Does anxiety explain why math-anxious people underperform in math?

The study investigates whether and to what extent in-the-moment (state) anxiety explains the well-established association between trait math anxiety and poorer math performance, and whether this relation depends on individual differences in emotion regulation. Prior theory suggests state anxiety consumes working memory resources needed for math, but this has not been directly tested with concurrent state measures. The work also examines whether emotion regulation capacity (indexed by HF-HRV) moderates links between trait math anxiety, state anxiety when facing math, and performance, with implications for targeting interventions.

Decades of research show robust negative associations between math anxiety and math performance across lab tasks and academic settings, independent of general anxiety. Proposed mechanisms emphasize reduced working memory/attentional control under anxiety and benefits of emotion regulation interventions (e.g., expressive writing, reappraisal). However, prior work rarely measured math-related state anxiety during tasks; associations between trait and state measures are mixed, especially for physiological indices (HR, SCL, PEP). Emotion regulation is multifaceted: tendencies (e.g., reappraisal, suppression) and capacities (neural regulation effectiveness). HF-HRV is a physiological index linked to emotion regulation capacity and prefrontal–subcortical connectivity, predicting stress coping and lower worry. Thus, both self-report and physiological indices of state anxiety and emotion regulation may differentially relate to math performance.

Design: Two-session study with online questionnaires followed by an in-lab psychophysiology session. Online N=288; in-lab N=83 (final analytic sample; some physiology missing by measure). Measures (online): Trait math anxiety via short MARS (sMARS; 25 items, 0–100), general trait anxiety via STAI-T, emotion regulation tendencies via ERQ (reappraisal, suppression). In-lab tasks and sequence: Sensors attached for ECG, impedance cardiography, and skin conductance. After a 3-min baseline physiology, participants completed 8 randomized blocks. Each block began with a veridical cue indicating the upcoming task (MATH or WORD). Ten seconds after cue onset, participants reported current anxiety (1–7). A 3-min anticipatory interval followed (fixation or one of three intervening cognitive tasks: local–global, antisaccade, or free recall). Then a 3-min main task (Math or Word) occurred, followed immediately by another anxiety rating. Four math and four word blocks were administered. Tasks:

• Math verification: equations of form (a×b)−c=d, difficulty calibrated (borrow operations), 26 trials per block (5.5 s per trial + 1.5 s ITI), 50% valid.
• Word reversal: 7-letter strings judged whether reversing yields a correctly spelled word, with matched difficulty, 26 trials per block, 50% valid. Performance: Accuracy aggregated across four blocks per domain (0–1). State anxiety indices: Self-reported state anxiety collected during anticipation and post-task in both domains (averaged across four blocks). Physiological indices:
• HR and SCL continuously recorded; SCL averaged over key 3-min periods.
• PEP (sympathetic control) via impedance cardiography; higher PEP = lower sympathetic drive.
• HF-HRV (parasympathetic vagal control) via spectral power (0.12–0.40 Hz), natural log ms^2; baseline HF-HRV used as trait emotion regulation capacity. Physiology extracted for baseline, anticipatory, and task periods (3-min windows; 1-min segments averaged; inclusion criteria required sufficient artifact-free segments). Analysis strategy:

1. Establish math-anxious underperformance via correlations between trait math anxiety and math accuracy, controlling for general anxiety and word performance.
2. Identify math-related state anxiety measures that relate to both math anxiety and math performance, controlling for relevant covariates (general anxiety; word performance) and the corresponding Word-block indices (to ensure math specificity).
3. Mediation: Test whether math-related state anxiety (anticipatory self-reported anxiety during math blocks) mediates the association between math anxiety and math performance. Variables standardized; covariates: general anxiety, word-related state anxiety, and word performance. Bootstrapped SEs and 95% CIs (10,000 iterations).
4. Moderation by emotion regulation: Test whether ERQ-reappraisal, ERQ-suppression, and baseline HF-HRV moderate the math anxiety → math-related state anxiety link (alpha adjusted to 0.017; covariates: general anxiety and word-block state anxiety).
5. Test whether HF-HRV moderates the math anxiety → math performance link (covariates: general anxiety, word performance) using baseline, anticipatory, and task HF-HRV.
6. Conditional process (moderated mediation): Assess whether the indirect effect (math anxiety → math-related state anxiety → math performance) varies with HF-HRV. Begin with a full model allowing moderation on a, b, and c′ paths; prune nonsignificant moderation (b path) to preserve degrees of freedom; report index of moderated mediation with bootstrapped CIs.

• Math-anxious underperformance: Trait math anxiety correlated negatively with math performance, r(81) = -0.469, p = 8×10^-6; remained when controlling for general anxiety and word performance, partial(79) = -0.432, p = 6×10^-5.
• Identifying state anxiety indices: Only self-reported state anxiety indices from the Math blocks related to both math anxiety and math performance when controlling for covariates and corresponding Word-block measures. • Anticipatory self-reported anxiety: partial(79) with math anxiety = 0.440, p = 4×10^-5; partial(79) with math performance = -0.459, p ≤ 2×10^-5. • Post-task self-reported anxiety: partial(79) with math anxiety = 0.308, p = 0.005; with math performance = -0.620, p ≤ 7×10^-10. • Physiological indices (HR, SCL, PEP) showed no significant associations with math anxiety or performance (ps > 0.05).
• Mediation: Anticipatory self-reported math-related state anxiety significantly mediated the math anxiety → math performance association. Bootstrapped indirect effect = -0.122, 95% CI [-0.237, -0.041], accounting for 33.2% of the total effect (95% CI [11.2%, 64.6%]); direct effect remained significant, c′ ≈ -0.245, p = 0.008.
• Moderation of math anxiety → state anxiety: ERQ-reappraisal and ERQ-suppression did not moderate (ps > 0.05). Baseline HF-HRV did moderate: β = -0.259, t(73) = -4.59, p = 2×10^-5. Simple slopes: Low HF-HRV (−1 SD): β = 0.621, p = 8×10^-11; Mean HF-HRV: β = 0.362, p = 2×10^-7; High HF-HRV (+1 SD): β = 0.103, p = 0.244.
• Moderation of math anxiety → performance by HF-HRV: Not significant, β = -0.032, t(73) = -0.400, p = 0.691; similarly nonsignificant using anticipatory and task HF-HRV.
• Conditional process (moderated mediation): HF-HRV moderated the a path (math anxiety → state anxiety; β ≈ -0.255, p = 3×10^-5) and c′ path (direct effect; β ≈ -0.270, p = 0.015), but not the b path (state anxiety → performance; β = 0.142, p = 0.163). Index of moderated mediation = 0.151, 95% CI [0.077, 0.284]. • At low HF-HRV (−1 SD): Indirect effect explained ~94% of total effect; direct effect ~6% (nonsignificant), indicating underperformance primarily via state anxiety. • At mean HF-HRV: Indirect effect explained about half; direct effect marginal. • At high HF-HRV (+1 SD): Indirect effect ~14% (nonsignificant); direct effect ~86% (significant), indicating mechanisms other than in-the-moment anxiety drive underperformance. Overall: In-the-moment anxiety explains a significant but partial portion of math-anxious underperformance on average; the explanatory role of state anxiety diminishes as HF-HRV (emotion regulation capacity) increases.

The findings directly confirm that heightened in-the-moment anxiety before performing math contributes to math-anxious underperformance, aligning with theories of anxiety consuming cognitive resources. However, this mechanism accounts for only a portion of the effect on average, indicating other pathways are important. HF-HRV, a physiological index related to emotion regulation capacity, moderates how strongly trait math anxiety translates into state anxiety when facing math: individuals low in HF-HRV show strong anxiety reactivity and their underperformance is largely mediated by state anxiety; those high in HF-HRV show little state anxiety reactivity but still underperform to a similar degree, implying alternative mechanisms (e.g., math avoidance leading to reduced practice, or effort allocation differences) likely drive their performance deficits. This mechanistic heterogeneity suggests that a single-process account is insufficient and that assessment of emotion regulation capacity can inform which interventions are likely to be effective. Self-report measures captured performance-relevant aspects of state anxiety better than physiological arousal, whereas HF-HRV outperformed self-report ERQ measures for indexing regulation capacity relevant to attenuating state anxiety.

This study provides the first direct evidence that in-the-moment anxiety mediates the relation between math anxiety and math performance, but only partially on average. The degree of mediation depends on HF-HRV: for low HF-HRV individuals, state anxiety largely explains underperformance; for high HF-HRV individuals, other mechanisms dominate. Contributions include identifying self-reported state anxiety (but not HR/SCL/PEP) as predictive of math anxiety and performance, demonstrating moderated mediation by HF-HRV, and highlighting mechanistic heterogeneity. Future research should identify additional mechanisms (e.g., avoidance behaviors, effort allocation, attentional control dynamics), test generalizability across ages and math domains, and evaluate whether HF-HRV can guide targeted interventions to maximize impact.

• Task/domain specificity: Mediation strength may vary with different math tasks, especially those relying on prior knowledge.
• Sample: College-aged participants; generalizability to younger or diverse populations is untested.
• Measures not collected: No direct measures of math avoidance, in-task effort, visual ability, or histories of learning differences (e.g., dyslexia, dyscalculia) or ADHD that could influence mechanisms and performance.
• Physiological inference limits: Physiological indices are indirect markers of psychological states; lack of one-to-one mapping may limit their sensitivity to performance-relevant anxiety facets.
• Some missing physiology data reduced Ns for specific analyses, though inclusion criteria and preprocessing followed best practices.