Mathematics Anxiety

What is Known and What is still to be Understood

Irene C. Mammarella, Sara Caviola, Ann Dowker, Irene C. Mammarella, Sara Caviola, Ann Dowker

• Publisher: Routledge
• Year: 2019
• eBook ISBN: 9780429576126
• Topic: Psychology
• Subtopic: Cognitive Psychology & Cognition
• Index: Psychology

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, mathematics anxiety has become a subject of increasing interest both in 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 mathematics anxiety from other forms of anxiety (i.e., general or test anxiety); the ways in which mathematics 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 revaluation of the negative connotations usually associated with mathematics anxiety and prompting avenues for future research, this book will be invaluable to academics and students in the field psychological and educational sciences, as well as teachers working with students who are struggling with mathematics anxiety

1
Models of Math Anxiety

Mark H. Ashcraft

Mathematics anxiety: “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations.”

(Richardson & Suinn, 1972, p. 551)

There is good reason to begin this volume with an introductory chapter on models of math anxiety – discussing the several models that have guided investigations of math anxiety almost necessarily involves a general review of the research on math anxiety, or at least the highlights of that research. As such, this chapter can serve as an introduction to the more specific, in-depth chapters that follow. As this introduction will show, the models that have been proposed for understanding math anxiety reflect researchers’ varying viewpoints about expected consequences of math anxiety as well as factors suspected of influencing it, researchers’ own theoretical orientations, and, to a degree, developments in the field that have made new kinds of research possible. Thus, the models show how our thinking about math anxiety has evolved and how different research orientations have enriched our understanding of math anxiety.

In the title of their recent review, Dowker, Sarkar, and Looi (2016) asked rhetorically “What have we learned in 60 years?” in our research on math anxiety. The 60 years in question date from the first modern research paper on the topic by Dreger and Aiken (1957) in which those authors tentatively advanced the term “number anxiety” as a label for the emotional reaction to numbers and mathematics. To be sure, there were precursors to this 1957 article; for example, Browne’s (1906) report on performance on the four arithmetic operations made passing reference to emotional reactions to math, and Gough (1954) contributed anecdotal evidence about students’ “mathemaphobia” (along with advice for other teachers). But the precursors were largely anecdotal or clinical; indeed, several were psychoanalytic writers who suggested that “failure in arithmetic may be related to maternal overprotection” (Dreger & Aiken, 1957, p. 344).

But the Dreger and Aiken paper was the first clear example of an empirical research approach. In their study, Dreger and Aiken added three math-focused questions to the Taylor Scale of Manifest Anxiety (and dropped three questions from the Taylor scale that had low validity), and also collected scores on an intelligence test, and final grades in a university math course; a subsample (n = 40) of the 704 participants were also given an arithmetic test while Galvanic Skin Response (GSR) deflections were recorded. All measures were inter-correlated, and the three math-focused questions were factor analyzed. The results showed that “number anxiety” appeared to be a separate construct from more general anxiety, that it was unrelated to general intelligence, and that it correlated negatively with math grades. All of these results have been replicated many times since this original report.

Math anxiety as a personality construct

The Dreger and Aiken (1957) paper began a tradition of research on math anxiety that treated math anxiety as a personality construct, that is, as a factor or dimension of the individual that needed to be explored in relation to other personality characteristics, factors, traits, or differences. An early effort in the research, not surprisingly, involved assessment. What test or survey was to be used to measure math anxiety? Although several different tests were devised, the Mathematics Anxiety Rating Scale (MARS), by Richardson and Suinn (1972), became the most widespread assessment tool for determining an individual’s level of math anxiety; it, along with its various revisions and versions for younger individuals, was the underlying test used in over half of the studies that appeared in Hembree’s (1990) and Ma’s (1999) influential meta-analyses on math anxiety.

The original MARS was a 98-item test, with the 98 items describing scenes or situations that might invoke math anxiety (having to reconcile a checkbook, checking a restaurant bill that you think has overcharged you, getting ready to take a math quiz). The test asked for a self-report of how anxious each situation would make the respondent feel, on a Likert scale of 1 (not anxious) to 5 (very anxious). Later versions of the test, including the sMARS (s for shortened), by Alexander and Martray (1989), a 25 item test extracted from the original MARS, and Hopko, Mahadevan, Bare, and Hunt’s (2003) Abbreviated Math Anxiety Scale (AMAS), a 9-item test, are also in wide use. All have good to excellent reliability and show substantial inter-correlations, ranging from .50 to .85 (Dew, Galassi, & Galassi, 1983; Hopko et al., 2003; see Chapter 2 for a full discussion).

Beyond the basic work on assessing math anxiety, considerable effort was devoted across the ensuing two decades to determine whether math anxiety was in fact a separate construct from general anxiety or the more specific construct of test anxiety. The well-known meta-analysis by Hembree (1990) devoted appreciable effort to this question and argued that math anxiety is indeed a separate construct, although one that overlaps with test and general anxiety to a degree (for further detail, see Chapter 7 in this volume). Repeatedly, the correlations between math anxiety and test anxiety were reasonably high, but not as high as those between alternate tests of math anxiety – for instance, various math anxiety tests tend to inter-correlate in the range of .50 to .85, whereas the overall math-to-test anxiety correlation (Hembree, 1990) is .52 (see also Dew, Galassi, & Galassi, 1984). The correlation between math anxiety and general anxiety is usually smaller; in Hembree’s (1990) meta-analysis, the value was .35.

Table 1.1 Selected correlations with math anxiety (MARS) summarized in Hembree’s (1990) and Ma’s (1999)

Correlation between MARS and:	r
Measures of anxiety
General anxiety	.35
Trait anxiety	.38
State anxiety	.42
Test anxiety	.52
Math attitudes
Usefulness of math	-.37
Enjoyment of math (pre-college)	-.75
Enjoyment of math (college)	-.47
Math Self-confidence (pre-college)	-.82
Math Self-confidence (college)	-65
Motivation	-.64
Avoidance
Extent of high school math	-.31
Intent to enroll (college)	-32
Performance measures
IQ	-17
Verbal aptitude / achievement	-.06
Math achievement (pre-college)	-.27
Math achievement (college)	-31
High school math grades	-.30
College math grades	-.27

(Adapted from Hembree, 1990; Ma, 1999)

Of more interest, research summarized in Hembree’s (1990) and Ma’s (1999) meta-analyses covered the relationships investigated since the advent of the MARS (and its successors) and a variety of personality and achievement factors. This work revealed an extensive list of worrisome correlations with math anxiety (see Table 1.1 for a list of factors and correlations). On the educational side, math anxiety correlates negatively with math achievement at both the pre-college and college levels, and also negatively with high school and college math grades. Math anxiety also correlates negatively with the extent of math taken in high school (elective coursework), and individuals’ intent to enroll in elective math courses in college; these correlations are routinely interpreted as indicators of avoidance. Note, however, that math anxiety has a fairly low correlation with overall intelligence (−.17), and is uncorrelated with IQ when only verbal aptitude or achievement is considered (−.06).

The correlations between math anxiety and attitudes concerning math are more strongly negative, and are also considered as supportive evidence for an overall pattern of avoidance. Math anxiety correlates negatively with enjoyment of math, self-confidence in math, motivation to learn math, and views about the usefulness of math.

Hembree’s (1990) paper considered the theoretical models for test anxiety as a guide for initial models of math anxiety and focused on two models in particular, the interference model and the deficits model. According to the interference model, test anxiety was thought to disrupt recall of prior learning. The model also claimed that interference included an individual’s worry during test taking, which would divert attention away from the test itself. The deficits approach, in contrast, claimed that an individual’s lower scores on a test were due to poor study habits and deficient test-taking skills. The individual in a test-taking situation, accordingly, would remember previous poor test performance, and this would cause test anxiety in the present moment. Because his earlier work on test anxiety had supported the interference account, Hembree proposed that math anxiety too might be better approached from the standpoint of the interference model.

Interestingly, very little of the research leading up to the time of Hembree’s meta-analysis appeared to advance theoretical proposals or models of math anxiety. Instead, the research focused on two general topics. First, researchers explored other personality characteristics and factors with which math anxiety was associated (for a related perspective on the lack of such theoretical work, see McLeod, 1989). This is the work just discussed, such as studies of the associations between math anxiety and factors like self-confidence in math, enjoyment of math, self-efficacy, and so forth. The other focus during this period was research relating math anxiety to educational outcomes, that is, math achievement. A variety of studies examined the negative association between math anxiety and grades, and between math anxiety and math achievement, with the overall correlations (in Hembree, 1990) found to be −.30 (pre-college) and −.27 (college) for grades, and −.27 (pre-college) and −.31 (college) for math achievement. Relationships of similar magnitude continue to be obtained, although the relationship is now believed to be more nuanced than a simple overall negative relationship (see, e.g., Ramirez, Chang, Maloney, Levine, & Beilock, 2016, and Chapter 4, this volume).

Math anxiety as a cognitive construct

Early on, researchers and theorists acknowledged that math anxiety, along with other forms of anxiety, involved a cognitive component (e.g., Dew et al., 1983). Early writings routinely noted that test anxiety involved both an affective component, emotionality, and a cognitive component, conscious worry. The theoretical model that brought this thinking into the realm of cognitive psychology was the important processing efficiency theory by Eysenck (1992; Eysenck & Calvo, 1992). According to this theory, worry is an internal process that occupies consciousness during an anxiety reaction. Critically, this preoccupation was predicted to consume the resources of the limited Working Memory system. Thus, Eysenck predicted quite specifically that an anxious individual should show disruption on a cognitive task to the extent that the task relies on working memory resources.

Interestingly, just before Hembree’s (1990) important meta-analysis on math anxiety, and likewise just before Eysenck’s (1992) theory, Ashcraft and Faust (1988) presented a conference report on an initial study concerning the cognitive consequences of math anxiety. Their study examined the underlying cognitive processes of doing mental arithmetic by individuals varying in their math anxiety; as noted when the study was subsequently published (Ashcraft & Faust, 1994), it appeared to be the first to pose the question whether math anxiety actually influenced the mental processing involved in doing arithmetic.

In this exploratory work, Ashcraft and Faust presented simple addition and multiplication problems (e.g., 4 + 3 = 7, 8 × 4 = 38), two-digit addition problems with and without a carry (e.g., 24 + 17 = 43), and a set of complex problems containing all four arithmetic operations (e.g., 18 + 16 = 34, 47 – 18 = 19, 12 × 14 = 168, 156 ÷ 12 = 13), all for true/false judgments. Participants were given the MARS assessment and were divided into four math anxiety groups.

For the most part, the simple addition and multiplication problems revealed no math anxiety effects, these problems showing only the standard effects found in regular tests of addition and multiplication, namely, that latencies and errors increased as the problems grew larger. But the two-column addition problems revealed two particularly interesting math anxiety effects. First, the higher anxiety groups were considerably slower to these problems than the lowest anxiety group. Second, the higher anxiety groups seemed particularly slowed down by the presence of a carry problem; that is, when a problem involved a carry, only the low anxiety group demonstrated efficient performance, whereas performance in groups 2, 3, and 4 was particularly disrupted.

In a second set of studies, Faust, Ashcraft, and Fleck (1996) replicated and extended the exploratory studies, and found several additional effects of math anxiety on cognitive performance. Three results deserve particular mention. First, in the initial experiment, we again studied performance of simple addition problems in the true/false task. But we expanded the range of values (termed “sp...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• CONTENTS
• Preface
• 1 Models of math anxiety
• 2 Different ways to measure math anxiety
• 3 Psychophysiological correlates of mathematics anxiety
• 4 Mathematics anxiety and performance
• 5 Acquisition, development and maintenance of maths anxiety in young children
• 6 Mathematics anxiety and working memory: what is the relationship?
• 7 The different involvement of working memory in math and test anxiety
• 8 Math anxiety in children with and without mathematical difficulties: the role of gender and genetic factors
• 9 Probing the nature of deficits in math anxiety: drawing connections between attention and numerical cognition
• 10 Gender stereotypes, anxiety, and math outcomes in adults and children
• 11 The role of parents’ and teachers’ math anxiety in children’s math learning and attitudes
• Concluding remarks
• Index