultural factors that could potentially influence mathematical learning and achievement. We then discuss the complexities associated with disentangling linguistic and cultural influences on numerical processing and development and conclude by acknowledging how studying the intersection between language, culture, and mathematics has flourished since the early groundbreaking research on these topics, exemplified by the work described in this volume that has certainly produced a deeper understanding of this intersection.

A Brief Historical Review of Research on the Roles of Language and Culture in Mathematical Cognition

The systematic, large-scale study of cross-national differences in students' mathematical development began in 1964 with the International Project for the Evaluation of Educational Achievement (IEA; Husén, 1967). The goal was to assess a broad range of mathematical skills of 13- and 17-year olds from developed nations and to examine potential influences on these skills, such as the amount of homework and family background, as we elaborate in “The Role of Culture in Mathematics Achievement”. The results revealed substantive cross-national differences in mathematics achievement at both ages. The second IEA study was conducted about two decades later and confirmed substantive cross-national variation in mathematical competencies (Crosswhite, Dossey, Swafford, McKnight, & Cooney, 1985). These cross-national studies have expanded over the years and are now conducted on a regular basis through the Program for International Student Assessment (PISA; https://www.oecd.org/pisa/aboutpisa/) and Trends in International Mathematics and Science Study (TIMSS; http://timssandpirls.bc.edu/). The story remains the same; there is substantive cross-national variation in mathematical competencies.

The systematic study of language influences on these cross-national differences began several decades after the first IEA and focused largely on the transparency of the base-10 structure of Arabic numerals in the corresponding number words (e.g., Miller & Stigler, 1987; Miura, 1987; Miura, Okamoto, Kim, Steere, & Fayol, 1993). For example, number words in most Asian languages are a direct reflection of the base-10 system, whereas number words in most European-derived languages are more arbitrary, at least until the 100s. For instance, the Chinese number word for 27 is translated as two ten seven, which makes it obvious to children that 27 is composed of 2 tens and 7 ones. This structure is less obvious in English or in most other European-based languages, especially for number words in the teens. These differences in turn can influence students' learning of some aspects of number and arithmetic (Fuson & Kwon, 1992). Studies of this type continue today, as illustrated in Chapter 4 by Okamoto and Chapter 10 by Göbel.

More recently, the study of number words has shifted to those that emerge in traditional populations (e.g., Butterworth, Reeve, & Reynolds, 2011; Gordon, 2004). These studies have revealed that people in many of these groups have a limited set of number words (e.g., the equivalent of “one, two, and three”), which allows researchers to separate the influence of number words from children's and adults' inherent understanding of relative quantity, as noted in Section “How Do Children Learn the Meaning of Number Words?” Cultures with more developed trading systems generally have an expanded set of number words that are often tailored to aid in specific functional tasks (Beller & Bender, 2008), as contrasted with the systematic mathematical system that children now learn with formal education. Within economically developed nations with multilingual populations, there is now a focus on how learning number words and other aspects of mathematics in two different languages influence children's mathematical development, as illustrated in Chapter 7 by Wicha et al., Chapter 8 by Salillas and Martínez, and Chapter 9 by Sarnecka et al.

Specific Linguistic Levels of Influence on Numerical Processing

In a recent editorial for a special issue of Frontiers in Psychology concerning linguistic influences on mathematical cognition, Dowker and Nuerk (2016) contend that the preponderance of research in this area has not gone beyond simplistic demonstrations that language influences number, thus failing to explore the specific level at which particular language effects operate. As a consequence, these authors devote their editorial to differentiating seven linguistic levels. We adopt these here as a framework both for introducing the various ways in which language can influence mathematical processing and for previewing the topics to be covered in the present volume. The specific levels identified by Dowker and Nuerk include lexical, semantic, syntactic, phonological, visuospatial orthographic, conceptual, and other language-related skills.

Lexical: The Composition of Number Words

The study of lexical factors in mathematical cognition has focused primarily on the effects of number words. As Dowker and Nuerk (2016) point out, the extent to which a language's number word structure is transparent (i.e., compatible with its written/digital number system) can influence numerical performance, even when number words are not involved in a mathematical problem. One such lexical property is what Dowker and Nuerk refer to as power transparency—the degree to which the construction of number words provides a clear and consistent representation of the base-10 system in the language. For example, in East Asian languages, the power of any number beyond 10 can be derived directly from the number word (e.g., “ten-one” for 11). And since such correspondences are more direct (i.e., more transparent) than in languages such as English where many number words are irregular (e.g., “eleven”), some researchers have maintained that the comparatively superior counting and arithmetic skills of Asians may be attributable, at least in part, to the greater transparency of their number words (see Chapter 13 by Bender and Beller, for a linguistic typological analysis of regularity in different numeration systems). However, as Dowker and Nuerk contend, findings based upon such comparisons are often confounded by numerous other cultural and educational differences between countries. (See Section “The Role of Culture in Mathematical Cognition” below for a delineation of these potentially confounding factors, along with the section on “Disentangling Linguistic and Cultural Influences”.)

Dowker and Nuerk (2016) also discuss another type of lexical influence known as the inversion property. For example, as Chapter 10 by Göbel describes it, in some languages, the number word starts with the unit followed by the decade (e.g., drei-und-zwanzig, three and twenty), which conflicts with the order of the digits in the Arabic form (e.g., 23). However, in languages such as English that contain noninverted number words, the number word sequence for two-digit numbers is decade first followed by unit (e.g., twenty-three), consistent with the Arabic notation (23). As Göbel describes it, the evidence suggests that children whose language contains decade-unit number word inversions make frequent inversion errors in numerical transcoding—writing numbers in response to spoken number words (e.g., writing 32 for three and twenty)—which seldom occurs for children whose language does not possess number word inversion (see also Chapter 4 by Okamoto, for a discussion of the role of inversion in number-line estimation).

Despite the strong evidence demonstrating that number word inversions can lead to numerical transcoding errors in children, as Dowker and Nuerk (2016) summarize, other research has shown that the inversion property does not influence all numerical and arithmetic skills. That being said, Göbel (Chapter 10 by Göbel) found that for 7- to 9-year olds, number word inversion can impact symbolic arithmetic when addition problems require carry operations (e.g., 27 + 6), in contrast to those that do not (e.g., 31 + 6). Moreover, Lonnemann and Yan (2015) recently demonstrated that inverted number words can complicate arithmetic processing even for ad...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Foreword: Mathematical Cognition, Language, and Culture: Understanding the Links
• Preface
• Chapter 1: Introduction: Language and Culture in Mathematical Cognitive Development
• Chapter 2: Analogical Mapping in Numerical Development
• Chapter 3: Linguistic and Experiential Factors as Predictors of Young Children's Early Numeracy Skills
• Chapter 4: Effects of Mathematics Language on Children's Mathematics Achievement and Central Conceptual Knowledge
• Chapter 5: How Does the “Learning Gap” Open? A Cognitive Theory of Nation Effects on Mathematics Proficiency
• Chapter 6: Mathematical Skills of Children With Specific Language Impairments: Testing Developmental Theory
• Chapter 7: Arithmetic in the Bilingual Brain
• Chapter 8: Linguistic Traces in Core Numerical Knowledge: An Approach From Bilingualism
• Chapter 9: Early Number Knowledge in Dual-Language Learners From Low-SES Households
• Chapter 10: How Culturally Predominant Reading Direction and Number Word Construction Influence Numerical Cognition and Mathematics Performance
• Chapter 11: Language, Culture, and Space: Reconstructing Spatial-Numerical Associations
• Chapter 12: Cultural Processes in Elementary Mathematics: Studies in a Remote Papua New Guinea Community
• Chapter 13: Numeration Systems as Cultural Tools for Numerical Cognition
• Index