## Abstract

Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.

## Introduction

Math anxiety can have a significant effect on math performance and achievement in school. It can be thought of as a type of performance-based anxiety (Hopko, McNeil, Zvolensky, & Eifert, 2001) that includes both increased physiological arousal and negative thoughts that can interfere with one's attempts to solve basic and complex math problems (Ashcraft & Kirk, 2001; Dew, Galassi, & Galassi, 1984; Levine, 1995; Richardson & Suinn, 1972).

High levels of math anxiety can have a significant and negative impact on the math performance level (Ashcraft & Faust, 1994; Ashcraft & Kirk, 2001; Ashcraft & Krause, 2007; Miller & Bichsel, 2004). Gender may affect this relationship, as women report higher levels of math anxiety than men (Miller & Bichsel, 2004; Zettle & Raines, 2000). In a study of gender and math anxiety, however, Hembree (1990) found that although women reported higher levels of math anxiety than men, this did not negatively affect their math performance level. At the very least, the presence of math anxiety, independent of gender, can result in higher numbers of errors and a greater time to completion on math-related tasks (Ashcraft & Faust, 1994; Faust, Ashcraft, & Fleck, 1996; Hopko et al., 2003). The math anxiety level also has a more significant negative effect on complex (“9 × 16”) versus simple (“2 + 4”) math problems (Ashcraft & Faust, 1994; Faust et al., 1996), but can also exert an influence on simple object counting (Maloney, Risko, Ansari, & Fugelsang, 2010) and judging numerical distances (Maloney, Ansari, & Fugelsang, 2011). Collectively these results indicate that the relationship between math anxiety and performance on math-related tasks is complex and multifaceted, but it is likely that the level of working memory resources needed to complete a complex versus a simple task may also impact the level of performance.

Math anxiety can also negatively affect other areas of cognitive and psychosocial functioning. For example, it exerts a negative effect on academic achievement—both in math (Ma, 1999; Zakaria & Nordin, 2008) and general scholastic aptitude (i.e., Scholastic Aptitude Test scores; Cassaday & Johnson, 2002), as well as on performance IQ tasks (Block Design and Picture Arrangement from the Wechsler Adult Intelligence Scale-III Edition [WAIS-III]; Hopko, Crittendon, Grant, & Wilson, 2005). In addition, math anxiety negatively affects some measures of working memory, including visual paper-folding (Miller & Bichsel, 2004), learning a visual sequence of letters (Ikeda, Iwanaga, & Seiwa, 1996), letter transformations (Eysenck, 1985), and verbal reasoning (Markham & Darke, 1991). Individuals with a high level of math anxiety tend to avoid upper-level, more complex math classes, which can in turn affect the levels of math achievement (Maloney & Beilock, 2012).

It is possible that math anxiety, including its associated negative cognitions and ruminations, taxes the working memory system (Ashcraft, 2002; Ashcraft & Moore, 2009; Eysenck & Calvo, 1992). Recent neuroimaging evidence indicates that math anxiety increases activation in the right amygdala but decreases activity in the posterior parietal and dorsolateral prefrontal cortices (Young, Wu, & Menon, 2012), areas also implicated in working memory (Hillary, 2008) and mathematical reasoning (Menon, Rivera, White, Glover, & Reiss, 2000). Math anxiety can impair working memory resources (Ashcraft & Kirk, 2001; Beilock, 2010) and thus may impair performance on measures of working memory ability.

The WAIS-IV (Wechsler, 2008) is a commonly used measure of adult intelligence. It assesses intelligence across four primary domains: verbal comprehension, perceptual reasoning, working memory, and processing speed. Factor analyses of the WAIS-IV normative and secondary samples have supported this factor structure, with working memory having been assessed by Digit Span (DS) and Arithmetic subtests (Canivez & Watkins, 2010; Holdnack, Zhou, Larrabee, Millis, & Salthouse, 2011). In our clinical practice, we have seen a series of patients who perform in the Average range on the DS subtest from the WAIS-IV Working Memory Index (WMI), but who then perform significantly below expectations on the Arithmetic subtest. A significant portion of these patients also self-reported high levels of math anxiety, both during their school-aged years and at present. These patients also completed the Letter-Number Sequencing (LNS) supplemental subtest, in order to more fully assess working memory function, and performed in the Average range, suggesting that math anxiety may have been negatively affecting their Arithmetic performance. The present study sought to examine relationships between the math anxiety level and performance on the individual WAIS-IV WMI subtests. It was hypothesized that math anxiety would negatively affect performance on the Arithmetic but not the DS or LNS subtests.

## Materials and Methods

### Participants and Procedure

The study was approved by the university's Institutional Review Board. Participants were 172 undergraduate students (70 men), ages 18–32 (mean age 19.10 [*SD* = 1.81]) enrolled in psychology courses at a regional campus of a large university who received course credit for participation in the study. Racial/ethnic status was as follows: 82.0% Caucasian, 5.2% African American, 4.1% Asian/Pacific Islander, 1.7% Hispanic, and 7.0% Biracial/Other.

All participants provided written informed consent. Participants first completed a series of questionnaires, including the Adult Manifest Anxiety Scale (AMAS)-College version (Reynolds, Richmond, & Lowe, 2003), Math Anxiety Rating Scale-Revised (MARS-R; Plake & Parker, 1982), and State-Trait Anxiety Inventory (STAI) state subscale (Spielberger, 1983), as part of a larger study. Next, they completed the DS, Arithmetic, and LNS subtests from the WAIS-IV (Wechsler, 2008). At the end of the study, participants completed the Math Computation subtest from the Wide Range Achievement Test-IV (WRAT-IV; Wilkinson & Robertson, 2006). All participants were then debriefed and course credit was assigned. Partway through data collection, the order of the WAIS-IV tasks was changed from the typical administration order to a secondary order (DS, LNS, Arithmetic) to determine if math anxiety, which may have increased on the Arithmetic section, influenced performance on LNS.

### Measures

The MARS-R (Plake & Parker, 1982) is a 24-item revision of the original 98-item MARS (Richardson & Suinn, 1972). Participants respond to items on a 5-point Likert-type scale, with responses ranging from 0 (not at all) to 4 (very much), with higher summed scores indicating higher levels of math anxiety. The MARS-R correlates highly with the MARS (*r* = .97; Plake & Parker, 1982). Evidence is inconsistent regarding the presence of subscales on the MARS-R, but total scores are moderately correlated with state anxiety from the STAI and with test anxiety from the Test Anxiety Inventory (Hopko, 2003). Internal consistency was high in our sample (*α* = 0.96).

The college student version of the AMAS (Reynolds et al., 2003) was administered. The college student version of the AMAS contains 49 items encompassing four scales: worry/oversensitivity, social concerns/stress, physiological anxiety, and test anxiety. Individuals respond to a series of statements regarding anxiety with either a “yes” or “no” answer, and scores are then summed on each subscale. Construct validity of the AMAS was shown through moderate correlations with other measures of anxiety, including the STAI and the Endler Multidimensional Anxiety Scales, and small correlations with the Tennessee Self-Concept Scale (Lowe, Peyton, & Reynolds, 2007). One-week (*r* = .82; Reynolds et al., 2003) and 8-week (*r* = .84; Lowe et al., 2007) test–retest reliability were both high for the test anxiety subscale, and internal consistency was high in our sample (*α* = 0.86).

The STAI (Spielberger, 1983) is a 40-item measure created to assess two aspects of anxiety: current (state) and generalized (trait). State anxiety may depend more on the situational cues in a given context, whereas trait anxiety is a more stable and enduring form of anxiety. Factor analyses support this 2-factor structure (Vagg, Spielberger, & O'Hearn, 1980). Only the state subscale score was used in the present study, with higher scores indicating a higher level of anxiety. The STAI was designed for use with college students and adults, and test–retest reliability was low for state (as designed for a state-dependent measure; 1-h *r* = .16–.33; Spielberger, 1983). In the present study, internal consistency was moderate for this subscale (*α* = 0.52).

The Math Computation subtest of the WRAT-IV (Wilkinson & Robertson, 2006) assesses basic computational written math skills. It was utilized in the present study as an estimate of participants' math proficiency level. Participants are asked to complete a series of 40 math problems, ranging from simple arithmetic to division by fractions. Performance on this task is calculated by counting the total number of correct answers. Internal consistency was high across all age groups assessed in the normative sample (*α* = 0.83–0.95; Wilkinson & Robertson, 2006).

The WMI from the WAIS-IV (Wechsler, 2008) assesses different components of working memory. The DS subtest has three sections of increasingly more difficult tasks: forwards, backwards, and sequencing (i.e., lowest to highest). The Arithmetic subtest assesses working memory by having participants complete mental arithmetic problems. The LNS subtest is an alternative working memory measure and is not typically included in the calculation of the WMI. The LNS subset is similar to the DS subtest, only using numbers and letters (i.e., individuals sequence numbers in order lowest to highest, followed by the letters in alphabetical order). Summed raw scores were calculated for each subtest, with higher scores indicating a greater level of performance.

### Data Analysis

First, scores on the STAI-state were examined to determine if any participants were experiencing a high level of state-dependent anxiety that may have affected test performance. Six participants reported high levels of state anxiety (i.e., scores over 2 SD above the mean anxiety level) and were removed from further analyses. Next, correlations were calculated between the study variables. A series of linear regression analyses were conducted on the following criterion variables (all utilized raw scores): DS-Forward, DS-Backward, DS-Sequencing, Arithmetic, and LNS. As gender relates to performance on the Arithmetic subtest (*see*Lynn & Irwing, 2008), and there is evidence that situational anxiety, such as can occur in testing situations, can also affect working memory resources (Sorg & Whitney, 1992), these factors were entered as covariates into the analyses. Specifically, gender, test anxiety, and math achievement level were entered in Step 1 and the MARS score in Step 2.

## Results

Means and standard deviations for the study variables are provided in Table 1. Significant correlations were noted between study variables (Table 2). Specifically, gender (coded as women 1 and men 2) was positively correlated with WRAT-math and Arithmetic (thus, male gender was associated with better performance on these tasks) but negatively correlated with test anxiety (indicating female gender was associated with higher levels of test anxiety). Math anxiety was positively correlated with test anxiety but negatively correlated with WRAT-math and Arithmetic scores. WRAT-math scores were positively correlated with DS-backwards, DS-sequencing, and Arithmetic scores and negatively correlated with test anxiety. Test anxiety was negatively correlated with DS-backwards and Arithmetic. Finally, intercorrelations between the WAIS-IV WMI subscales were as expected (i.e., high positive correlations between tasks).

Variable | M | SD | Range |
---|---|---|---|

AMAS-Test Anxiety | 8.23 | 4.14 | 0–15 |

MARS-R | 36.19 | 19.39 | 1–96 |

STAI-State | 38.13 | 8.94 | 20–56 |

WRAT-IV Math Computation | 39.83 | 5.53 | 25–53 |

Digit Span-Forwards | 10.17 | 2.05 | 5–16 |

Digit Span-Backwards | 7.83 | 1.98 | 4–15 |

Digit Span-Sequencing | 8.53 | 1.76 | 4–14 |

Arithmetic | 12.16 | 2.94 | 7–20 |

Letter-Number Sequencing | 18.92 | 2.71 | 11–26 |

Variable | M | SD | Range |
---|---|---|---|

AMAS-Test Anxiety | 8.23 | 4.14 | 0–15 |

MARS-R | 36.19 | 19.39 | 1–96 |

STAI-State | 38.13 | 8.94 | 20–56 |

WRAT-IV Math Computation | 39.83 | 5.53 | 25–53 |

Digit Span-Forwards | 10.17 | 2.05 | 5–16 |

Digit Span-Backwards | 7.83 | 1.98 | 4–15 |

Digit Span-Sequencing | 8.53 | 1.76 | 4–14 |

Arithmetic | 12.16 | 2.94 | 7–20 |

Letter-Number Sequencing | 18.92 | 2.71 | 11–26 |

*Notes*: AMAS = Adult Manifest Anxiety Scale; MARS-R = Math Anxiety Rating Scale Revised; STAI = State-Trait Anxiety Inventory; WRAT-IV = Wide Range Achievement Test-fourth edition.

Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Gender | — | −.120 | .174* | −.269** | .019 | .040 | .120 | .324** | .020 |

MARS | — | −.282** | .417** | −.081 | −.083 | −.117 | −.318** | −.085 | |

WRAT-IV | — | −.211** | .019 | .217** | .192** | .572** | .080 | ||

AMAS-C | — | −.123 | −.161* | −.107 | −.227** | .019 | |||

DS-F | — | .396** | .200** | .152* | .439** | ||||

DS-B | — | .309** | .332** | .521** | |||||

DS-S | — | .276** | .343** | ||||||

Arith | — | .337** | |||||||

LNS | — |

Variable | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Gender | — | −.120 | .174* | −.269** | .019 | .040 | .120 | .324** | .020 |

MARS | — | −.282** | .417** | −.081 | −.083 | −.117 | −.318** | −.085 | |

WRAT-IV | — | −.211** | .019 | .217** | .192** | .572** | .080 | ||

AMAS-C | — | −.123 | −.161* | −.107 | −.227** | .019 | |||

DS-F | — | .396** | .200** | .152* | .439** | ||||

DS-B | — | .309** | .332** | .521** | |||||

DS-S | — | .276** | .343** | ||||||

Arith | — | .337** | |||||||

LNS | — |

*Notes*: MARS = Math Anxiety Rating Scale; WRAT = Wide Range Achievement Test-IV, Math subtest; AMAS-C = Adult Manifest Anxiety Scale, College Version, Test Anxiety subscale; DS-F = WAIS-IV Digit Span subtest, Forwards; DS-B = WAIS-IV Digit Span subtest, Backwards; DS-S = WAIS-IV Digit Span subtest, Sequencing; Arith = WAIS-IV Arithmetic subtest; LNS = WAIS-IV Letter-Number Sequencing subtest.

**p* ≤ .05.

***p* ≤ .01.

Results of the linear regression analyses indicated differing relationships between math anxiety and working memory task performance. There were no significant predictors of DS-Forward, DS-Sequencing, or LNS (all *p*s > .146; Table 3). For DS-Backwards, the overall analysis of variance (ANOVA) was significant, *F*(4,154) = 2.42, *p* = .051, *R*^{2} = .059. Participants who scored higher on the WRAT-math (*B* = 0.069, *p* = .021) performed better on DS-Backwards than those who scored lower. For Arithmetic, the overall ANOVA was significant, *F*(4,154) = 24.67, *p* < .001, *R ^{2}* = .391. Those high in math anxiety performed worse than those low in math anxiety (

*B*= −0.023,

*p*= .030). In addition, scores on Arithmetic were higher for men than women (

*B*= 1.210,

*p*= .002) and for those scoring high on the WRAT-math than those scoring low (

*B*= 0.259,

*p*< .001).

Criterion | Predictors | F | p | R ^{2} | B | p |
---|---|---|---|---|---|---|

DS-F (raw) | 0.60 | .660 | .015 | |||

Gender | −0.071 | .840 | ||||

AMAS-C | −0.057 | .205 | ||||

WRAT Math | −0.007 | .830 | ||||

MARS | −0.003 | .737 | ||||

DS-B (raw) | 2.42 | .051 | .059 | |||

Gender | 0.000 | .999 | ||||

AMAS-C | −0.066 | .121 | ||||

WRAT Math | 0.069 | .021 | ||||

MARS | 0.005 | .594 | ||||

DS-S (raw) | 1.73 | .146 | .043 | |||

Gender | 0.262 | .384 | ||||

AMAS-C | −0.012 | .754 | ||||

WRAT Math | 0.051 | .061 | ||||

MARS | −0.003 | .697 | ||||

Arith (raw) | 24.67 | .000 | .391 | |||

Gender | 1.210 | .002 | ||||

AMAS-C | 0.003 | .948 | ||||

WRAT Math | 0.259 | .000 | ||||

MARS | −0.023 | .030 | ||||

LNS (raw) | 0.46 | .763 | .012 | |||

Gender | 0.323 | .479 | ||||

AMAS-C | 0.041 | .480 | ||||

WRAT Math | 0.015 | .706 | ||||

MARS | −0.011 | .353 |

Criterion | Predictors | F | p | R ^{2} | B | p |
---|---|---|---|---|---|---|

DS-F (raw) | 0.60 | .660 | .015 | |||

Gender | −0.071 | .840 | ||||

AMAS-C | −0.057 | .205 | ||||

WRAT Math | −0.007 | .830 | ||||

MARS | −0.003 | .737 | ||||

DS-B (raw) | 2.42 | .051 | .059 | |||

Gender | 0.000 | .999 | ||||

AMAS-C | −0.066 | .121 | ||||

WRAT Math | 0.069 | .021 | ||||

MARS | 0.005 | .594 | ||||

DS-S (raw) | 1.73 | .146 | .043 | |||

Gender | 0.262 | .384 | ||||

AMAS-C | −0.012 | .754 | ||||

WRAT Math | 0.051 | .061 | ||||

MARS | −0.003 | .697 | ||||

Arith (raw) | 24.67 | .000 | .391 | |||

Gender | 1.210 | .002 | ||||

AMAS-C | 0.003 | .948 | ||||

WRAT Math | 0.259 | .000 | ||||

MARS | −0.023 | .030 | ||||

LNS (raw) | 0.46 | .763 | .012 | |||

Gender | 0.323 | .479 | ||||

AMAS-C | 0.041 | .480 | ||||

WRAT Math | 0.015 | .706 | ||||

MARS | −0.011 | .353 |

*Notes*: DS-F = WAIS-IV Digit Span subtest, Forwards; DS-B = WAIS-IV Digit Span subtest, Backwards; DS-S = WAIS-IV Digit Span subtest, Sequencing; Arith = WAIS-IV Arithmetic subtest; LNS = Letter-Number Sequencing; AMAS-C = Adult Manifest Anxiety Scale, College Version, Test Anxiety subscale; WRAT Math = Wide Range Achievement Test-IV, Math subtest; MARS = Math Anxiety Rating Scale.

We further examined LNS performance, broken down by the order of WMI subtest administration. If math anxiety “carried over” following the completion of the Arithmetic subtest, then scores on LNS should be lower in those who completed this task after Arithmetic. An independent-samples *t*-test indicated that participants who completed the typical WAIS-IV order (DS, Arithmetic, LNS) did not perform differently from those who completed the alternate order (DS, LNS, Arithmetic), *t*(163) = 1.314, *p* = .191. Thus, the negative effects of math anxiety appear limited to the Arithmetic subtest.

## Discussion

The present study sought to examine the relationships between math anxiety and performance on the WAIS-IV WMI subscales. As hypothesized, math anxiety was a significant predictor of Arithmetic but not DS or LNS performance, even after accounting for gender, math achievement, and test anxiety. Although previous research has shown math anxiety to negatively affect performance on various working memory tasks (Eysenck, 1985; Ikeda et al., 1996; Markham & Darke, 1991; Miller & Bichsel, 2004), our results suggest that the type of working memory task utilized matters. Tasks that utilize mathematical operations to assess working memory skills, such as Arithmetic, may activate underlying math anxiety, in turn negatively affecting scores. Neuroimaging studies have indicated that math anxiety increases activation in structures associated with working memory and mathematical reasoning (Young et al., 2012), which may help explain the present results.

We also found that the math achievement level, as assessed with the WRAT-IV math computation subtest, was the predictive of both Arithmetic and DS-backwards performance. The link between math achievement and DS-backwards, a task that does not involve mathematical operations per se, may be due in part to the multifaceted nature of the DS task. DS-backwards may assess cognitive reasoning skills, such as may also be operating during Arithmetic, rather than frank cognitive efficiency, which is likely operating during DS-forwards.

The results of this study have implications for clinical practice. The assessment of working memory skills with the WAIS-IV WMI is just one set of measures used in clinical practice, but other measures of working memory used by clinicians may also fall victim to the negative effects of math anxiety. Tasks such as the Paced Auditory Serial Addition Task (PASAT; Gronwall, 1977) or Auditory Consonant Trigrams (ACT; Stuss, Stethem, & Poirer, 1987), when administered to those high in math anxiety, may result in underestimates of working memory abilities. In addition, some tasks assessing working memory may in fact assess multiple cognitive systems, including attention, working memory, cognitive reasoning, visuospatial perception, and visual reasoning, depending on the specific task. Although previous confirmatory factor analyses of the WAIS-IV have supported a WMI comprised of DS and Arithmetic, loadings on the WMI factor were higher for DS and LNS than Arithmetic across studies (Benson, Hulac, & Kranzler, 2010; Canivez & Watkins, 2010). At least in those with high math anxiety, we recommend utilizing DS and LNS to estimate working memory abilities on the WAIS-IV. Working memory tasks are often used in the evaluation of such clinical syndromes as Attention-Deficit/Hyperactivity Disorder (ADHD) and head injury, where working memory skills may be impaired. Thus, accurate assessment of these abilities—and not of math-related anxiety—is necessary.

We also found a significant correlation between gender and math achievement level, in that men tended to have higher scores on the WRAT-IV math than women. This finding correlates with previous studies showing gender differences in math abilities in older children and adolescents (Heil & Jansen-Osmann, 2008; Liu, Wilson, & Paek, 2008; Rosselli, Ardila, Matute, & Inozemtseva, 2009). The only previous research found examining gender effects on the WRAT found an absence of gender differences on the WRAT-R (Haddad & Bardos, 1990). Our results indicate that gender may influence performance on math achievement tests and that this should be taken into account in the interpretation of WRAT-IV test scores.

There were several limitations to the present study. We utilized a sample of undergraduate students who did not present for clinical evaluation. As noted earlier, weaknesses in working memory are often used as indicators of dysfunction in clinical conditions such as ADHD and Mild Traumatic Brain Injury (TBI). To determine the potential diagnostic implications of math anxiety on WMI scores, the clinical correlation of the present findings in a clinical sample (e.g., ADHD, TBI, Multiple Sclerosis) is warranted. We limited our assessment of working memory to WAIS-IV subtests. It is unclear to what extent the present results may generalize to other working memory tasks with a math component that are typically used in neuropsychological batteries, including the PASAT and ACT. Based on our results, it is not unreasonable to suspect that math anxiety may impact performance on these measures as well; however, this will require additional investigation.

In conclusion, we found preliminary evidence that math anxiety has a significant negative effect on Arithmetic but not DS or LNS from the WAIS-IV, above and beyond that accounted for by gender, math achievement, and test anxiety. Future studies should further examine this relationship in an evaluation-seeking sample for clinical correlation. In clinical practice, if a significant split is noted in scores between DS and Arithmetic, the level of math anxiety should be evaluated and the LNS subtest administered. An examination of the extent of the negative effects of math anxiety on other numerically-based working memory tasks is warranted in order to determine which clinical tasks may be prone to interference from this form of anxiety.

## Conflict of Interest

None declared.

## References

*g*defined as working memory capacity