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MATHEMATICS ANXIETY Feelings of apprehension and fear brought on by mathematical performance can affect correct mathematical application and can influence the achievement and future paths of individuals affected by it. In recent years, math anxiety has become a subject of increasing interest in both educational and clinical settings. This ground-breaking collection presents theoretical, educational and psychophysiological perspectives on the widespread phenomenon of mathematics anxiety. Featuring contributions from leading international researchers, Mathematics Anxiety challenges preconceptions and clarifies several crucial areas of research, such as the distinction between math anxiety from other forms of anxiety (i.e., general or test anxiety); the ways in which math anxiety has been assessed (e.g. throughout self-report questionnaires or psychophysiological measures); the need to clarify the direction of the relationship between math anxiety and mathematics achievement (which causes which). Offering a re-evaluation of the negative connotations usually associated with math anxiety and prompting avenues for future research, this book will be invaluable to academics and students in the psychological and educational sciences, as well as teachers working with students who are struggling with math anxiety. Irene C. Mammarella is Associate Professor at the University of Padua, Italy. Her research interests include the role of working memory and emotional aspects in specific learning disorders, and other neurodevelopmental disorders. She is the cofounder of a clinical university centre for neurodevelopmental disorders (LabDA srl) and coauthored the book Nonverbal learning disabilities (Guilford Press, 2016). Sara Caviola is a Lecturer in Developmental Psychology, at the School of Psychology, University of Leeds, UK. She won a Marie Skłodowska-Curie fellowship and spent two years at the Centre for Neuroscience in Education, University of Cambridge. Her main interests include analyses of cognitive and emotional underpinnings of mathematical cognition, in both children and adult populations. Ann Dowker is University Research Lecturer at the Department of Experimental Psychology, Oxford University, UK. She has edited and coedited several books, and is the author of Individual Differences in Arithmetic: Implications for Psychology, Neuroscience and Education (Psychology Press, 2005; second edition to be published in 2019). She is the lead researcher on the Catch Up Numeracy intervention project. MATHEMATICS ANXIETY What is Known and What is Still to be Understood Edited by Irene C. Mammarella, Sara Caviola and Ann Dowker First published 2019 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2019 selection and editorial matter, Irene C. Mammarella, Sara Caviola and Ann Dowker; individual chapters, the contributors The right of Irene C. Mammarella, Sara Caviola and Ann Dowker to be identified as the authors of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice : Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book has been requested ISBN: 978-0-367-19033-0 (hbk) ISBN: 978-0-367-19039-2 (pbk) ISBN: 978-0-429-19998-1 (ebk) Typeset in Bembo by Apex CoVantage, LLC CONTENTS Preface vii 1 Models of math anxiety 1 Mark H. Ashcraft 2 Different ways to measure math anxiety 20 Krzysztof Cipora, Christina Artemenko and Hans-Christoph Nuerk 3 Psychophysiological correlates of mathematics anxiety 42 Chiara Avancini and Dénes Szűcs 4 Mathematics anxiety and performance 62 Ann Dowker 5 Acquisition, development and maintenance of maths anxiety in young children 77 Dominic Petronzi, Paul Staples, David Sheffield and Thomas Hunt 6 Mathematics anxiety and working memory: what is the relationship? 103 Maria Chiara Passolunghi, Marija Živković and Sandra Pellizzoni 7 The different involvement of working memory in math and test anxiety 126 Ee Lynn Ng and Kerry Lee vi Contents 8 Math anxiety in children with and without mathematical difficulties: the role of gender and genetic factors 141 Sara Caviola, Irene C. Mammarella and Yulia Kovas 9 Probing the nature of deficits in math anxiety: drawing connections between attention and numerical cognition 156 Orly Rubinsten, Hili Eidlin Levy and Lital Daches Cohen 10 Gender stereotypes, anxiety, and math outcomes in adults and children 178 Carlo Tomasetto 11 The role of parents’ and teachers’ math anxiety in children’s math learning and attitudes 190 Julianne B. Herts, Sian L. Beilock and Susan C. Levine Concluding remarks 211 Irene C. Mammarella, Sara Caviola and Ann Dowker Index 222 PREFACE During a cold December afternoon, we were discussing a research project related to mathematical learning and related emotional difficulties, drinking cups of tea and coffee, when we realized the absence of a handbook entirely dedicated to this topic. Almost simultaneously we looked at each other (Irene and Sara) and had the same insight: why not try to edit a book on this topic? Once we realized that we had decided to follow through on the idea, we found ourselves lost (deep) in conversation, trying to list, organize and select all the fundamental topics we thought were worth including in the book. Thus, we wrote to Ann, who possesses tremendous expertise in this field, and asked her to join us. Happily, she immediately embraced the project. The final struc- ture of this book followed on from a symposium that we organized for the first international conference on Mathematical Cognition and Learning Society held in Oxford (Sara and Ann) in April 2018, and includes chapters from leading researchers in psychology, neuroscience and education from all over the world. There is a shared understanding that learning mathematics involves a com- plex interplay of cognitive, motivational and emotional processes (Carey, Hill, Devine, & Szücs, 2016; Dowker, Sarkar, & Looi, 2016; Hill et al., 2016; Mam- marella, Hill, Devine, Caviola, & Szűcs, 2015). Indeed, mathematical difficulties may be associated with not only specific mathematical learning disorders but also domain-general cognitive weaknesses (e.g. phonological memory, working memory, executive functions) and negative emotions (Maloney & Beilock, 2012; Vukovic, Kieffer, Bailey, & Harari, 2013). Interest in the interference of these negative affective factors, usually defined in the literature by the term ‘mathematics anxiety’, has grown from the students’ mathematics outcomes observa- tions: these feelings of apprehension and fear aroused during a mathematical performance can hamper or even impede its correct execution (Ashcraft & Kirk, 2001; Dowker et al., 2016). viii P reface For the domain of mathematics as a whole, long-standing quantitative research concerning the relationship between students’ math anxiety and their general mathematical achievement has been carried out, and the literature has mostly revealed a substantial negative relationship between the two (Ashcraft, Krause, & Hopko, 2007; Ashcraft & Moore, 2009; Carey et al., 2017; Hem- bree, 1990; Ma, 1999). In his meta-analysis, Hembree (1990) pointed out that cognitive-behavioural interventions developed for the treatment of test anxiety or general anxiety were effective in reducing or eliminating the effects of math anxiety on mathematics performance. Interventions merely focused on changes in classroom curricula, relaxation therapy or group counselling were less effective. Later studies have investigated the effects of more transitory disruptions involving ‘choking’ in response to threat, and have focused on relieving the cognitive symptoms of anxiety, and particularly their impact on working memory resources, with some promising results (Ramirez & Beilock, 2011; Supekar, Iuculano, Chen, & Menon, 2015). Since the overall aim of the book is to gain a greater understanding of math anxiety and, consequently, of ways to prevent or ameliorate the phenomenon, it is important to obtain converging evidence from as many fields as possible. Developmental psychologists, educationists, neuroscientists, educational and clinical psychologists, teachers and policymakers often tend to proceed indepen- dently, sometimes neglecting relevant findings from the research and practice outside their own disciplines. Just as with mathematical cognition in general, math anxiety research intersects with a wide array of sub-fields, such as cognitive and educational psychology, neuroscience and developmental psychology. In this book, we broadened the perspective, bringing together converging international researchers working on different areas with the aim to shed light on a) the theoretical background of math anxiety, b) the development of this phenomenon in both typical and atypical populations, c) the main cognitive processes involved and d) the importance and role of different social contexts. The result is a collection of eleven essays and constitutes a comprehensive survey of state-of-the-art studies on important facets of math anxiety. The book begins with two chapters about the theoretical backgrounds and the psychophysiological consequences of math anxiety. The first chapter, by Mark H. Ashcraft, provides a comprehensive summary of four major approaches to understanding the phenomenon and highlights the strengths and weaknesses of each of them. The chapter can be viewed as an overview and introduction to the in-depth chapters that comprise the entire volume. It is followed by Cipora, Artemenko and Nuerk’s chapter, which presents an exhaustive review of math anxiety measurement techniques, and by the chapter of Avancini and Szűcs, who discuss how math anxiety induces physiological reactions within individuals, and how psychophysiological measures may offer new ways to assess this phenomenon without relying on self-report questionnaires. The subsequent group of chapters discuss the development features of math anxiety. In particular, Ann Dowker points out the relationships and differences Preface ix between math anxiety and other related constructs (e.g. general- and test-anxiety, and attitudes to mathematics), and discusses reasons for the well-established negative relationship between math anxiety and maths performance. Dominic Petronzi and colleagues, after discussing issues regarding math anxiety measurement, propose a review of the literature surrounding the onset of math anxiety, focusing on several factors that may influence the development of such feelings of apprehension: e.g. negative evaluation from peers and teachers, pessimistic attitudes, low self-efficacy and reduced motivation. Another important aspect involves the cognitive processes, especially working memory processes often associated with math anxiety. Two chapters specifi- cally address this topic, providing a detailed summary of the current research. Passolunghi and colleagues discuss the relationship between math anxiety and mathematical performance by reviewing studies of both children and adult populations. The relationship between math anxiety and mathematics achievement is further analysed by Ng and Lee. In their chapter, they focused on not only math anxiety but also test anxiety, and discuss the overlap between these two constructs. A different insight is offered by the subsequent chapter, where Rubinsten and colleagues, after defining the meaning of attentional bias, report the most recent studies aimed at investigating whether math anxiety is character- ized by an attentional bias toward math-related stimuli. Caviola, Mammarella and Kovas give an overview of the literature in not only typical but also atypical populations, and in particular on children with mathematics difficulties or developmental dyscalculia. Their chapter tries to provide a fresh framework of the individual differences (considering both genetic and environmental factors) involved in young children’s low mathematics performance. In the following chapter, Tommasetto presents the most recent research on how gender differences in math anxiety are moderated by gender stereotypes (and self-concept beliefs). Finally, the last chapter, by Herts, Beilock and Levine, provides a detailed description about the social determi- nants of children’s and adolescents’ math anxiety by examining their parents’ and teachers’ math achievements and attitudes. Parents’ and teachers’ math anxiety is conceptualized as a moderator, determining the strength and direction of the relationships between children’s math anxiety and math education outcomes. Thus, the purpose of this book is to stimulate theoretical reflection on the ways in which math anxiety can influence the achievement and consequently the future paths of individuals. Findings with regard to gender differences, cognitive networks, types of assessment and psychophysiological correlates may help generate a better definition of math anxiety and clarify what is known about it. In this respect, a novel contribution of this book is to bring together different research fields into one single volume. In doing so, we also hope to challenge preconceptions about math anxiety and offer a re-evaluation of the negative connotations usually associated with the term. September 2018