^{*}

^{a}

^{a}

What causes math anxiety? According to a cognitive deficits view, early weaknesses in basic number and spatial skills lead to poor performance and hence negative affect. A strong version of this view suggests that the relation between math anxiety and math performance among adults will be explained by deficits in spatial and basic number skills. In the present research, we tested a model to account for the relations among math anxiety, math performance, and cognitive skills (i.e., working memory, basic number and spatial skills) among adults (N = 90). We replicated the modest correlations observed between math anxiety and these cognitive skills. However, we did not find a direct link between basic number and spatial skills and math anxiety; instead, these relations were mediated by complex math performance. We conclude by rejecting the hypothesis that math anxiety in adults is linked directly to individual differences in spatial and basic numerical skills and suggest instead that the present results are consistent with the alternative view in which even basic numerical tasks, under certain conditions may evoke an anxiety response and mask skill proficiency. Finally, we note that caution should be applied when extrapolating correlational results to make causal claims about whether cognitive skills may be precursors in the development of math anxiety.

Math anxiety is a negative response to participation in mathematical activities that has consequences for adults’ behavior (

Crucially, Ashcraft and colleagues (see

A

Notably, basic number skills correlate highly with adults’ mathematical performance on complex mathematical tasks (

One major limitation of the recent body of work on cognitive deficits and math anxiety is no single study has included a full range of cognitive predictors, that is, basic number skills, working memory, and spatial abilities, nor has mathematical performance been assessed. An alternative explanation of the correlations between basic number skills and math anxiety is that it reflects what we might call general number avoidance: Adults who are math anxious may show performance decrements in any task that involves numbers, especially in mildly stressful situations (e.g., speeded tasks). Rather than reflecting cognitive and spatial deficits, on this view, the correlations between basic numerical processes and math anxiety may reflect a generalized negative response to numerical tasks that has been acquired over the course of many years.

Alternative explanations for the inter-relations between cognitive skills and math anxiety are shown in

Strong version of the cognitive deficits model showing fundamental cognitive skills (specifically basic number and spatial skills) fully mediating the math-performance and math-anxiety relation.

Second, as shown in

The spatial deficits model showing spatial skills mediating the relation between mathematical skills and math anxiety.

In contrast, if acquired negative responses to number tasks explain the concurrent relations among these variables, then the relations shown in

The negative exposure explanation showing the relation between basic number skills and math anxiety is mediated by the relation between complex mathematical skills and math anxiety.

Some of the confusion and inconsistency in the literature on the relations between math anxiety and math performance has occurred because researchers have not clearly defined or assessed basic numerical competencies separately from more complex mathematical skills. Thus, in the present research we assessed both basic number skills and complex mathematical skills. To further refine the cognitive deficits hypothesis, we also measured spatial skills and basic number skills. To avoid the possibility that a single measure of basic number skills has some privileged relation with math anxiety, in the present research basic number skills were modeled as a latent factor with three indicator variables; symbolic magnitude comparison (

According to a

This hypothesis is a specific implementation of the strong cognitive skills hypothesis in which spatial skills are assumed to capture the shared variability between math performance and math anxiety.

As an alternative to a strong cognitive deficits model, the negative exposure explanation suggests that the correlation between basic number skills and math anxiety will be shared with complex skills. Shared relations between basic skills and complex math performance may account for some variance in math anxiety but more complex mathematical skills will also uniquely predict math anxiety. Importantly, this view holds that relations between math anxiety and math performance among adults will not be accounted for by deficits in basic cognitive and numerical skills.

In summary, the goal of the present research was to capture the observed correlations among the various cognitive predictors of math performance, and provide a more integrated description of how math anxiety is related to these predictors, as well as to complex mathematical performance. Young adults completed two mathematical performance measures, three tests of basic number skills, two small-scale spatial tasks, and control measures of verbal, visual-spatial, and executive working memory. Working memory is strongly related to math performance among adults (

Ninety adults were recruited from a Canadian university and the surrounding area (

Participants were tested in a quiet space either individually or in pairs. Total testing took approximately one hour. The order of the tests was: Math surveys, memory measures, magnitude comparison, mental rotation task, order judgement, number sets task, hidden figures and mathematical outcomes. This ordering was designed to provide a mix of short and simple tasks with more complex and time-demanding tasks, with the goal of minimizing fatigue and maximizing attention. Several additional measures were administered but are not discussed in the present analysis. Information about these tasks can be found in

Math anxiety was assessed with the 9-item Abbreviated Math Anxiety Scale (i.e., the AMAS;

Three memory measures were administered; forward digit span, backward digit span, and spatial span.

Three measures of basic number skills were administered; magnitude comparison, order judgment, and the number sets task.

Participants were instructed to place a check mark beside ordered sequences and an X beside unordered sequences. After a demonstration and practice, the participant was instructed to complete the task as quickly and accurately as possible. Scoring followed the same procedure as the magnitude comparison task, number correct per second. Results reported are the number of correct items per second averaged between Forms A and B.

Participants completed two small-scale spatial processing tasks: Mental rotation and hidden figures.

Two arithmetic assessments were used to index mathematical performance.

The means, standard deviations and ranges for all measured variables are reported in

The math anxiety measure (AMAS) had an observed mean of 22.6 (

Measure | Skew | Min | Max | ||
---|---|---|---|---|---|

Math Anxiety (AMAS) | 22.60 | 8.51 | 0.60 | 9 | 45 |

Working Memory | |||||

Forward Digit Span | 6.73 | 1.28 | -0.01 | 4 | 9 |

Backward Digit Span | 4.88 | 1.46 | 0.51 | 2 | 9 |

Spatial Span | 7.56 | 1.29 | -0.48 | 4 | 10 |

Number Skills | |||||

Symbolic Magnitude Comparison^{a} |
1.46 | .32 | 0.50 | 0.84 | 2.48 |

Order Judgement Task^{a} |
.54 | .20 | 0.43 | 0.25 | 1.04 |

Number Sets Task^{b} |
1.60 | .37 | 0.45 | 0.95 | 2.81 |

Spatial Skills | |||||

Mental Rotation Task^{c} |
9.40 | 4.71 | 0.23 | 1 | 21 |

Hidden Figures Task^{c} |
4.49 | 3.12 | 1.08 | 0 | 16 |

Complex Mathematics Skills | |||||

Addition^{d} |
15.26 | 6.87 | 0.84 | 4 | 35 |

Subtraction^{d} |
11.28 | 5.68 | 0.62 | 1 | 31 |

Multiplication^{d} |
6.69 | 5.33 | 0.91 | 0 | 22 |

Procedural Arithmetic – BMA3^{c} |
6.89 | 2.42 | 0.08 | 1 | 11 |

^{a}[number correct/sec.]. ^{b}[#correct-false alarms/sec.]. ^{c}number correct. ^{d}[number correct/min.].

Correlations among the individual tests are shown in

To reliably characterize the constructs for further analysis, individual measures were used to create composite scores. For basic number skills, three tasks were available to capture the construct: Number order, magnitude comparison and the number sets task. A principal component analysis was used to create the number skills factor score. The correlations among the three memory measures (forward digit, backwards digit, and spatial span) were not very high. Spatial span and backwards digit span however had similar patterns of correlation with the basic number and complex mathematical measures whereas forward digit span was only correlated with math anxiety. Spatial span and backwards digit span were thus chosen to index working memory as they were related to mathematical performance. These two measures were standardized and averaged to create a working memory composite score. The two small-scale spatial measures, mental rotation and the hidden figures task were also standardized and averaged to create a spatial processing composite score.

The correlations among the composite variables are shown in

Variable | Gender | Cognitive Measures |
Complex Mathematics |
|||
---|---|---|---|---|---|---|

WM | NS | SS | CFT | BMA3 | ||

Math Anxiety (AMAS) | .22* | -.05 | -.30** | -.25* | -.37** | -.43** |

Gender | .16 | -.18 | -.29** | .00 | .01 | |

Working Memory (WM) | .42** | .32** | .32** | .43** | ||

Number skills (NS) | .43** | .72** | .55** | |||

Spatial skills (SS) | .18 | .36** | ||||

Calculation fluency (CFT) | .64** | |||||

Procedural Arithmetic (BMA3) |

*

Our first step in evaluating how best to model the observed correlations was to evaluate the hypotheses described in the introduction using the PROCESS mediation software for SPSS (

To test Hypothesis 1, we conducted separate mediation analyses for the two complex mathematical measures (i.e., calculation fluency, procedural arithmetic). The question we addressed was whether basic number skills accounted for any of the relation between either complex mathematics measure and math anxiety. As shown in

Predictor | Mediator | Direct effect |
Indirect effect (mediation) |
||||
---|---|---|---|---|---|---|---|

unstandardized |
unstandardized |
standardized |
|||||

95% CI | 95% CI | β | 95% CI | ||||

Hypothesis 1 | |||||||

(a) Calculation Fluency | Number skills | -0.02 | -0.12, 0.06 | -0.05 | -0.23, 0.11 | ||

(b) Procedural Arithmetic | Number skills | -0.16 | -0.59, 0.20 | -0.05 | -0.16, 0.05 | ||

Hypothesis 2 | |||||||

(c) Calculation Fluency | Spatial skills | -0.02 | -0.06, 0.00 | -0.03 | -0.11, 0.00 | ||

(d) Procedural Arithmetic | Spatial skills | -0.13 | -0.48, 0.08 | -0.04 | -0.14, 0.02 | ||

(e) Number skills | Spatial skills | -0.54 | -1.38, 0.24 | -0.06 | -0.16, 0.03 | ||

Hypothesis 3 | |||||||

(f) Number skills | Calculation fluency | -0.58 | -2.30, 1.84 | ||||

(g) Number skills | Procedural arithmetic | -0.71 | -2.66, 1.25 |

*

Illustration of the mediation effects reported in

To test Hypothesis 2, we used spatial skills as the mediating variable. As shown in

Note, non-standardized coefficients are reported as suggested on the Process Macro website (

Hypothesis 3 tests a weak version of the Cognitive Deficits Model where relations between basic number skills and math anxiety are shared with relations between complex math skills and math anxiety. As shown in

Our next step was to situate the results of our mediation analyses within a broader model where all measured cognitive predictors were included. First, however, we clarified the relations between spatial skills and gender.

Spatial ability, gender, and math anxiety were all significantly (albeit weakly) inter-correlated (see

The analyses conducted to test Hypotheses 1 through 3 suggested that a model in which complex math skills mediate relations between number skills and math anxiety would be a reasonable fit for the present data. In the modified version, we show that weaknesses in basic numerical skills are related to math anxiety indirectly through complex math performance and that complex math performance accounts for additional unique variance in math anxiety. Spatial skills were not directly related to math anxiety, but may have an indirect relation through basic numerical skills. This model re-situates a cognitive deficit as specifically numerical, although the number skills themselves are linked to individual variability in domain-general cognitive skills. Further, this alternative model situates the connection between math performance and math anxiety at the level of more complex mathematical skills, while accounting for the patterns of simple correlations observed in previous research. This alternative model thus provides an integrated perspective on the pattern of relations among the cognitive variables, and shows that, among the range of potential predictors that we included in our study, complex math performance has the most direct connection to math anxiety. Note that this model does not include other possible predictors of math anxiety (specifically online working memory or specific negative experiences), but focuses solely on numerical and cognitive predictors and gender. The model was tested with structural equation modelling, as described below.

Two versions of the model were tested, one for each complex mathematical task, that is, calculation fluency and procedural arithmetic. Both basic number skills and calculation fluency were modelled as latent variables as shown in ^{2 =} 10.26,

Measurement model of relations between indicator and latent variables representing basic number skills and calculation fluency.

As shown in

The specific model including calculation fluency is shown in ^{2} value was not significant indicating the model did not differ significantly from the observed data (Model χ^{2}(31) = 34.37,

As shown in ^{2} for predicting basic number skills was 32% (^{2} = 0.079,

The model predicting math anxiety through procedural arithmetic (BMA3) is shown in ^{2}(17) = 16.24, ^{2} = 0.12,

*

We note two key differences between the calculation fluency model (Model 1;

In the present study, we developed and tested a statistical model to account for the interrelations among math anxiety, math performance, basic number skills and domain-general cognitive factors (i.e., spatial ability and working memory). To develop this model, we first tested hypotheses from the literature that proposed relations between basic cognitive deficits and math anxiety. Next we integrated these results to clarify the direct and indirect relations among these variables. By fitting path models, we showed that adults’ performance on calculation fluency and procedural arithmetic measures were moderately predictive of math anxiety. Most importantly, the relations between basic number skills and math anxiety were indirect in both models, that is, those relations were completely mediated by the more complex mathematics skills. Further, the relations between domain-general cognitive skills (i.e., spatial skills and working memory) and math anxiety were also indirect, mediated through either basic numerical and/or complex mathematical skills.

Our results show that research in which correlations between any of the fundamental cognitive and numerical skills and math anxiety are observed needs to be considered carefully in terms of what those correlations may or may not imply about causes and sources of math anxiety. The current work addresses limitations of previous research because multiple indicators of basic number skills, spatial skills and mathematical performance were assessed and modelled simultaneously. However, the model is still limited in that it does not capture any environmental influences on math anxiety and only explains a moderate portion of the variance in math anxiety. These results suggest that the links between cognitive skills and math anxiety should be interpreted cautiously within a broader perspective.

Correlational studies of math anxiety and basic cognitive skills (i.e., magnitude comparison, counting and mental rotation) have been used by some researchers to support the hypothesis that deficits in basic spatial and number skills may be risk factors for the development of math anxiety (

Similarly, no support was found for the hypothesis that spatial ability mediates the relation between math anxiety and gender for adults (cf.

To provide an integrated account of the pattern of data, we proposed and tested path models of the relations among the variables. The analyses clearly show that individual differences in domain-general cognitive predictors (working memory and spatial skills) are related to math anxiety indirectly either through complex math skills or through basic number skills. The latter are, in turn, related to math anxiety indirectly through complex math skills. One interpretation of this model is that math anxiety is a consequence of deficits in basic number skills (i.e., in acquiring those skills) that, in turn, accounts for poor performance on the more complex mathematical outcomes. This interpretation assumes that the deficits observed in basic number skills precede and contribute to the development of math anxiety (

Some support for the interpretation that numbers-based deficits precede math anxiety comes from research on children with developmental dyscalculia (i.e., deficits in basic number skills) who have much higher math anxiety levels than typically-developing children (

A second interpretation of our results is that the relation between basic number skills and math anxiety reflects the online attentional demands of the number tasks rather than a specific, long-standing deficit in number skills. This interpretation is consistent with the

The models also showed clearly that the relation between spatial skills and math anxiety is indirect for this adult sample; again, any claims about causality are not strongly supported by this pattern because basic and complex number skills fully mediated the relation between spatial skills and math anxiety. In contrast,

Finally, we found that the relation between spatial skills and mathematical performance was fully accounted for by shared relations with basic number skills. This finding adds to the literature on the relation between number and spatial skills. There is a strong body of research linking spatial skills, specifically visualization and mental rotation, to arithmetic performance in adults (see

In the current study, deficits in domain-general spatial and working memory skills among adults did not account for the relation between math anxiety and math performance and were indirectly related to math anxiety through more complex mathematical skills. A

In spite of the suggestion that math anxiety may arise in part from basic low-level deficits in numerical processing (

Variable | AMAS | Mathematics Outcomes |
||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Memory Spans |
Basic Number Skills |
Spatial Skills |
SF | Calculation fluency |
BMA3 | |||||||||

DSF | DSB | SS | MC | Order | # sets | MRT | HFT | add | sub | mult | ||||

gender | .22* | .11 | .07 | .19 | -.12 | -.16 | -.22* | -.21* | -.27* | -.09 | -.01 | .00 | .02 | .01 |

AMAS | -.26* | -.09 | -.01 | -.25* | -.28** | -.29* | -.12 | -.29** | -.33** | -.30** | -.39** | -.35** | -.43** | |

DS forward | .36** | .14 | .01 | .14 | .06 | .06 | .23* | .16 | .08 | .08 | -.02 | .20 | ||

DS back | .24* | .18 | .28** | .29** | .19 | .24* | .40** | .22* | .19 | .19 | .35** | |||

Spatial span | .36** | .31** | .37** | .30** | .11 | .37** | .33** | .25* | .21 | .32** | ||||

Mag compar | .66** | .78** | .23* | .28** | .69** | .64** | .58** | .56** | .41** | |||||

ordering | .79** | .27* | .41** | .72** | .66** | .64** | .58** | .55** | ||||||

Number set | .46** | .32** | .76** | .64** | .59** | .57* | .55** | |||||||

Rotation | .36** | .25* | .07 | .01 | .04 | .33** | ||||||||

Hidden fig. | .22* | .23* | .27* | .20 | .27** | |||||||||

Simple Flu | .63** | .64** | .55** | .54** | ||||||||||

CF Addition | .82** | .79** | .58** | |||||||||||

CF Subtract | .80** | .60** | ||||||||||||

CF Multiply | .61** |

*

Model | Spatial skills on AMAS through number and complex math | Number skills on AMAS through complex math | WM on AMAS through number and complex math | WM on complex math through number | Gender on AMAS through spatial, number and complex math |
---|---|---|---|---|---|

Model 1: Calculation Fluency | -.33* | -.11* | .25** | .04 | |

Model 2: Procedural Arithmetic | -.08* | -.21** | -.16** | .48** | .03* |

*

This research was supported by a Discovery Grant from the National Sciences and Engineering Research Council of Canada to J. LeFevre.

The authors have declared that no competing interests exist.

We would like to thank both Kelsey MacKay and Brianna Herdman for their assistance in data collection as well as the members of the MathLab at Carleton for their input and guidance.

The underlying data for this article can be made available by contacting the authors.