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Math Anxiety and Working Memory in Elementary School 1
Running head: MATH ANXIETY IN ELEMENTARY SCHOOL
Math Anxiety, Working Memory and Math Achievement in Early Elementary School
Journal of Cognition and Development, in press.
Gerardo Ramirez, Elizabeth A. Gunderson, Susan C. Levine, & Sian L. Beilock
Department of Psychology and Committee on Education
The University of Chicago
This research was supported by the NSF Science of Learning Center Grant SBE
0541957, the Spatial Intelligence and Learning Center (SILC), to Sian Beilock and Susan
Levine; by NSF CAREER DRL-0746970 to Sian Beilock; and by the National Center for
Education Research Grant Number R305C050076 to Gerardo Ramirez and Elizabeth
Gunderson.
Address correspondence to Sian L. Beilock, Department of Psychology, 5848 South
University Avenue, The University of Chicago, Chicago, Illinois 60637. Send electronic mail
to beilock@uchicago.edu.
Math Anxiety and Working Memory in Elementary School 2
Abstract
Although math anxiety is associated with poor mathematical knowledge and low course grades
(Ashcraft & Krause, 2007), research establishing a connection between math anxiety and math
achievement has generally been conducted with young adults, ignoring the emergence of math
anxiety in young children. In the current study, we explored whether math anxiety relates to
young children’s math achievement. One hundred and fifty-four first and second grade children
(69 boys, 85 girls) were given a measure of math achievement as well as working memory
(WM). Several days later, children’s math anxiety was assessed using a newly developed scale.
Paralleling work with adults (Beilock, 2008), we found a negative relation between math anxiety
and math achievement for children who were higher but not lower in working memory. High
working memory individuals tend to rely on WM-intensive solution strategies, and these
strategies are likely disrupted when WM capacity is co-opted by math anxiety. We argue that
early identification and treatment of math anxieties is important because these early anxieties
may snowball and eventually lead students with the highest potential (i.e., those with higher
WM) to avoid math courses and math-related career choices.
Keywords: Working memory, Math anxiety, Stress
Math Anxiety and Working Memory in Elementary School 3
Math Anxiety and Math Achievement in Early Elementary School
Math anxiety has long been recognized to play a role in the math achievement of middle-
and high-school students (Hembree, 1990). Various studies have linked math anxiety to
increased worries about math failure (Richardson & Woolfolk, 1980), to an avoidance of math
and/or numerical tasks (Krinzinger, Kaumann, & Willmes, 2009), and to an increased cortisol
response when performing math tasks (Faust, 1992; Mattarella-Micke, Mateo, Kozak, Foster, &
Beilock, 2011). Even the prospect of doing math has been found to be enough to elicit a negative
emotional response among students with high math anxiety (Lyons & Beilock, 2010). Math
anxiety is worrisome because it negatively impacts mathematical knowledge, math grades, and
standardized test scores in young adults (Ashcraft & Krause, 2007; Suinn, Taylor & Edwards
1988). Moreover, math anxiety is likely to impact the achievement of many students given that
survey results show that the majority of individuals in the U.S., regardless of cultural and
economic background, dislike and fear mathematics (Zasllavkey, 1994; Burns, 1998), and report
having negative experiences with math as early as elementary school (Jackson & Leffingwell,
1999).
Although math anxiety has been extensively studied, little is known about the emergence
of math anxiety in young children. Indeed, most studies of math anxiety have focused on middle-
school or high-school students and the few published studies investigating math anxiety in
elementary school have focused on children who are in the 4th grade or beyond (Bush, 1991;
Chiu & Henry, 1990; Suinn, Taylor & Edwards 1988). For example, Suinn, Taylor and Edwards
(1988) asked 1,119 fourth, fifth and sixth graders to complete a 26-item math anxiety
questionnaire, and found that students’ level of math anxiety was negatively correlated with
achievement scores on the Stanford Achievement Test of mathematics skills.
Math Anxiety and Working Memory in Elementary School 4
In the present study we examine whether math anxiety is present even earlier in
elementary school, in 1st and 2nd grade students. To our knowledge, this is the first study to
explore whether math anxiety is present at such a young age. We believe that it is important to
address math anxiety at the earliest possible ages since early math anxiety may ―snowball‖ in
ways that lead to increased anxiety, dislike, and avoidance of math (Wigfield & Meece, 1988).
Further, identifying math anxiety early is the first step in designing interventions to ameliorate
these anxieties, which in turn may contribute to higher math achievement in the population.
In examining math anxiety in young children, we formulated our specific hypothesis
based on the rich findings on math anxiety in older students. This literature has revealed that
math anxiety may negatively impact math performance by co-opting the limited working
memory (WM) resources that are crucial for successful math problem solving, which we refer to
as ―working memory disruption‖ (Ashcraft & Kirk, 2001; Ashcraft & Moore, 2009; Engle,
2002).
In one study examining the impact of math anxiety on WM, Ashcraft and Kirk (2001)
asked both low- and high-math-anxious college students to perform two-column addition
problems requiring a carry operation, which placed a load on working memory. Participants
performed these problems in combination with a secondary letter memory task that involved the
maintenance of either 2-letter strings or 6-letter strings in memory. When under the 2-letter load,
math error rates among participants who were higher in math anxiety were only slightly larger
than those who were lower in math anxiety. However, when under the 6-letter load, participants
who were higher in math anxiety produced significantly more math errors than lower-math-
anxious individuals. The authors concluded that the high letter load was particularly detrimental
to the participants who were higher in math anxiety because their worries about math co-opted
Math Anxiety and Working Memory in Elementary School 5
WM resources that might otherwise have been available to perform the difficult math problems.
These findings suggest that math anxiety exerts an online effect on students’ math performance
particularly in highly demanding test situations because anxieties deplete WM resources
(Beilock, 2008).
A related approach in the literature examining the impact of math anxiety on math
performance in older students has examined WM as an individual difference variable. Simply
put, some people have more of this cognitive capacity than others (Engle, 2002). Typically, the
more WM capacity people have, the better their performance on academic tasks such as problem
solving and reasoning (Engle, 2002) and the better they are at regulating their emotional
experiences (Schmeichel, Volokhov & Damaree, 2008; Schmeichel & Demaree, 2010). Thus,
one might imagine that those with higher WM would be best equipped to deal with the
difficulties associated with anxiety in educational settings. Lower WM individuals, on the other
hand, are thought to have limited capacity for problem computations to begin with, which means
that anxiety-induced consumption of WM may shrink this available capacity below the level
needed to successfully solve difficult math problems.
However, there is also a less intuitive prediction that can be made regarding how math
anxiety might relate to the math performance of individuals lower and higher in WM. Namely,
higher WM individuals might be more prone to poor performance as a function of math anxiety.
If high WM students rely heavily on problem-solving strategies that load WM, and math anxiety
specifically targets the WM system, this may make high WM students’ performance susceptible
to the impact of anxiety. In contrast, low WM students may rely on shortcuts or heuristic
strategies to solve math problems precisely because they cannot hold demanding problem-
Math Anxiety and Working Memory in Elementary School 6
solving algorithms in WM. Under this view, if anxiety negatively impacts the WM system, low
WM students would in a sense have little or nothing to lose compared to high WM students.
There is actually strong support for this less intuitive idea in research with adults
examining how performance pressure interacts with WM. For instance, Beilock and Carr (2005)
asked high and low WM individuals to complete a block of math problems under a low pressure
condition and then under a high pressure condition, which was meant to place individuals under
a heightened state of anxiety. In the absence of pressure, students with high WM outperformed
low WMs in their problem-solving accuracy. However, when individuals were asked to solve a
similar block of math problems under high pressure, high WM students’ math performance fell
to the level of those with low WM. Importantly, these effects were limited to difficult math
problems that required the most WM. In subsequent work, Beilock and colleagues (Beilock &
DeCaro, 2007) showed that both low WM and high WM students reported the same level of state
anxiety during math problem solving, suggesting that it was differential reliance on WM rather
than different perceptions of the situation that drove these patterns of performance.
Based on these findings, we hypothesized that young children who are high in WM may
be most vulnerable to performing poorly in math as a function of self-reported math anxiety.
Hence, we predicted that if math anxiety exists among our young study sample, it would be
negatively associated with math achievement particularly among high WM children (Barrouillet
& Lépine, 2005; Ackerman, 1988). Furthermore, in order to establish that our math anxiety
measure relates specifically to math achievement and is not simply a proxy measure for general
academic anxiety, we asked students to complete a measure of reading achievement as well as a
measure of math achievement. Our prediction was that higher WM children would show a
negative relation between self-reported math anxiety and math but not reading achievement.
Math Anxiety and Working Memory in Elementary School 7
Method
Participants
Children from 5 public schools in a large urban school district participated in this study.
This research was conducted as part of a larger study investigating the affective factors that
impact early learning (Beilock, Gunderson, Ramirez & Levine, 2010). Parental consent forms
were obtained from each child participating in the study. A total of 162 signed parental consent
forms were returned. From this sample, 94 were first grade students (47 male, 47 female) and 68
were second grade students (28 male, 40 female). The average age was 7.05 (SD=.59) with a
range from 5.37 to 8.81 years. The mean household income was $36,985 (SE =2.140). The
poverty line for a household of four in the United States, which is set annually by the US
Department of Health and Human Services, was $22,050 in 2009 (the year our data were
collected).
Tasks
The following tasks were administered to all children in the study. It should be noted that
although our scoring of these tasks did not take grade level into account, we control for grade
level in our analyses.
Total Digit Span: As a measure of WM, we used the Digit Span subtest score, which is a
composite of the forward and backward span tests on the Wechsler Intelligence Scale for
Children—Third Edition (WISC-III; Wechsler, 1991). The forward digit span task is a
commonly-used measure of immediate verbal short term memory and the backward digit span
task has been generally used as measure of executive attention in neuropsychological and
developmental research. We chose to use the combined forward and backward digit span scores
(total digit span) since WM is thought to be comprised of memory processes, measured by
Math Anxiety and Working Memory in Elementary School 8
forward digit span, and executive attention processes, measured by backward digit span (Engle,
2002).
In the forward digit span task, the child is read a series of digits (e.g. ―4, 9, 2‖) at a rate of
1 digit per second and is asked to immediately repeat them back. If they do this successfully
across two trials of the same set size, they are given a set size that is one digit longer. The set
size increases by one unit until the child fails on both trials at a particular set size. The possible
set sizes for the forward digit span ranged from 2 items up to 8 items. The backward digit span
task is a more challenging variation that also involves presenting digits at a rate of 1 digit per
second but then requires the child to recall the presented items in the reverse order. For example,
if the experimenter says ―6, 2, 9‖ the child is supposed to repeat back ―9, 2, 6.‖ The set size for
the backward digit span task begins at 2 items and goes up to a maximum of 7 items. For the
purpose of this study, the total digit span score consisted of the combined number of correct
trials on the forward and backward digit span tasks. Although the digit span task uses number
words as stimuli, it has been shown to be a measure of phonological memory span rather than a
measure of mathematical problem-solving ability (Anderson, 2007). Additionally, children’s
digit span scores were not related to math anxiety in our data (See Table 1 for descriptive
statistics for both 1st and 2nd grade levels).
Woodcock-Johnson III Applied Problems subtest: As a measure of math performance, we
administered the Woodcock-Johnson III Applied Problems subtest (Woodcock, McGrew, &
Mather, 2001), a nationally-normed, comprehensive test battery used for assessing the academic
achievement skills of individuals aged 2 through 90 years. On the Applied Problems subtest,
students are presented with increasingly difficult math-related word problems that require
comprehension of the nature of the problem, identification of relevant information, and
Math Anxiety and Working Memory in Elementary School 9
performance of relevant calculations. For instance, some of the early problems on this subtest
involve single digit arithmetic as well as identifying the correct time on a clock, whereas, later
problems require children to solve two digit arithmetic problems, money calculations and
calculations involving simple fractions. Testing continues until both a basal (6 items in a row
correct) and ceiling (6 items in a row incorrect) are established. Because of experimenter error, a
few participants only completed between three and five items for the basal or ceiling level. These
participants were scored as if they had completed the full basal or ceiling level. Moreover,
excluding these participants did not alter the significance of the results reported below in any
way. For all analyses involving the Applied Problems subtest, we used the W score, a
transformation of the raw score into a Rasch-scaled score with equal intervals (a score of 500 is
the approximate average performance of a 10-year-old).
Woodcock-Johnson III Letter-Word Identification subtest: Reading performance was
assessed using the Letter-Word Identification subtest of the Woodcock-Johnson III Tests of
Achievement. This subtest measures the ability to identify letters and words at increasing
difficulty levels. It is administered using the same basal and ceiling procedure as the Applied
Problems subtest. The W score was used in all analyses involving the Letter-Word Identification
subtest.
Child Math Anxiety Questionnaire (CMAQ): Our 8-item measure of math anxiety was
adapted from the Mathematics Anxiety Rating Scale for Elementary children (MARS-E: Suinn,
Taylor & Edwards, 1988), which was constructed for 4th-6th graders. In most cases, the questions
retained the original content but used math problems that were age appropriate. Some items
asked children their attitudes about solving particular problems that were drawn from
mathematics teaching workbooks for children in the early elementary grades (e.g. ―There are 13
Math Anxiety and Working Memory in Elementary School 10
ducks in the water, there are 6 ducks on land, how many ducks are there in all?‖). Other items
asked children about specific situations they might be confronted with at school concerning math
(e.g. ―being called on by a teacher to explain a math problem on the board‖). We asked children
to make their responses about each question using a sliding scale that featured a calm face on the
far right, a semi-nervous face in the middle and an obviously nervous face on the far left (see
appendix). We encouraged all children to use the full continuum of the scale, which allowed us
to derive numerical scores in between the faces. The numerical scale (which was invisible to
children) ranged from 1 to 16. We used the word ―nervous‖ when probing children for their
attitude and began the math anxiety session by giving students examples of what it means to be
nervous (e.g., ―looking down from the top of a really tall building‖). Each child’s CMAQ score
was calculated by taking an average of the 8 items.
Using Cronbach’s alpha, reliability for our 8 item math anxiety scale was found to be .55.
Although a coefficient alpha (Cronbach, 1951) of .70 is generally considered "acceptable" in
most social science research situations, it is important to highlight that an alpha coefficient below
.70 is quite common in published studies investigating attitudes among primary school children
(Giles & Heyman, 2003; Erdley, Cain, Loomis, Dumas-Hines, & Dweck, 1997). One reason is
that Cronbach’s alpha is highly influenced by the number of items in a scale. Most early
elementary scales must be shorter to accommodate time restrictions placed on school research so
that children do not miss too much classroom time and so they do not get fatigued. To keep our
testing session as short as possible, our measure of math anxiety in children was composed of
only 8 items (compared to adult and adolescent math anxiety measures that typically contain 26
to 95 items).
Procedure
Math Anxiety and Working Memory in Elementary School 11
All sessions were conducted one-on-one with an experimenter and took place during the
first three months of the school year. Each child was tested in a quiet area of the school. Testing
was spread across two sessions over the course of two to seven days. Students were assessed on
achievement measures during one day (session 1) and on math anxiety on a separate day (session
2) to minimize the influence of anxiety measures on achievement, and vice versa.
The achievement session began with an introduction that the child would be playing
some number and letter games. The three achievement measures were administered in one of two
orders, counterbalanced across children. Half of the children completed the WJ Letter-Word ID
task, followed by the WJ Applied Problems task, followed by the WISC-III Digit Span subtest.
The other half of the children completed the tasks in the reverse order. These three tasks
combined took an average of 15 minutes to administer.
For the math anxiety session, children were given the CMAQ embedded within other
questionnaires for a larger study. The CMAQ was described as a question game in which the
experimenter would ask the child a series of questions for which the child could answer using the
sliding scale. Before beginning the CMAQ, all the children were given a series of instructions to
help them understand the meaning of the word ―nervous‖ and to orient them about how to use
the sliding scale. Children also were given a few example questions and provided with feedback
about how to properly respond with the sliding scale to ensure that students had an idea of what
it means to be nervous. After children completed each session, they were thanked for their
participation and escorted back to their classroom.
Results
Our final sample consisted of 88 first grade students (42 male, 46 female) and 66 second
grade students (27 male, 39 female) for a total sample size of 154. Five additional participants
Math Anxiety and Working Memory in Elementary School 12
were removed from our analyses because they had a score missing on one or more of our four
measures (i.e., total Digit Span, Woodcock-Johnson III Applied Problems test, Letter Word
Identification, CMAQ). Three additional participants shown to be highly influential points using
Cook’s distance (Cook, 1977) in our primary regression analysis described below were also
removed.
Child Math Anxiety Questionnaire
We calculated children’s responses on the CMAQ using a mean across all items.
Children’s responses on the CMAQ did not differ as a function of grade [t(152)=1.042, p>.25] or
gender [t(152)=1.520, p>.10]. As shown in Figure 1, children’s responses on the CMAQ were
normally distributed with a mean of 8.07 (SD=2.86). Thus, even in early elementary school,
some students reported feeling nervous about various situations involving math. Importantly,
CMAQ scores did not correlate with children’s digit span scores controlling for grade level
[r(151)=.021, p=.80]. Nor did children’s CMAQ scores correlate with family’s annual gross
income [r(133)==.047, p=.589]. Thus, children as early as first and second grade reported feeling
―nervous‖ for various math-related situations, but these feelings of nervousness were not
associated with our measure of WM or traditional proxies of parental involvement.
Relation between math anxiety, WM, and math achievement
We began by regressing children’s math achievement on their math anxiety, WM (using
total digit span) and the interaction of math anxiety x WM. We also included children’s grade
level as a covariate. There was a significant main effect of grade [β=.335, t=5.474, p<.01] and
WM [β=.869, t=4.931, p<.01], but not math anxiety [β=.420, t=1.726, p>.05]. However, the
main effect of WM was qualified by a significant math anxiety x WM interaction [β=-.658, t=-
2.242, p =.026]. Figure 2 plots the predicted math achievement of children who are ±1 SD from
Math Anxiety and Working Memory in Elementary School 13
the mean in math anxiety and ±1 SD from the mean in WM. Note that WM and math anxiety in
figures 2 and 3 are treated as continuous variables, but are plotted at ±1 SD for descriptive
purposes.
As shown in Figure 2, the relation between math anxiety and math achievement is quite
different when plotted as a function of individual differences in WM. For students relatively
higher in WM (HWMs), there was a pronounced negative relation between math anxiety and
math achievement. This relation was not evident among students relatively lower in WM
(LWMs).
The above results are in line with findings in the adult literature showing that individuals
who rely more heavily on WM when solving math problems (i.e., those with high levels of WM)
are most impacted by anxiety because worries about the situation likely deplete the cognitive
resources that support their math performance (Beilock, 2008). If this explanation applies to our
results as well, that is, if math anxiety disrupts the performance of students who use
computationally difficult problem-solving strategies, then our predicted WM x math anxiety
interaction should be especially apparent for more difficult problems that likely require more
WM and encourage more varied problem-solving strategies.
Although we chose to use a standardized measure of math performance (WJ Applied
Problems) rather than to experimentally manipulate problem demand, we nevertheless sought to
examine children’s performance on higher- versus lower-demand problems within this
standardized task. To do this, we selected a section of the WJ math achievement test that a large
majority (over 97%) of the children encountered (items # 15-24) and excluded the four
participants who did not encounter these problems (bringing the total sample size for this
analysis to N=150). Since the WJ is organized progressively, so that items appearing later in the
Math Anxiety and Working Memory in Elementary School 14
test are more challenging than items appearing earlier, we divided these selected items in half as
a method of defining easy problems (items 15-19) versus difficult problems (items 20-24)1. We
then re-examined children’s performance on easy and hard problems separately, considering easy
versus hard problems to be a proxy for low- versus high-WM-demanding problems.
When we re-ran our main analysis using performance on the easy items as a DV, we
found a main effect for WM [β =.600, t=2.693, p<.01] but not for math anxiety [β = .350,
t=1.146, p>.05] or grade [β =.058, t=.746, p>.05 and did not find a significant WM x math
anxiety interaction [β=-.329, t=-.894, p>.05]. By contrast, when we reran our main analysis using
performance on the hard items as a DV, we found a main effect of grade [β =.210, t=2.83,
p<.01], WM [β =.828, t=3.886, p<.01], math anxiety [β =.590, t=2.021, p=.045], as well as the
critical two way WM x math anxiety interaction [β =-.770, t=-2.189 p=.030]. In other words,
when high WM children have high math anxiety, their performance is specifically impaired on
those math problems that typically require more complex, WM-demanding strategies.
Relation between math anxiety, WM, and reading achievement
1 The hard items differed from easy items in several important ways. In terms of subtraction problems, hard items
depicted images of objects that were scattered randomly (e.g., crayons piled on top of each other in an unorganized
fashion) making them difficult to count. In addition, these problems contained two-digit minuends. In contrast, easy
subtraction items depicted objects that were well organized in a linear fashion (e.g., pennies ordered along a line)
and contained single digit minuends. In terms of addition problems, hard items were worded to prime a max
problem solving approach (i.e., 3+6) whereas easy addition problems were worded to prime a min problem solving
approach (i.e., 6+3). This difference in wording is significant as a shift from max to min strategies is associated with
an increase in ease of processing and fewer errors (Geary, Hoard, Byrd-Craven & Desoto, 2004; Geary et al., 1992;
Siegler, 1987). Lastly, hard items asked children to read an analog clock which required children to recall specific
knowledge on how to tell time, whereas easy items simply asked children to point to a clock that displayed a specific
time (e.g., 7 o’clock), which only involved the recognition of specific numbers and clock configurations (e.g., 7).
Math Anxiety and Working Memory in Elementary School 15
To account for the possibility that our measure of math anxiety was tapping general test
or school-related anxiety, we also asked whether math anxiety was related to children’s reading
achievement. Importantly, when we re-ran the above analysis with reading achievement as the
outcome variable, we found a significant effect of grade [β =.373, t=5.823, p<.01] and WM
[β=.434, t=3.43, p<.01] but not math anxiety [β= -.099, t= -.443, p>.05]. In addition, we did not
find the critical interaction of math anxiety x WM [β= .011, t = .041, p>.05, see Figure 3]. Thus,
children’s CMAQ scores relate to math achievement and not reading achievement, suggesting
that our measure of math anxiety carries specific implications for math achievement per se rather
than for general academic achievement.
Discussion
A growing body of evidence highlights the importance of taking into account both
cognitive as well as affective factors in understanding students’ academic achievement.
However, most of the research on the relation of math anxiety and math achievement has been
carried out on middle school to college-age students. The work reported here shows that a self-
report measure of math anxiety is already associated with math achievement in children as early
as first and second grade. Moreover, our math anxiety measure was not related to children’s
reading achievement, suggesting it is not just a proxy for general academic anxiety.
Importantly, the association between math anxiety and math achievement is not present
in all 1st and 2nd grade students. Rather, the negative relation between math anxiety and math
achievement is present among children who are relatively high in WM but not among those who
are relatively low in WM. These results mirror findings in adults showing that the impact of
math anxiety on math achievement is specific to math performance for those with higher levels
of WM (Beilock & Carr, 2005; Beilock & DeCaro, 2007).
Math Anxiety and Working Memory in Elementary School 16
There are several possible explanations for the interaction between math anxiety and
level of WM. The explanation we favor is that children who rely more heavily on WM when
solving math problems (i.e., those with high levels of WM) are most impacted by math anxiety
because worries about the situation deplete or interfere with the cognitive resources that support
their math performance (Beilock & Carr, 2005; Beilock & DeCaro, 2007). Indeed, this
phenomenon is likely to occur in children as well as adults, since WM strongly influences
problem strategies and math performance even at a young age (Barrouillet & Lépine, 2005;
Barrouillet et al., 2004; Gavens & Barrouillet, 2004; Lépine, Barrouillet, & Camos, 2005).
High WM children, for example, are more likely to use direct retrieval as opposed to
finger counting when solving math problems (Barrouillet & Lépine, 2005) and retrieval
efficiency is particularly disrupted by interference (Barrouillet et al., 2004; Gavens &
Barrouillet, 2004; Lépine, Barrouillet, & Camos, 2005; Mattarella-Micke & Beilock, 2010). In
contrast, low WM children’s math achievement may remain relatively unaffected by math
anxiety precisely because they use less sophisticated (and less WM-demanding) problem-solving
strategies. Hence, the association between math anxiety and math achievement may be present
among high WM (but not low WM) children because math anxiety disrupts the resources that
high WM children rely on to retrieve basic facts from long-term memory and to inhibit
competing answers (Geary, Hoard, Byrd-Craven & DeSoto, 2004). Math anxiety may make high
WM children more prone to retrieval interference, resulting in a slower and less efficient
retrieval process. It is also possible that math anxiety-induced disruption of WM leads high WM
children to switch their problem-solving strategies as a means of circumventing the burden of
math anxiety on WM. Indeed, past work with adults (Beilock & DeCaro, 2007) and children
(Barrouillet & Lépine, 2005) suggests that factors that constrain WM (e.g., anxiety during math
Math Anxiety and Working Memory in Elementary School 17
tests, operand size) lead students to switch to less WM-demanding, less successful problem-
solving approaches.
There are however, several other alternative accounts for the relationship we found
between math anxiety and WM. For instance, higher-WM children may simply get farther along
on the math test than lower-WM children, and this could cause them to encounter more WM-
demanding problems that are specifically impaired by math anxiety. However, this does not
seem to be the case, as we found an interaction between WM and math anxiety even on problems
that virtually all students in our sample encountered.
Another possibility is that higher-WM children are simply more emotionally aware of
their math difficulties, which would lead these children to give more accurate self-reports of
math anxiety (leading to our observed correlation between math anxiety and math performance
among high WM students specifically). Although this is an interesting idea, there is research
suggesting that, when presented with negatively valenced images, when given negative feedback
about their abilities, or when provoked towards anger, higher-WM individuals are actually less
likely than their lower-WM counterparts to report experiencing negative emotions or to respond
in an emotional manner (Hofmann, Gschwendner, Friese,Wiers, & Schmitt, 2008; Joorman &
Gotlin, 2008; Schmeichel & Demaree, 2010; Schmeichel, Volokhov, & Demaree, 2008). Thus,
one could also imagine that lower-WM (rather than higher-WM) children would be more aware
of their low ability and better able to accurately report on their math difficulties and anxiety.
Future research is needed to explore these ideas.
Further support for the WM disruption account that we favor comes from our
examination of performance as a function of problem computational difficulty (e.g., easy vs.
hard). If the WM disruption account is in fact at work, then we should show a WM x math
Math Anxiety and Working Memory in Elementary School 18
anxiety interaction only among problems that are computationally demanding. This is exactly
what we found. Our results align well with work examining the impact of anxiety on math
performance in the adult literature, which typically reports that performance on the most
computationally demanding problems is affected by math anxiety (Ashcraft & Kirk, 2001;
Beilock & Carr, 2005; 2007). Of course, more direct support for the WM disruption hypothesis
could be provided by simply examining the problem-solving strategies that children employ as a
function of individual differences in WM and math anxiety. However, our use of a standardized
task as a measure for math performance precluded asking children to explicitly report their
problem-solving strategies as this would have disrupted the validity of the of the task2.
Given the correlational nature of the current work, we cannot make a causal claim about
the relationship between math anxiety and math performance nor can we conclusively determine
the specific mechanism that accounts for why high- but not low-WM children demonstrate a
negative relationship between math anxiety and math ability. Although it is not possible to
experimentally manipulate trait math anxiety, future studies that examine young children’s
2 One could also posit that there are some top-notch students (i.e. those with higher WM) who experience
math anxiety because they perform well in most domains (i.e. reading) except math. If top-notch students who
perform well in the domain of reading are developing math anxiety because of their particularly poor performance in
math, then we would expect that these students would show a stronger negative relationship between math ability
and math anxiety than those with low reading ability. To evaluate this possibility, we performed a median split of
reading ability on our students with higher WM. We found that among students with lower reading ability, math
ability and math anxiety were moderately associated [r(32)=-.402,p=.018] but this was not the case among children
with higher reading ability [r(34)= -.201,p=.239]. In other words, the pattern of results was the opposite of that
predicted by this alternative interpretation of the relation between WM, math anxiety, and math achievement.
Math Anxiety and Working Memory in Elementary School 19
responses to stressful, math testing situations may help to determine the causal relations between
math anxiety, WM, and performance in young children.
Undoubtedly, cognitive factors like working memory play an important role in academic
achievement by themselves as well (Gathercole, Alloway, Willis, & Adams, 2006). Our data is
consistent with this notion as Figures 2 and 3 show striking working memory differences in both
math and reading performance, suggesting the utility of using WM as a predictor of skill
acquisition and as an index of which children may potentially encounter academic difficulties.
The aforementioned results bolster the significance of the work reported here as it suggests that
young students who are quite competent may show sub-optimal math performance because math
anxiety usurps their potential cognitive advantage.
Thus, our data suggest that individual differences in cognitive factors such as working
memory and math knowledge do not tell the whole story about why many students perform
poorly in math. Educators should not only consider math learning in terms of concepts,
procedures, math curricula and instruction but also the emotions and anxieties children may
bring to the learning situation.
Even though this study puts forth an account of how math anxiety can affect math
performance online while children are solving math problems, we recognize that math anxiety
may also have an effect on math performance through an avoidance of math tasks (Hembree
1990; Krinzinger, Kaumann, & Willmes, 2009) perhaps by reducing expectations of success and
the subjective value of math (Eccles, Adler, Futterman, Goff, Kaczala, Meece, & Midgley, 1983;
Wigfield & Meece, 1988) as well by changing the achievement goals that students adopt in the
domain of math (Butler, 1999; Smiley & Dweck, 1994). Hence, early math anxiety may lead to a
snowball effect that exerts an increasing cost on math achievement by changing students’
Math Anxiety and Working Memory in Elementary School 20
attitudes and motivational approach towards math, increasing math avoidance behaviors,
interfering with cognitive processing when they are solving difficult math problems, and
ultimately reducing math competence. Avoidance and motivational factors may become more
prevalent later in schooling when students have to rely more on intrinsic forms of motivation and
are given more autonomy in choosing their math courses, college majors and career paths (e.g.,
National Mathematics Advisory Panel, 2008; Ryan & Pintrich, 1997).
Indeed, prior work suggests that math anxiety is associated with lower enrollment in math
intensive majors during college (Hembree, 1990). This can be particularly problematic as math
anxiety is endemic in college students who choose a career path in elementary school education
(Hembree, 1990) and previous work suggests that math anxious teachers impact their students’
math achievement (Beilock, Gunderson, Ramirez & Levine, 2010). These findings suggest that
addressing math anxiety at the teacher level may be an effective starting point in ameliorating
math anxiety in young children and improve children’s math achievement.
Of course, the effectiveness of interventions at the teacher level (Ping, Bradley,
Gunderson, Ramirez, Beilock, & Levine, 2011; Simon & Schifter, 1993) may work best when
used in conjunction with interventions at the student level as well (Betz, 1978; Hendel & Davis,
1978; Vance &Watson, 1994). Instruments such as the CMAQ used in the current work may
provide an effective tool in helping to identity young children whose insecurities about math may
prevent them from reaching their intellectual zenith. Since previous studies have examined math
anxiety interventions primarily among college students, it is important to develop interventions
that are specific to young child populations that are initially developing math anxiety. Our work
suggests that making students aware of alternative problem solving techniques that can withstand
the impact of math anxiety on working memory may be one such way to lessen the math anxiety-
Math Anxiety and Working Memory in Elementary School 21
math performance relationship. Such teaching activities , though infrequent in the earliest grades,
have been shown to improve the performance of low achieving students (Moely et al.,1992).
In conclusion, our results highlight the potential of math anxiety to negatively impact
children’s math achievement as early as first and second grade. The finding that children who are
higher in WM may be most susceptible to the deleterious effects of math anxiety is particularly
worrisome because these students arguably have the greatest potential for high achievement in
math. Investigating the development of math anxiety from the earliest grades will not only
increase our understanding of the relation between math anxiety and math performance across
the school years, but is also a critical first step in developing interventions designed to ameliorate
these anxieties and increase math achievement.
Math Anxiety and Working Memory in Elementary School 22
Acknowledgements
We thank the children, teachers and parents who gave their time to this research, and the research
assistants who helped carry it out: Claire Bradley, Jillian Aurisano, Nina Fleichler, Katie Foster,
Elizabeth Hickey, Laura Kasten, and Kristin Rotar.
Math Anxiety and Working Memory in Elementary School 23
References
Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition:
Cognitive abilities and information processing. Journal of Experimental Psychology:
General, 117(3), 288–318.
Anderson, U. (2007). The contribution of working memory to children’s mathematical word
problem solving. Applied Cognitive Psychology, 21(9), 1201-1216.
Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety,
and performance. Journal of Experimental Psychology: General, 130 (2), 224-237.
Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math
anxiety. Psychonomic Bulletin & Review, 14(2), 243-248.
Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in
performance. Journal of Psychoeducational Assessment, 27(3), 197-205.
Barrouillet, P., Bernardin, S., & Camos, V. (2004). Time constraints and resource sharing in
adults’ working memory spans. Journal of Experimental Psychology: General, 133(1),
83–100.
Barrouillet, P., & Lépine, P. (2005). Working memory and children’s use of retrieval to solve
addition problems. Journal of Experimental Child Psychology, 91(3), 183-204.
Beilock, S. L. & Carr, T. H. (2005). When high-powered people fail: Working memory and
"choking under pressure" in math. Psychological Science, 16(2), 101-105.
Beilock, S. L., & DeCaro, M. S. (2007). From poor performance to success under stress:
Working memory, strategy selection, and mathematical problem solving under
pressure. Journal of Experimental Psychology: Learning, Memory, & Cognition,
33(6), 983-998.
Math Anxiety and Working Memory in Elementary School 24
Beilock, S.L., Gunderson, E.A., Ramirez, G., & Levine, S.C. (2010). Female teachers' math
anxiety affects girls' math achievement. Proceedings of the National Academy of
Sciences, 107(5), 1060-1063.
Betz, N. (1978). Prevalence, distribution, and correlates of math anxiety in college
students. Journal of Counseling Psychology, 25(5), 441-448.
Burns, M. (1998). Math: Facing an American phobia. Sausalito, CA: Math Solutions
Publications.
Bush, W. S. (1991). Factors related to changes in elementary students' mathematics anxiety.
Focus on Learning Problems in Mathematics, 13(2), 3343.
Butler, R. (1999). Information seeking and achievement motivation in middle childhood and
adolescence: The role of conceptions of ability. Developmental Psychology, 35(1), 146-
163.
Chiu, L-H., & Henry, L.L. (1990). The Development and validation of the mathematics
anxiety rating for children. Journal of Measurement and Evaluation in
Counseling and Development 23(3), 121–212.
Cook, R.D., 1977. Detection of influential observations in linear regression. Technometrics
19(1), 15–18.
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika,
16(3), 297-334.
Eccles, J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J., and Midgley,C.
(1983). Expectancies, values and academic behaviors. In Spence, J. T. (ed.),
Achievement and Achievement Motives, W. H. Freeman, San Francisco.
Math Anxiety and Working Memory in Elementary School 25
Engle, R. W. (2002). Working memory capacity as executive attention. Current Directions in
Psychological Science, 11(1), 19-23.
Erdley, C., Cain, K., Loomis, C., Dumas-Hines, F., & Dweck, C.S. (1997). The relations among
children's social goals, implicit personality theories and response to social failure.
Developmental Psychology, 33(2), 263-272.
Faust, M. W. (1992). Analysis of physiological reactivity in mathematics
anxiety. Unpublished doctoral dissertation, Bowling Green State University,
Bowling Green, Ohio.
Gathercole, S.E., Alloway, T.P., Willis, C. & Adams, A-M. (2006) Working memory in children
with reading disabilities. Journal of Experimental Child Psychology, 93(3), 265-281
Gavens, N., & Barrouillet, P. (2004). Delays of retention, processing efficiency, and attentional
resources in working memory span development. Journal of Memory and Language,
51(4), 644–657.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choice in simple
and complex addition: Contributions of working memory and counting knowledge for
children with mathematical disability. Journal of Experimental Child Psychology, 88(2),
121–151.
Giles, J.W. & Heyman, G.D. (2003). Preschoolers’ beliefs about the stability of antisocial
behavior: Implications for navigating social challenges. Social Development, 12(2), 182-
197.
Geary, D. C., Bow-Thomas, C. C., & Yao, Y. (1992). Counting knowledge and skill in cognitive
addition: A comparison of normal and mathematically disabled children. Journal of
Experimental Child Psychology, 54, 372–391.
Math Anxiety and Working Memory in Elementary School 26
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research
in Mathematics Education, 21(1), 33-46.
Hendel, D.W., & Davis, S. O. (1978). Effectiveness of an intervention strategy for reducing
mathematics anxiety. Journal of Counseling Psychology, 25(5), 429-434.
Hofmann, W., Gschwendner, T., Friese, M., Wiers, R. W., & Schmitt, M.(2008). Working
memory capacity and self-regulatory behavior: Towardan individual differences
perspective on behavior determination byautomatic versus controlled processes. Journal
of Personality and Social Psychology, 95, 962–977.
Jackson, C., & Leffingwell, R. (1999). The role of instructors in creating math anxiety in
students from kindergarten through college. Mathematics Teacher, 92(7), 583-587.
Joormann, J. & Gotlib, I.H. (2008) Updating the contents of working memory in depression:
Interference from irrelevant negative material. Journal of Abnormal Psychology, 117(1),
182-192
Krinzinger, H., Kaufmann, L., & Willmes, K. (2009). Math anxiety and math ability in
early primary school years. Journal of Psychoeducational Assessment, 27(3), 206-225
Lépine, R., Barrouillet, P., & Camos, V. (2005). What makes working memory spans so
predictive of high level cognition? Psychonomic Bulletin and Review, 12(1), 165-170.
Lyons I.M. & Beilock, S.L. (2010, November). Mathematics Anxiety: Separating the math from
the anxiety. Poster presented at the annual Psychonomics meeting in St. Louis,
MO.
Mattarella-Micke, A., & Beilock, S.L. (2010). Situating math problems: The story
matters. Psychonomic Bulletin & Review, 17(1), 106-111
Mattarella-Micke, A., Kozak, M.N., Foster, K. & Beilock, S.L. (in press). The Relation
Math Anxiety and Working Memory in Elementary School 27
between salivary cortisol and math performance depends on individual
differences in working memory and math anxiety. Emotion.
Moely, B.E., Hart, S.S., Leal, L., Santulli, K.A., Rao, N., Johnson, T., et al. (1992). The teacher's
role in facilitating memory and study strategy development in the elementary school
classroom. Child Development, 63(3), 653-672
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the
National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
Ping, R.M., Bradley, C., Gunderson, E.A., Ramirez, G., Beilock, S.L. & Levine, S.C. (2011,
July). Alleviating anxiety about spatial ability in elementary school teachers. Poster
presented at the 33rd Annual Conference of the Cognitive Science Society, Boston, MA
Richardson, F. C, &. Woolfolk, R. L. (1980). Mathematics anxiety. In I. G. Sarason
(Ed.), Test anxiety: Theory, research and application (pp. 271-288). Hillsdale,
NJ: Erlbaum.
Ryan, A. M., & Pintrich, P. R. (1997). ―Should I ask for help?‖ The role of motivation and
attitudes in adolescents’ help seeking in math class. Journal of Educational Psychology,
89(2), 329-341.
Schmeichel, B.J. & Demaree, H.A. (2010). Working memory capacity and spontaneous emotion
regulation: High capacity facilitates self-enhancement in response to negative feedback.
Emotion, 10(5), 739-744.
Schmeichel, B. J., Volokhov, R., & Demaree, H. A. (2008). Working memory capacity and the
self-regulation of emotional expression and experience. Journal of Personality and
Social Psychology, 95(6), 1526-1540.
Math Anxiety and Working Memory in Elementary School 28
Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s
addition. Journal of Experimental Psychology: General, 116, 250–264.
Simon, M. A. & Schifter, D. (1993). Toward a constructivist perspective: The impact of a
mathematics teacher inservice program on students. Educational Studies in
Mathematics, 25(4), 331-340.
Smiley, P.S., & Dweck, C.S. (1994) Individual differences in achievement goals among young
children. Child Development, 65(6), 1723-1743.
Suinn, R.M., Taylor, S., & Edwards, R.W. (1988). Suinn Mathematics Anxiety Rating Scale for
Elementary school students (MARS-E): Psychometric and normative data. Educational
and Psychological Measurement, 48(4), 979-986.
Volokhov, R.N., & Demaree, H.A. (2010). Spontaneous emotion regulation to positive and
negative stimuli. Brain & Cognition, 73(1), 1-6.
Vance, W. R., Watson, T. S. (1994). Comparing anxiety management training and systematic
rational restructuring for reducing mathematics anxiety in college students. Journal of
College Student Development, 35(4), 261-266.
Wechsler, D. (1991). Wechsler Intelligence Scale for Children—Third Edition. San Antonio, TX:
The Psychological Corporation.
Wigfield, A. & Meece, J.L. (1988) Math Anxiety in elementary and secondary school students.
Journal of Educational Psychology. 80(2), 210-216
Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson III Tests of
Achievement. Itasca, IL: Riverside Publishing.
Zaslavsky, C. (1994). Fear of Math, How to Get Over It and Get On with Your Life. New
Brunswick, NJ: Rutgers University Press.
Math Anxiety and Working Memory in Elementary School 29
Tables and Figures
Table 1. Overall and grade level descriptive statistics for total digit span, math achievement,
reading achievement, math anxiety and child age. First grade students scored significantly below
second grade students (ps<.05) on all measures except for math anxiety (CMAQ), on which there
was no significant grade difference.
All students
(N=154)
1st Grade
(N=88)
2nd Grade
(N=66)
Mean (SD)
Mean (SD)
Mean (SD)
Total Digit Span
10.15 (2.49)
9.58 (2.42)
10.91 (2.40)
Math W Score
451.23 (18.56)
443.57 (16.29)
461.44 (16.55)
Reading W Score
436.79 (34.44)
422.11 (31.73)
456.36 (27.64)
CMAQ
8.07 (2.86)
8.28 (2.89)
7.79 (2.81)
Math Anxiety and Working Memory in Elementary School 30
Child Age
7.05 (0.59)
6.68 (0.46)
7.53 (0.30)
Figure 1. Histogram displaying the distribution of children’s CMAQ scores.
Math Anxiety and Working Memory in Elementary School 31
Figure 2. Students’ math achievement as a function of individual differences in working memory
(WM) and math anxiety. Working memory and math anxiety are plotted at 1 SD above and
below the mean. Children relatively higher in WM showed a pronounced negative relation
between math anxiety and math achievement.
Math Anxiety and Working Memory in Elementary School 32
410
420
430
440
450
460
470
Lower Math
Anxiety Higher Math
Anxiety
Math Anxiety
Math Achievement (W Score)
Lower WM
Higher WM
Figure 3. Students’ reading achievement as a function of individual differences in working
memory (WM) and math anxiety. Working memory and math anxiety are plotted at 1 SD above
and below the mean. Children relatively higher in WM showed higher reading achievement than
LWM children. However, these differences do not appear to be dependent upon math anxiety.
Math Anxiety and Working Memory in Elementary School 33
410
420
430
440
450
460
470
Lower Math
Anxiety Higher Math
Anxiety
Math Anxiety
Reading Achievement (W Score)
Lower WM
Higher WM
Math Anxiety and Working Memory in Elementary School 34
Appendix
Child Math Anxiety Questionnaire items
1. How do you feel when taking a big test in your math class?
2. How would you feel if you were given this problem: There are 13 ducks in the water.
There are 6 ducks in the grass. How many ducks are there in all?
3. How would you feel if you were given this problem: You scored 15 points. Your friend
scored 8 points. How many more points did you score than your friend?
4. How do you feel when getting your math book and seeing all the numbers in it?
5. How do you feel when you have to solve 27 + 15?
6. How do you feel when figuring out if you have enough money to buy a candy bar and a
soft drink?
7. How do you feel when you have to solve 34 – 17 ?
8. How do you feel when you get called on by the teacher to explain a math problem on the
board?
