Introduction

Individuals with high math anxiety (HMA), characterized by intense apprehension and negative emotions towards mathematics, often exhibit math-avoidance behaviors1,2. This avoidance leads to a harmful cycle of minimal practice, poor performance, and increased anxiety, further perpetuating the avoidance of math-related tasks3. Such behaviors significantly impact academic achievements and career choices, particularly in STEM fields where math skills are crucial4,5,6.

Empirical studies confirm the prevalence of math avoidance among individuals with math anxiety, demonstrating a preference to avoid complex mathematical evaluations3,7,8. Despite these observations, the neurocognitive mechanisms driving math avoidance in HMA individuals remain unclear. Understanding how these individuals navigate the conflict between approaching potential rewards and avoiding due to fear of failure and cognitive effort is essential for understanding their behavior.

Recent research has enhanced our understanding of the neural underpinnings of effort-based decision-making9,10. Key neural structures in this process include the orbitofrontal cortex (OFC), ventral striatum (particularly the nucleus accumbens, NAc), and ventromedial prefrontal cortex (vmPFC), forming the ventral valuation network (VVN), which assesses potential rewards and values of decisions11,12,13. Effort-based decision-making is believed to reflect interactions between valuation systems and cognitive control systems, with control operations guided by a utility-maximization framework14. Based on this perspective, we hypothesized that the ventral valuation network (VVN) would engage in dynamic interaction with cognitive control regions to facilitate the efficient allocation of cognitive resources, support goal-directed behavior, and reorient attention toward subjectively valued tasks15,16,17.

In our study, we employed a novel approach-avoid conflict (AAC) paradigm to explore the characteristics during effort-based decision-making in HMA individuals. We presented participants with choices including the difficulty of math problems and potential monetary rewards, aiming to examine how cognitive cost (task difficulty) and benefit (reward) differentially impact decision-making in both HMA individuals and their low math anxiety counterparts, while their arithmetic abilities are comparable, and to observe the variations in neural responses during math avoidance behavior among HMAs. Participants were encouraged to accept calculation challenges to maximize their earnings in the AAC tasks. The task difficulty (high and low) and the corresponding monetary reward (high and low) were orthogonally set. By dissecting the roles of cognitive effort and reward processing, our study aims to reveal the core influencing factors and underlying neural mechanisms towards the math avoidance behavior in individuals with HMA.

Increased perceived cognitive costs (such as low confidence in math abilities) and diminished sense of reward from solving math problems or receiving external rewards can both contribute to a decreased subjective value. Here, we addressed two primary questions: (1) whether individuals with high math anxiety exhibit increased sensitivity to perceived cognitive costs, diminished sensitivity to rewards, or a combination of both, and how these factors influence their decision-making when allocating cognitive effort to mathematical tasks; and (2) how neural activation and functional connectivity patterns—particularly within the VVN and cognitive control regions—differ in HMA individuals during decision-making processes. To explore these questions, we combined the AAC paradigm with computational, multidimensional functional profiling18, allowing us to dissociate the latent parameters driving decision dynamics. We employed data-driven methods to evaluate whether a combination of behavioral parameters, brain activation, and functional connectivity could optimally characterize the avoidance tendencies of HMA individuals. Specifically, we decomposed the cognitive components of approach-avoidance decisions of the Drift Diffusion Model (DDM), a well-established sequential sampling framework that conceptualizes decision-making as an evidence accumulation process toward a threshold. The DDM has been successfully applied to model effort-based decisions and associated response time distributions in contexts where individuals weigh cognitive costs against potential rewards19,20,21. We extended this framework to capture decision-making under motivational conflict, in which the aversiveness of cognitive effort competes with the anticipated rewards of task engagement. This approach allowed us to consider multiple sources of variability that may underline distinct decision-making patterns in individuals with high math anxiety. By exploring the roles of cognitive effort and reward processing and examining neural differences related to math avoidance, we seek to provide a deeper understanding of the challenges faced by HMA individuals towards their math avoidance behaviors.

Results

The math avoidance of math anxiety group

The experimental task is shown in Fig. 1. To explore how math avoidance behavior was influenced by math anxiety group, task difficulty and the reward magnitude, we first set up a Generalized Linear Mixed Effects (GLME) model. In this model, participants’ acceptance of solving the upcoming math problem on each trial is considered as independent variable, the task difficulty level, reward magnitude and math anxiety group are considered as dependent variables. The model included math anxiety group, task difficulty, and reward magnitude as fixed effects, and participant-specific random intercepts as random effects. The results showed that the model BIC is 6399, the mode intercept effect was significant (B = −2.14, SE = 0.52, z = 4.13, p < 0.001). The coefficients of determination (ΔR²) for the fixed effects and the full mixed-effects model were 0.43 and 0.74, respectively, indicating that the fixed effects explained 43% of the total variance in the dependent variable, while the full model accounted for 74%. Based on the estimated effect size of the fixed effects, we calculated the power analysis using G*Power22, which yielded a high statistical power (1 − β = 0.99).

Fig. 1: Task paradigm.
Fig. 1: Task paradigm.
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In each trial of the experiment, participants were presented with information regarding the difficulty of the upcoming arithmetic problem and the corresponding monetary reward for successfully solving it. The asterisks represent task difficulty, with two asterisks indicating low-difficulty problems and five asterisks indicating high-difficulty problems. The reward magnitude associated with each problem is displayed below the asterisks. Based on this information, participants decided whether to attempt the problem (accept) or skip it (reject). If they chose “accept”, they were shown the arithmetic problem along with four answer choices, having 6 seconds to select whether the correct answer was displayed on the left or right side among the options. Choosing “reject” concluded the trial, and a new one promptly began with a different task difficulty and associated reward. Participants did not receive immediate feedback on their decisions or answers, preventing such information from influencing subsequent trials.

The experimental effect showed: 1) Main effect: the math anxiety group effect was not significant; the task difficulty (B = 2.84, SE = 0.26, z = 10.83, p < 0.001), and monetary reward (B = 0.35, SE = 0.03, z = -10.16, p < 0.001) also exhibited significant main effects. Participants tended to accept the math problems under lower task difficulty condition or more monetary reward; 2) Two way Interaction: a math avoidance trend in the higher task difficulty condition for high math anxious people was identified, evidenced by a significant two-way interaction between task difficulty and math anxiety group (B = 1.74, SE = 0.37, z = 4.69, p < 0.001). High math anxious individuals accepted fewer calculation tasks in the high difficulty condition (Fig. 2). Post-hoc comparison revealed that for low task difficulty, the group effect was not significant (odd ratio = 2.20, SE = 1.59, z = 1.10, p = 0.272), while for high task difficulty, HMA accepted significant fewer math problem challenges (odd ratio = 7.44, SE = 4.95, z = 3.02, p = 0.003). The interaction between reward magnitude and math anxiety group was not significant. The interaction between task difficulty and reward magnitude was significant (B = 0.13, SE = 0.04, z = 3.63, p < 0.001). Post-hoc comparison revealed that for both low and high task difficulty conditions, the reward magnitude effects were significant, the trend in high task difficulty was significantly smaller than that in low task difficulty (estimate = 0.11, SE = 0.02, z = 4.45, p < 0.001). 3) Three-Way Interaction: The interaction among math anxiety group, task difficulty, and reward magnitude was not significant.

Fig. 2: Behavioral results.
Fig. 2: Behavioral results.
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The two-way interaction between task difficulty and math anxiety group. Under low task difficulty conditions, the two groups accepted a comparable number of math problems. However, under high task difficulty conditions, the HMA group accepted significantly fewer math challenges.

Computational modeling of effort-based decision-making

We then fit participants’ effort-based choice with DDM, which provides an account of the underlying processes which give rise to choice and reaction time (RT) distributions and provides further insight into the origin of potential group differences in their behavioral pattern (see Fig. 3a and Method). We fitted the effort-based decisions regression model by assuming that trial-by-trial values of task difficulty and reward drive evidence accumulation (captured by the drift rate parameter v) towards choosing to “accept” or “reject” an offer, to assess the impact of task difficulty and reward magnitude across high and low anxious individuals. The regression coefficients for task difficulty and reward magnitude in the model can be interpreted as indices of participants’ sensitivity to difficulty and reward, respectively. Two regression models were specified: one model incorporated the interaction term between task difficulty and reward magnitude (Model 1), whereas the other model included only the main effects without interaction (Model 2) (See Method). We evaluated the model’s fit using simulated data and utilized the Deviance Information Criterion (DIC) for model comparison. Model 1, which included an interaction term between task difficulty and reward magnitude, exhibited a superior fit relative to its counterpart, as evidenced by a lower DIC value (Model 1 DIC: 11534, Model 2 DIC: 12167). Then Model 2 was chosen for the subsequent analysis. Uncertainty in the posterior distribution was quantified and reported using the 95% highest density interval (HDI). For Model 1, an analysis involving all participants revealed: 1) Task Difficulty: Its impact on the drift rate was substantial and significantly greater than zero (p (βtask difficulty < 0) = 0); 2) Monetary Reward: Its influence was not significant (p (βreward < 0) = 0.18); 3) Interaction between Task Difficulty and Reward: This was significantly less than zero (p (βtask difficulty * reward > 0) < 0.001); 4) Group comparison: The HMA group exhibited a significantly elevated impact of task difficulty on drift rate compared to the low math anxiety (LMA) group (p (HMA < LMA) = 0.01, Fig. 3b). The coefficient of reward did not show significant differences between the two groups (p (HMA < LMA) = 0.46, Fig. 3c). No significant difference was found in the interaction between the two factors across the groups (p (HMA < LMA) = 0.63). The consistency of these results with those obtained from repeated measures ANOVA and GLME suggests a robust pattern of findings. For model 2, both the task difficulty (p (βtask difficulty < 0) = 0) and monetary reward (p (βreward > 0) = 0) showed significant influence on decision making.

Fig. 3: Modeling results.
Fig. 3: Modeling results.
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a Illustration of drift diffusion model applied to approach-avoidance conflict task; (b) group posterior distribution of coefficient of task difficulty (βtask difficulty); (c) group posterior distribution of coefficient of reward magnitude (βreward).

Chain mediation analysis

Previous results have established that a higher level of math anxiety was correlated with a more pronounced difference in “accept” choices, signifying a stronger inclination towards math avoidance behavior in tasks of higher difficulty for higher math anxiety people. To investigate the mechanisms underlying increased math avoidance in individuals with HMA, we conducted a series of chain mediation analyses. These analyses examined whether task difficulty sensitivity (mediator 1, M1) and BOLD (Blood-Oxygen-Level Dependent) activity (mediator 2, M2) mediate the relationship between math anxiety scores (X) and math avoidance behavior (Y). The chain mediation models allow us to explore the mediating effect of multiple variables that causally influencing another.

Given the lack of significant group differences under low task difficulty conditions, this condition was used as a baseline. Math avoidance (Y) was operationalized as the difference in the number of “accept” trials between high and low difficulty conditions.

Consistent with GLME and computational modeling results suggesting that avoidance behavior in HMA is more sensitive to task difficulty than to reward, we focused on individual differences in task difficulty sensitivity. This was quantified as the regression coefficient for task difficulty from the DDM, representing M1.

To probe the neural correlates of avoidance behavior, we identified six regions of interest (ROIs, see Supplementary Information): the precuneus (Montreal Neurological Institute (MNI), [−4, −50, 54]), mid-cingulate cortex (MCC, MNI [−10, −32, 46]), temporoparietal junction (TPJ, MNI [48, −52, 22]), posterior insula (PI, MNI [−38, −18, 22]), hippocampus (HPC, MNI [28, −12, −10]), and NAc (MNI [30, 2, −8]). Mean activation values within 8 mm radius spheres around each ROI were extracted as M2 and used in six separate chain mediation models.

In these models, indirect path 1 (X-M1-Y) represents the pathway from math anxiety scores to task difficulty sensitivity, leading to math avoidance tendency; indirect path 2 (X-M2-Y) indicates the connection from math anxiety scores to brain activity, impacting the differences in ‘accept’ choices; Indirect path 3 (X-M1-M2-Y) encompasses a more complex route, highlighting the influence of math anxiety on task difficulty sensitivity, which in turn affects brain activity, culminating in decision-making behavior. We hypothesize that elevated levels of math anxiety may influence decision-making in several ways: (1) by amplifying sensitivity to task difficulty (indirect path 1); (2) by diminishing the differences in brain activation between high and low task difficulties within the six ROIs identified (indirect path 2), or (3) a combination of both effects (indirect path 3). Any of these influences could lead to math avoidance behavior (fewer “accept” choices in conditions of higher task difficulty compared to lower task difficulty).

As illustrated in Fig. 4, significant chain mediation effects were observed in three of the above-mentioned ROIs: the HPC, the PI and the MCC. For the HPC, the indirect effect for all the three pathways were significant. The effect value is 0.15 for indirect path1 (95%CI: (0.00–0.29]), 0.09 for indirect path 2 (95% CI: (0.00–0.21]), and 0.05 for indirect path 3 (95% CI: (0.00–0.10]). Similarly, for the PI, the indirect effect for all the three pathways were significant. The effect value is 0.18 for indirect path1 (95%CI: (0.00–0.33]), 0.09 for indirect path 2 (95% CI: [0.02–0.16]), and 0.02 for indirect path 3 (95% CI: (0.00–0.06]). But for the MCC, the indirect path 1 and path 3 were significant, while the indirect path 2 (X-M2-Y) was not significant. The effect value is 0.17 for indirect path 1 (95% CI: (0.00–0.32]), and 0.03 for indirect path 3 (95% CI: (0.00–0.07]). The remaining three ROIs (i.e., the precuneus, the TPJ and the NAc) did not display any significant chain mediation effects.

Fig. 4: Chain mediation results.
Fig. 4: Chain mediation results.
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These mediation models examine the mechanisms linking math anxiety to math avoidance. In each model, the independent variable (X) represents math anxiety scores, and the dependent variable (Y) reflects the level of math avoidance. The first mediator (M1) captures individual sensitivity to task difficulty in predicting avoidance behavior, while the second mediator (M2) represents the activation strength of a specific brain region during decision-making. The numbers next to the arrows indicate regression coefficients in the mediation models, and asterisks denote significance levels (*p < 0.05, **p < 0.01, ***p < 0.001). a Mediation model with hippocampal (HPC) activation as M2. b Mediation model with posterior insula (PI) activation as M2. c Mediation model with mid-cingulate cortex (MCC) activation as M2. *p < 0.05, ** p < 0.01, *** p < 0.001.

Classification based on Brain Functional connectivities

We further investigate how functional connectivities (FC) among the six critical ROIs (namely, Precuneus, MCC, TPJ, PI, HPC, NAc) that identified in the brain activation analysis (see Supplementary Information) could distinguish the high from low math anxiety group. The functional connecitvities were calculated between each pair of the ROIs by PPI analysis. We trained classifiers on math anxiety groups including features of functional connectivities between the 21 pairs of ROIs in the contrast of high minus low task difficulty. A classifier, trained on math anxiety groups utilizing functional connectivity features among 21 edges among the six ROIs, successfully distinguished between HMA and LMA individuals with an accuracy of 70.49%. This classification robustness was substantiated through a permutation test, repeated 5000 times, yielding a significant p-value of 0.009. Further analysis aimed to identify the most diagnostic functional connectivity edges. We found that specific functional connectivities—such as those between the PI and MCC, the HPC and precuneus, as well as the TPJ and NAc — were key in distinguishing individuals with high versus low levels of math anxiety (Fig. 5).

Fig. 5: Functional connectivity among the six ROIs.
Fig. 5: Functional connectivity among the six ROIs.
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The red dots indicate the locations of the six ROIs, the purple lines represent the functional connections between them, and the thicker lines denote connections with greater weights in distinguishing between the HMA and LMA groups in the classification analysis.

Discussion

This study integrates computational modeling and fMRI to investigate the cognitive and neural mechanisms underlying math avoidance behavior in individuals with HMA. Using an approach-avoidance paradigm, we replicated previous findings that HMAs are more likely to exhibit math avoidance behavior3,23, particularly under high task difficulty conditions. As both cognitive cost (task difficulty) and anticipated reward contribute to the computation of subjective value — which can bias decision-making — we examined whether and how these two factors independently or jointly influence avoidance behavior in HMA individuals. The results suggest that task difficulty, rather than reward magnitude, plays a more pivotal role in driving avoidance behavior among individuals with HMA). Heightened sensitivity to task difficulty may constitute a key cognitive mechanism underlying their increased avoidance tendencies. Meanwhile, the neuroimaging findings highlight that the ventral valuation system and brain regions involved in cognitive control processing can differentiate between individuals with high and low math anxiety during decision-making.

Both task difficulty and reward magnitude demonstrated a significant effect on decisions, irrespective of HMA/LMA status, as evidenced by the results of both the GLME and DDM regression models. But only task difficulty emerged as a key factor driving avoidance behavior in individuals with HMA, which is supported by three lines of evidence: a significant interaction between task difficulty and group in the GLME analysis, a significant group difference in the task difficulty coefficient obtained from the DDM regression model, and a significant mediation role of task difficulty sensitivity between math anxiety scores and the math avoidance tendency, which indicate the heightened math anxiety increases sensitivity to task difficulty, subsequently leading to an increase in avoidance behavior. Notably, we observed significant differences in calculating abilities between the two groups, neither in pre-experimental computational tasks nor in computational tasks during the experiment, suggesting the motivation to engage in math related task was independent of the actual math performance, its primary influencing factor maybe the subjective estimation of task difficulty. Considering the evidence mentioned above, we can tell that for HMAs, the complexity of the task holds more sway in their decision-making process than the potential rewards offered, highlighting a distinct aspect of how math anxiety influences cognitive and motivational processes. The absence of a main effect of monetary reward in the DDM model (model 1, considering the interaction between task difficulty and reward magnitude) might be overshadowed by the interaction effect. As the model without interaction (model 2) showed significant effect of both task difficulty and monetary reward, upon adding the interaction term to the model, the main effect of reward ceased to be significant, while the interaction term exhibited a significant effect on decision-making. However, we cannot rule out the possibility that the reward magnitudes used in our design, although effective at the group level, may not have been sufficient to produce robust modulation effects for HMA individuals, who might require substantially greater incentives to overcome their cognitive aversion. Future studies might explore a wider range of reward values or personalized incentive schemes to better capture individual variability in reward responsiveness.

The neural findings also highlighted the role of task difficulty for HMA. On the brain imaging level, the interaction effect between task difficulty and math anxiety group elicited significant brain activation in the regions such as the cuneus, supplementary motor area, right TPJ, MCC, Rolandic operculum, left PI, right HPC, the NAc, the superior temporal gyrus, and some areas in the occipital gyrus, which located in the ventral valuation network and the regions responsible for cognitive control. The HMA group showed weaker brain activation discrepancy between high and low task difficulty among these areas than their LMA peers. In contrast, the interaction effect between reward magnitude and math anxiety group showed no significant effect on the brain activation, which is consistent with the behavioral observations. An elevated level of math anxiety may heighten sensitivity to task difficulty, which in turn increases neural activity in regions such as the HPC, PI, and MCC, ultimately contributing to greater avoidance tendencies. These findings collectively provide a cohesive understanding of the cognitive mechanisms behind math avoidance behavior in highly math-anxious individuals. They underscore the dominant role of cognitive effort evaluation in hindering the pursuit of corresponding rewards in math-related tasks.

In addition to unveiling the effect of elevated task difficulty sensitivity in HMA underlying their math avoidance behavior at both the behavioral and neural level, our study delved deeper into how the brain facilitates this avoidant behavior among HMA individuals, particularly in differentiating them from their LMA counterparts during math-related decision-making processes. We identified six key brain regions - the left PI, the MCC, the precuneus, the right TPJ, the HPC and the NAc - using a conjunction analysis. This analysis focused on brain regions that exhibited a significant interaction between group and task difficulty, as well as regions correlating with individual task difficulty sensitivity. The followed up mediation results showed that the MCC, HPC and PI could act as mediators in the relationship between the increased math anxiety and the increase the math-avoidant behavior in two pathways: Firstly, elevated math anxiety levels amplified individual task difficulty sensitivity, subsequently reducing the disparity in brain activity between high and low task difficulties in the MCC, HPC, and PI, leading to math avoidance behavior. Secondly, enhanced math anxiety directly suppressed the brain activity discrepancy between the two task difficulties in the HPC and PI, resulting in math avoidant behavior. Furthermore, our findings indicate that the functional connectivity differences between high and low task difficulty conditions among the PI, MCC, precuneus, TPJ, HPC, and NAc robustly differentiate individuals with high math anxiety from those with low math anxiety. Notably, FC between the PI and MCC, between the HPC and precuneus, as well as between the TPJ and NAc, emerged as the most discriminative features.

The VVN and brain regions associated with cognitive control emerged as critical neural substrates distinguishing HMA from counterparts in terms of math avoidance behavior. The NAc is a major component of the mesolimbic dopamine pathway, a key brain circuit in the VVN of reward processing24. The NAc is influenced by dopamine inputs from the ventral tegmental area (VTA), a midbrain region known for its involvement in dopamine-related functions that promote approach behaviors25. The activation signal discrepancy of high and low task difficulty in NAc, along with the FC signal discrepancy between NAc and other regions, such as TPJ, suggest that value computation is a key factor in the approach-avoid conflict. These computational processes appear to be distinctly modulated in HMA and LMA individuals, highlighting the nuanced ways in which math anxiety impacts the neural underpinnings of decision-making related to math tasks.

The current findings involving the cognitive control network, including the MCC, precuneus, and TPJ, align well with the Expected Value of Control (EVC) theory. EVC posits people integrate information about the expected reward and efficacy of task performance to determine the expected value of control, and then adjust their control allocation (i.e., mental effort) accordingly26. In our task, participants considered their effectiveness in solving arithmetic problems and the corresponding rewards to determine the expected value of cognitive control, guiding their decisions to ‘accept’ or ‘reject’ the challenges. HMA individuals who are lack of self-efficacy in one’s own mathematical abilities might generate lower expected value of cognitive control which lead to less allocation of mental effort to “accept” the arithmetic problem solving.

Various previous findings have confirmed the function of cognitive control during decision-making under certainty in MCC, precuneus, and TPJ15,27. Kuo et al.27 first revealed that the precuneus are more active in slow and controlled decision making than that in fast and emotional decision making, with this activity positively correlating with cognitive effort. Pearson, Hayden, and Raghavachari28 found that the posterior cingulate cortex/precuneus hosts distinct neuron sets that activate based on the strategic direction of decision-making – one set before exploratory decisions and another before exploitative decisions. The MCC activity indicates cognitive control’s role in suppressing risk-taking behaviors29 and encoding goal-directed action sequences17. In individuals with lower levels of math anxiety, who are more likely to ‘accept’ challenging problems, there may be heightened MCC involvement to anticipate the action of calculating. The TPJ is a central node within the bottom-up attention control system, which has been suggested to be the driving force for attention reorienting30, and was assumed to represent higher-order cognitive resources16. Its higher activity during higher task difficulty decision choice indicates the allocation of higher cognitive resource demand.

In recent years, the human HPC has been shown to play a critical role in approach-avoidance conflicts, crucial for adapting behavior under uncertain conditions31,32,33,34,35. Studies have observed increased HPC activity in response to heightened levels of threat in approach-avoidance situations. Additionally, lesions to the HPC, such as those observed in temporal lobe epilepsy patients, have been linked to a reduction in passive avoidance behavior, though not active avoidance behavior31. The PI is known for its role in processing both exteroceptive environmental/sensory information (like touch and pain) and interoceptive information (such as heart rate and body orientation)36,37,38. Its activation during approach-avoidance conflicts might be interpreted as processing potential aversive outcomes signaled by somatosensory afferents. Furthermore, it has been discovered that dense glutamatergic input from the HPC and the insular cortex is essential in initiating fear and sustaining anxiety responses39. Our mediation analysis suggests that the diminished signal change in the HPC and PI could result either directly from high levels of math anxiety or indirectly from increased task difficulty sensitivity induced by heightened math anxiety. This, in turn, contributes to an individual’s tendency to avoid challenging mathematical tasks. These findings provide insight into the neural mechanisms underpinning the choice to avoid math-related challenges, especially in the context of heightened math anxiety.

In conclusion, our study, integrating computational modeling and fMRI, has consistently demonstrated that the math avoidance behavior in individuals with high math anxiety is primarily driven by heightened sensitivity to task difficulty, while their sensitivity to rewards remains unaffected. This behavioral pattern can be neurologically linked to the activity within the ventral valuation network (particularly the NAc) and the cognitive control network, including regions such as the precuneus, MCC, and TPJ, along with the HPC and PI. These brain regions are also crucial in decision-making under uncertainty. By dissecting the roles of cognitive effort and reward processing in the decision-making processes of individuals with high math anxiety, our study sheds light on the potential behavioral and underlying neural mechanisms, which offering valuable directions for understanding and addressing the mathematical avoidance behavior prevalent among individuals with high math anxiety.

Finally, some limitations should be noted. First, our investigation into reward processing focused solely on reward-seeking behavior, rather than threat-avoidance. Bishop et al.40 proposed that anxiety individuals’ overestimation of aversive outcome probability and magnitude, which lead to engagement in avoidance behaviors and increased punishment sensitivity. Further research exploring various situations is necessary to deepen our understanding in reward processing. Secondly, the range of reward magnitudes employed, although effective at the group level, may not have been sufficient to elicit strong motivational modulation in individuals with HMA. It is possible that HMA individuals require substantially greater incentives to overcome their aversion to cognitively demanding tasks. As such, the absence of significant effects related to reward sensitivity in this group should be interpreted with caution. Future research could benefit from incorporating a broader spectrum of reward values or utilizing individualized incentive schemes to more accurately assess variations in reward responsiveness across different levels of math anxiety. Thirdly, although we found significant differences in the overall choices between the two groups under the more difficulty task, both the LMA and HMA accept pattern are complex (reflect possibly 3 different clusters). Specifically, there is a group that almost never accepts difficult offers. This might be a strategic response, either to avoid effort or to increase the likelihood to give a correct answer under temporal pressure. Since a wrong answer to an accepted math problem results in no reward, not accepting a difficult problem is adaptive. Another group had high levels of acceptance, even for difficult problems. This seems to reflect a strategic choice, possibly driven by a motivation to always attempt to earn money. Only the third group had intermediate acceptance rates and seemed to have traded off effort and reward. Future research should focus on these complex decision-making patterns and conduct deeper analyses on individual differences. This study clarified the cognitive and neural mechanisms underlying math avoidance behavior in individuals with high math anxiety. Specifically, compared to reward processing, their heightened sensitivity to task difficulty may play a more significant role in driving avoidance behavior. Moreover, abnormal functional connectivity between brain regions associated with value processing and those related to cognitive control may be linked to the avoidance behavior observed in highly math-anxious individuals. This research enhances our understanding of math-avoidant behavior and provides potential directions for effective interventions.

Methods

Participants

We initially recruited and screened 316 participants using the Shortened Math Anxiety Rating Scale (SMARS)41, from which we selected 66 individuals for further assessment. Participants with SMARS scores above 90 were assigned to the HMA group (n = 33), and those with scores below 45 were assigned to the LMA group (n = 33).

To assess potential confounding variables, we administered the State-Trait Anxiety Inventory (STAI)42 to measure general anxiety levels and used an in-house calculation task to evaluate arithmetic ability. The calculation task consisted of 95 two-digit subtraction problems. Participants were instructed to choose the correct answer from two options (one correct, one incorrect) presented on-screen, where the incorrect answer differed from the correct one by either 1 or 10. Responses were made using designated keys (“Q” or “P”), and participants were given a two-minute time limit. Results from both assessments confirmed that the two groups were comparable in terms of general anxiety (t(64) = 1.53, p = 0.13) and calculation abilities (t(64) = 0.06, p = 0.95). The selected sixty-six participants subsequently underwent the fMRI scanning. none of whom had a history of neurological or psychiatric disorders. Five who had excessive head movements in rotation (> 3°) or in translation (> 3 mm) during the scanning were excluded, leaving 61 participants in the final sample: 31 in low math anxiety group (15 females), 30 in high math group (15 females), age: 20.59 ± 2.22 years (mean ± standard deviation). Both groups differed in the math anxiety scores (MHMA = 96.73, MLMA = 36.39, t(59) = 22.24, p < .001), but did not significantly differ in the calculation ability (MHMA = 30.67, MLMA = 30.45, t(59) = 0.15, p = 0.88), as well as trait anxiety (MHMA = 45.50, MLMA = 40.61, t(59) = 1.81, p = 0.08) and state anxiety (MHMA = 39.23, MLMA = 41.90, t(59) = 1.08, p = 0.28).Written informed consent was obtained from all participants before the experiment. All participants were right-handed and had normal or corrected-to-normal vision. The study was conducted in accordance with the ethical standards of the Declaration of Helsinki and was approved by the Medical Ethics Committee of Shenzhen University Medical School. Prior to participation, all individuals were informed about the experimental procedures and provided written informed consent.

Experimental task and procedures

Participants completed 200 trials in an approach-avoid task across four sessions, where monetary rewards were offered as an incentive for calculating effort. The tasks were set at two difficulty levels: high (multiplication, e.g., 52.99*0.3) and low (subtraction, e.g., 43.99-11). Monetary rewards also varied, ranging from low (3-9 yuan) to high (13-19 yuan). Participants were advised to round off decimals before solving the arithmetic problems, with decimals included solely to increase overall task difficulty. Participants were encouraged to accept calculation challenges to maximize their earnings.

In each trial of our experiment, participants were given 3 seconds to decide whether to accept a calculation challenge. This decision was based on the indicated task difficulty and the potential monetary reward for correctly solving the arithmetic problem. Upon accepting the challenge, participants had to solve the math problem and choose the correct answer from four options, all within a 6-second window. If participants accepted the challenge and answered correctly, they received the specified monetary reward. If they accepted but failed to solve the problem, no reward was given. Choosing to reject the challenge ended the trial, and participants proceeded to the next trial without earning any reward, and there is no additional cost for avoidance. To ensure unbiased decision-making in subsequent trials, participants were not provided with immediate feedback on their choices or answers. Prior to the fMRI scanning, they completed 10 practice trials to become acquainted with the task. Additionally, five warm-up trials were conducted inside the fMRI scanner. The final monetary compensation for participants was determined based on a random selection of 10 trials, not the entirety of the trials completed. This approach was designed to maintain motivation and engagement throughout the experiment, as each trial had the potential to contribute to their overall earnings.

Neuroimaging data acquisition and preprocessing

We used a Siemens Prisma 3.0 T MRI machine for data acquisition. High-resolution structural images were acquired through a 3D sagittal T1-weighted magnetization-prepared rapid acquisition with gradient-echo sequence, using the following parameters: repetition time = 2300 ms, echo time = 2.26 ms, flip angle = 8°, field of view = 232 mm × 256 mm, acquisition matrix = 232 mm × 256 mm, slice thickness = 1 mm, voxel size = 1 mm × 1 mm × 1 mm.

Then, a gradient-echo T2-weighted echo-planar imaging sequence was used for acquiring resting-state functional images with the following parameters: repetition time = 1500 ms, echo time = 30 ms, flip angle = 70°, field of view = 192 mm × 192 mm, acquisition matrix = 94 mm × 94 mm, 46 slices covering the entire brain, slice thickness = 3 mm, voxel size = 2.04 mm × 2.04 mm × 3 mm.

The MRI data were preprocessed in Statistical Parametric Mapping software (SPM12; http://www.fil.ion.ucl.ac.uk/spm). After all images were slice-time corrected, the motion-corrected functional images were co-registered to the 3D-T1 images and then spatially normalized into MNI space by applying the deformation field as estimated by segmentation, with a spatial resolution of 2 × 2 × 2 mm³. The normalized images were spatially smoothed using a Gaussian kernel (full-width-at-half-maximum = 6 mm).

The math avoidance of math anxiety group

In order to include the individual differences as random effect, we leveraged a generalized linear mixed-effects model (GLME). Trials with no response were discarded, which added up to 1.3% of the total numbers. The model included a random intercept of participant and fixed effects of task difficulty, reward magnitude, and math anxiety status as a dichotomous variable. All interactions between task difficulty, reward and math anxiety status were included. The parameter estimate of z-statistic and P-value was reported. Statistical significance was inferred when P-values were <0.05 and corrected for multiple comparisons where appropriate.

Computational modeling of effort-based decision-making

Model setting. In this study, the dynamics of decision-making processes in approach-avoidance were quantified using the Drift Diffusion Model (DDM), employing the HDDM toolbox43. The DDM provides an algorithmic interpretation of binary decision processes, assuming that evidence accumulates noisily until reaching a decision boundary, thereby facilitating a decision to either accept or reject. In the approach-avoidance task, the decision threshold (a) reflects a balance between speed and choice consistency, rather than speed-accuracy, while the drift rate (v) measures the rate of evidence accumulation towards approaching or avoiding offers. The bias parameter (z) indicates the starting point of the accumulation process. Non-decision time (t) is responsible for the time spent on sensory encoding and motor response. To align with the structure of the experimental task, the values of a, z, and t were held constant across conditions, while the drift rate (v) was adjusted based on task difficulty and reward magnitude.

We fitted the effort-based decisions regression model to the participants’ choice and reaction time, by assuming that trial-by-trial values of task difficulty and reward drive evidence accumulation (captured by the drift rate parameter v) towards choosing to “accept” or “reject” an offer, to assess the impact of task difficulty and reward magnitude across high and low anxious individuals. We assumed reward values would be accumulated as evidence for an approach response, whereas the task difficulty would contribute evidence for an avoidance response, indicated by coefficients that were significantly different from 0 in the DDM regression model. Two separate DDM regression models were applied to participants’ data. We fitted two different DDM regression models to participants’ data. One included an interaction term between task difficulty and reward magnitude (Eq. 1), while the other did not (Eq. 2). Comparisons between the models were performed using DIC, which considers model complexity, with lower DIC values indicating a better-fitting model.

$$\begin{array}{l}{\rm{v}} \sim {{\rm{\beta }}}_{\mathrm{intercept}}+{{\rm{\beta }}}_{\mathrm{taskdifficulty}}* \mathrm{taskdifficulty}+{{\rm{\beta }}}_{\mathrm{reward}}* \mathrm{reward}\\ +{{\rm{\beta }}}_{\mathrm{interaction}}* \mathrm{taskdifficulty}* \mathrm{reward}\end{array}\,$$
(1)
$${\rm{v}} \sim {{\rm{\beta }}}_{{\rm{intercept}}}+{{\rm{\beta }}}_{{\rm{task\; difficulty}}}* {\rm{task\; difficulty}}+{{\rm{\beta }}}_{{\rm{reward}}}* {\rm{reward}}$$
(2)

Subsequently, posterior distributions for variables v (along with its subcomponents), z, a, and t were generated for both entire-group and individual-subject levels. Bayesian inference evaluated the impact of task difficulty and reward on the overall drift rate across the group, where each regression equation coefficient represented the sensitivity of the participant’s drift rate to specific variables. To investigate potential differences attributed to varying math anxiety levels, separate model runs were conducted for high and low math anxiety groups, maintaining consistent prior distributions.

Model validation. We utilized Bayesian hierarchical estimation to fit the DDM to the data with 20,000 samples each. The first 2000 samples were discarded as burn-in to allow the sample to identify the best fitting values in the parameter space. To ensure the models converged on the same estimated parameter values, we ran them 5 times and evaluated the r-hat statistic. All parameters had an r-hat statistic below 1.1, indicating convergence. The r-hat statistic measures the degree of variation between chains relative to variation within chains, with values close to 1 indicating indistinguishable samples.

To assess the models’ ability to capture choice and response time patterns, we compared observed and model-generated data. The posterior predictive check demonstrated that the model accurately captured changes in choice patterns and the distribution of response times across reward and aversiveness combinations. Refer to Supplementary Fig. 1 for the posterior predictive checks for each subject.

ROI localization from Brain activity

In our study, the decision phase, highlighted in the red box in Fig. 1, was modeled to investigate the associated BOLD responses. A general linear model localized brain activation across four experimental conditions: low and high task difficulties paired with low and high rewards. The model included six head-motion parameters as nuisances, and low-frequency drifts were removed using a high-pass filter with a 128 s cutoff.

Our initial focus was on identifying the neural mechanisms underpinning the impact of task difficulty and reward magnitude on avoidance behavior in individuals with high math anxiety. Notably, since the reward magnitude did not have a significant influence on math avoidance behavior in highly math-anxious individuals (refer to Behavioral and Brain activity results), our analysis concentrated on understanding the distinct effects of task difficulty on the math anxiety group during decision-making. This involved the interaction effect between task difficulty and math anxiety group. To further understand how the task difficulty discretely influenced decision making individually, we explored how the brain activities covariated with the coefficient of task difficulty (βtask difficulty) in the DDM regression model. Finally, In order to localize which brain regions that were sensitive to task difficulty also showed group differences in the high minus low task difficulty contrast, we performed conjunction analysis for the above two results: 1) the brain map of interaction between the task difficulty and the math anxiety group: (high - low task difficulty) * (LMA – HMA); 2) the correlation map between βtask difficulty and brain activation contrast between high and low task difficulty condition.

Significance level was set to p < 0.005 uncorrected at the voxel level and to an extent threshold of p < 0.05 with false discovery rate correction (FDR) at the cluster level. A random-effects analysis for the entire group was performed in SPM12 on the parameter-estimated images for all participants.

Chain mediation analysis

The mediation analysis was utilized to explore how math anxiety could contribute to the individual variances observed in this propensity. We assumed that individual task sensitivity, as well as brain activities that were sensitive to task difficulty might be the candidate mediators.

Conjunction analysis in the above section revealed six brain regions—precuneus, MCC, TPJ, PI, HPC, and NAc—that were both sensitive to task difficulty and exhibited group differences (refer to brain activation results). We then extracted mean parameter estimates of the brain activations from an 8 mm-radius sphere centered on each of peak the six ROIs, and used model 6 in PROCESS44 to construct a chain mediation models to analyze whether βtask difficulty (mediation variable 1) and brain activations within the 6 brain areas (mediation variable 2) mediate the association between math anxiety scores (input variable) and the differences of “accept” choice between high and low task difficulty (output variable). The bootstrap method is used to randomly sample 5000 times from the original sample to estimate the indirect effect value. We chose 95% corrected confidence intervals (CI) of the indirect effect value to test whether it does not include zero, it suggests that the indirect effect is statistically significant at the 0.05 level.

Classification based on brain functional connectivities

In this section, we investigated how functional connectivities (FC) among the six brain regions, that identified in the brain activation results, could distinguish between individuals with HMA and LMA. Using Psycho-Physiological Interaction (PPI) analysis45, we focused on six brain regions previously identified as relevant to math avoidance behavior in HMA individuals. We defined our seed regions using the peak MNI coordinates of these six brain areas. For each participant, we extracted the mean time series from each seed region, adjusting them with the F-contrast of the regressors. We then identified individual peak voxels within an 8mm-radius sphere around each seed region’s peak coordinate, ensuring they met a significance threshold of p < 0.05. The PPI General Linear Model (GLM) included several components: (1) the main effect of seed-region activity, (2) the main effect of contrasting high versus low task difficulty, and (3) the interaction between these elements. These were represented as PPI.Y, PPI.P, and PPI.ppi in the design matrix. To account for potential confounds, we also included six head-motion parameters as covariates and applied a high-pass filter with a cutoff at 128 s to remove low-frequency drifts from the signal. Functional connectivities were determined within 8mm-radius spheres centered on the six seed regions, resulting in a network comprising 21 edges. These connectivity strengths were used as classification features. We trained classifiers on math anxiety groups. Then the linear support vector machine was used as the kernel function and the 10-fold cross-validation was used to calculate the accuracy of training.