Edited by: Christoph M. Michel, University of Geneva, Switzerland
Reviewed by: Nicolas Langer, Child Mind Institute, USA; Jianhui Wu, Institute of Psychology, Chinese Academy of Sciences, China
*Correspondence: Manousos A. Klados
†Shared authorship.
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There have been several attempts to account for the impact of Mathematical Anxiety (MA) on brain activity with variable results. The present study examines the effects of MA on ERP amplitude during performance of simple arithmetic calculations and working memory tasks. Data were obtained from 32 university students as they solved four types of arithmetic problems (one- and two-digit addition and multiplication) and a working memory task comprised of three levels of difficulty (1, 2, and 3-back task). Compared to the Low-MA group, High-MA individuals demonstrated reduced ERP amplitude at frontocentral (between 180–320 ms) and centroparietal locations (between 380–420 ms). These effects were independent of task difficulty/complexity, individual performance, and general state/trait anxiety levels. Results support the hypothesis that higher levels of self-reported MA are associated with lower cortical activation during the early stages of the processing of numeric stimuli in the context of cognitive tasks.
Mathematics plays a crucial role in everyday life, affecting academic achievement, job decisions and performance (Jones et al.,
Given the significant variability in previous studies of performance correlates of anxiety (e.g., Basten et al.,
While these studies have provided initial evidence of changes in neural activity associated with MA, important questions remain unanswered. Pertinent issues that the present research was designed to address include: (a) the specificity of math-related anxiety as a characteristic trait that is distinct from both general trait anxiety and general situational anxiety in impacting brain activity; (b) the spatial and temporal features of math-anxiety related effects on neurophysiological activity during the performance of arithmetic tasks. The former issue was addressed by concurrently obtaining measures of both general and math-related trait anxiety as well as state anxiety during the testing session from all participants. The later issue was addressed by obtaining measures of brain activity with adequate temporal resolution to determine during which time window(s) of event-related potential records anxiety effects would occur during processing of numeric stimuli.
In this framework traditional measures of electrophysiological reactivity (ERP amplitude) were obtained in typically achieving young adults who were grouped on the basis of self-reported, anticipatory math anxiety. In addition, ERPs were collected during performance of a common working memory task (single-digit n-back) in view of the close dependence of arithmetic performance upon working memory capacity (e.g., Raghubar et al.,
The primary goal of the study was to assess systematic variability as a function of the level of trait math-related anxiety reported by participants prior to their engagement in arithmetic tasks. We hypothesized that participants reporting higher levels of trait math anxiety would demonstrate reduced ERP amplitudes prior to response selection (Qi et al.,
With permission from the Bioethics Committee of the Medical School of Aristotle University of Thessaloniki (in agreement with the Declaration of Helsinki), 1000 university students were administered the Greek adaptation of the nine-item Abbreviated Math Anxiety Scale (AMAS; Hopko et al.,
All participants were administered a working memory task (N-back with three levels of load/difficulty) and four arithmetic tasks (Single Digit Addition, Double-Digit Addition, Single Digit Multiplication, and Double-Digit Multiplication). In the one-back condition participants pressed one mouse button to indicate that the current stimulus (single digit) was the same with the one immediately preceding it and the other button for a “No” answer. In the two- and three-back conditions, participants were asked to compare the current stimulus with the one presented either two or three positions before, respectively. A total of 40 trials (single digit numbers) were presented in each n-back condition.
Each arithmetic task consisted of 40 trials (problems), except Double-Digit Multiplications involving 20 trials in order to avoid frustration of both groups due to their difficulty, presented in a randomized order across participants. Each stimuli was presented visually and remained on the screen until the participant indicated whether it was correct or not by pressing the right or left mouse button, respectively, while the split of the false answers was small. The correspondence of response keys to type of response was counterbalanced across participants. The order of tasks was also counterbalanced across participants.
The abbreviated version of AMAS consists of nine items representing common situations faced by students (e.g., “Thinking about an upcoming math test one day before” and “Starting a new chapter in a math book”; Hopko et al.,
The Spielberger State-Trait Anxiety Inventory (STAI A-B; Spielberger et al.,
EEG recordings were performed in a dark and sound attenuated room during performance of each of the four arithmetic tasks and the three n-back conditions. Participants were seated in a comfortable chair and the stimuli were presented on a monitor located about 80 cm in front of the participant. ERPs, time-locked to the onset of each visual stimulus, were recorded via a Neurofax EEG-1200 system from 57 electrode sites according to a modified international 10/10 system using an Electrocap (Fp1, Fp2, F3, F4, C3, C4, P4, O1, O2, F7, F8, T7, T8, P7, P8, Fz, Cz, Pz, TP8, Afz, FCz, CPz, FC1, FC2, CP1, CP2, FC5, FC6, CP5, CP6, Fpz, Oz, F1, Poz, F2, C1, C2, P1, P2, AF3, AF4, FC3, FC4, CP3, CP4, PO3, PO4, F5, F6, C5, C6, P5, P6, FT7, FT8, TP7, referenced offline to linked mastoids). Vertical and horizontal eye movements were recorded through EOG from left/right canthal, supra- and infra-orbital electrodes. All electrode impedances were kept below 2 kΩ. High- and low-pass filters were set at 0.004 and 200 Hz, respectively, with a sampling rate of 500 Hz. Recorded epoch length was 1200 ms including a 200 ms prestimulus baseline. Prior to segmentation, signals were filtered offline between 0.5 and 45 Hz (with a notch filter at 47–53 Hz) and submitted to an ICA procedure (extended-ICA; Bell and Sejnowski,
Participants were asked to avoid alcohol intake on the day before and caffeine consumption on the day of the experiment; they were also asked to sleep as adequately and comfortably as possible on the night before. All recordings were performed in mid-morning sessions.
Response accuracy on the n-back and arithmetic tasks was assessed with d Prime (
where
The effect of math anxiety on performance was assessed at the group level through three-way ANOVAs on
Time windows used to compute ERP amplitude measures were determined upon inspection of global field power (GFP) waveforms separately for each group. As shown in Figure
The False Discovery Rate (FDR; Benjamini and Hochberg,
In addition to AMAS scores on which the two groups differed by design, higher levels of situational anxiety were reported by participants in the HMA as compared to the LMA group,
As shown in Supplementary Table 1, after controlling for general state and trait anxiety levels, the tendency for higher RTs and lower
Although the Group by Task interactions did not approach significance (
Although the Group by Condition interaction did not approach significance (
Significant Math Anxiety Group main effects (
Math Anxiety Group main effects (LMA > HMA) meeting the stringent alpha level of 0.002 were restricted to three sites: FCz, C1, C5 (between 180–220 and 280–320 ms). Mean amplitude during 380–420 ms increased linearly with working memory load (1-back > 2-back > 3-back) at CP5 and CP3 (
Electrophysiological data presented here support the hypothesis that higher levels of self-reported math anxiety are associated with lower cortical activation during performance of simple arithmetic calculation tasks, especially when the MA individuals didn’t achieve same performance as their control peers. An interesting finding that is discussed in more detail below, is that these effects were first evident during the early processing stages of task performance (i.e., within the first 200 ms after stimulus onset), several 100 ms before the participants’ responses were registered. With respect to the second goal of the study, Math Anxiety group effects were also documented on ERP amplitude during performance of the n-back task, albeit less extensively than the effects during performance of the arithmetic tasks. Moreover, the data corroborated our hypotheses that math anxiety group effects on electrophysiological measures were not significantly affected by individual differences in general, negative emotional reactivity (trait or state).
Despite earlier mixed results on the effects of anxiety on task-related ERP measures (e.g., Knyazev et al.,
The presented findings support that the significant differences between our two groups, are mainly located in the (pre-) frontal cortex. According to the existing literature (Smith and Jonides,
From a neurocognitive standpoint, our findings are only partially consistent with the predictions of the Attentional Control Theory (ACT; Eysenck et al.,
An alternative developmental/educational account posits that negative emotions regarding their adequacy in math develop “naturally” in students who are not as cognitively adept to acquire the most demanding math skills. Such emotional responses and cognitions are then likely to prevent them from engaging in academic activities related to math, therefore widening the gap with their more adept peers. Over the years these avoidance behaviors may further reinforce negative emotional reactions toward math tasks (Richardson and Suinn,
It should be noted that the design of the experiment and analyses employed in the current study did not permit us to assess additional predictions of ACT, namely that anxious individuals are also likely to exert greater cognitive effort and make use of more cognitive resources in order to achieve performance standards displayed by persons with low anxiety. Such compensatory cognitive strategies are likely to engage neurophysiological processes which will take place during later stages of numeric stimulus processing, extending beyond the narrow time window examined here. Moreover, both the precise timing and type of compensatory strategies engaged by high math-anxious participants are likely to show significant individual variability which will further reduce their capacity to produce time-locked ERPs. This may further account for the failure to find clear evidence of ERP modulation as a function of task difficulty (for arithmetic tasks) and working memory load (for the n-back tasks).
The limited sensitivity of the method used to measure and model cortical activation in the present study should be taken into account in interpreting the current results. Thus, both the magnitude of cortical activation were assessed at the sensor level, not possessing adequate spatial resolution to detect compensatory increases in neural responsivity as predicted by ACT. fMRI and EEG source-level data derived in the context of similar experimental paradigms are forthcoming to address this issue (Babiloni et al.,
Additional limitations inherent to the study design should be noted. Thus, failure to find MA effects in later portions of the ERPs may have been an artifact of the time window used to estimate the aformentioned parameters, so that critical operations involved in the more demanding two-digit calculation tasks may have taken place at later time windows (which were not reliably time-locked and estimated in the present study). Failure to find significant variability in GFP after approximately 500 ms post-stimulus onset may simply reflect difficulty in eliciting time-locked neurophysiological activity in response to tasks that require extensive processing. This limitation may also be manifested in the absence of clear-cut arithmetic task main effects and interactions, given that the analysis window empirically established on the basis of GFP waveforms captured neurophysiological activity elicited during the early stages of arithmetic calculation. These stages are likely to be dominated by processes common to the elaboration of numeric stimuli across tasks. Moreover, future studies should attempt to manipulate arithmetic task difficulty more systematically and perhaps also employ measures of synchronization/desynchronization at the single trial level in order to circumvent the stationarity requirement in the analysis of average ERP data.
A final important limitation of the present study, relates to the sample size which may have been sufficient for group-level analyses as well as for preliminary estimation of bivariate associations. However, a larger study size is required to perform more complex analyses, such as mediated regression, which will be ideally suited to assess the hypothesized role of ERPs’ parameters as mediators of the association between math anxiety and performance. Larger data sets are also required in order to assess the potential non-linear effects of math anxiety and the interaction of affective and cognitive abilities. Generally, however, it has been difficult to model the complex associations between math anxiety and corresponding beliefs and schemas regarding mathematics, cognitive capacities (such as processing speed, working memory, and problem solving ability), and actual performance on arithmetic tasks that vary in difficulty. One reason for this difficulty may be that associations may not be linear—it is well known that the relation between anxiety and performance is curvilinear and the shape of the anxiety-performance function may change with task difficulty. This quest is further complicated by the interdependence of performance measures as indices of math capacity. Thus, anxiety may have a positive effect on RT and calculation accuracy up to a certain level beyond which reductions in RT may be associated with reduced accuracy (Ashcraft and Faust,
Despite the aforementioned limitations, this is the first study investigating electrophysiological measures of cortical function during the solution of arithmetic tasks varying in difficulty and operational complexity as a function of self-reported math anxiety. Our findings indicate that higher levels of self-reported math anxiety are associated with lower cortical activation during the early stages of performance of simple arithmetic calculation tasks. Regardless of the precise neurocognitive mechanisms, an important implication of the present results concerns the need to take into account individual differences in math anxiety levels in neuroimaging studies involving numerical stimuli.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The Supplementary Material for this article can be found online at:
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