Math ability plays a critical role in adaptive functioning in modern society, since it represents the ability to apply mathematical knowledge in the real world to understand phenomena, and formulate decisions [1]. Despite this, mathematics remains a domain characterised by significant learning challenges, and declines in this skill have been reported internationally, a trend that predates the global coronavirus pandemic [1]. Low mathematical skills have a range of consequences at both the societal [2] and the individual level, including future career choices. In the 21st century, STEM (science, technology, engineering, mathematics) competencies are in high demand and well paid, but a lack of foundational skills in these areas, represented by math ability, may prevent individuals from pursuing these careers [3]. Therefore, there is an increasing interest among educators and stakeholders in the correlates of good mathematical performance.

In particular, math anxiety has been studied extensively in recent decades. It refers to the negative emotions that some individuals experience in relation to numbers and to solving mathematical problems [4]. It has been shown to influence the career paths of young adults by dissuading them from pursuing university programmes with dense math content [[5], [6], [7]]. Math anxiety is also experienced by math-skilled individuals, who are often attracted to STEM disciplines at university [8]. For example, reduced enrolment and lower grades in STEM courses are predicted by higher levels of math anxiety [9]. Higher levels of math anxiety are consistently associated with lower performance on math-related tasks at all ages [[10], [11], [12]], and account for up to 14 percent of the variance in math achievement scores on international assessments [13].

In the past years, several reliable self-report questionnaires have been developed to assess math anxiety [14]. These questionnaires require individuals to retrospectively evaluate their past experiences and emotions, which may not correspond to the actual psychological experience during a mathematical task [15,16]. This distinction is consistent with the broader framework of trait and state anxiety, initially developed for general anxiety and more recently applied to math anxiety [4]. Trait math anxiety refers to a stable tendency to feel anxious in mathematical situations, whereas state math anxiety represents a transient, context-specific anxiety response associated with physiological responses [15]. While most research has focused on self-reported trait measures, state emotions experienced during a mathematics test have been largely overlooked. However, investigating changes in emotional and motivational states during numerical tasks may be crucial to understand the factors that influence success in mathematical performance.

Changes in physiological activity can be used to track changes in psychological states. The activity of peripheral organs is influenced by central regulatory systems, such as the hypothalamic-pituitary-adrenal (HPA) axis and the autonomic nervous system (ANS), which work to maintain internal homeostasis in response to external demands. The HPA axis, a hormonal system, initiates a cascade of events over several minutes, culminating in the release of cortisol from the adrenal cortex [17]. The ANS, through its sympathetic and parasympathetic branches, innervates and rapidly modulates the activity of various peripheral organs, such as the heart and sweat glands. The HPA axis and the ANS work together to ensure an appropriate behavioural response [18]. Consequently, physiological measures representing the activation of these systems are used as indicators of arousal to understand individual differences in behaviour.

The most common physiological measures of arousal include salivary cortisol, skin conductance level (SCL) and heart rate variability (HRV). Salivary cortisol concentrations reflect the response of the HPA axis to external or internal events aimed at restoring homeostasis [19]. SCL represents the tonic electrodermal response caused by the activation of the sweat glands, which are innervated by the sympathetic branch of the ANS [20]. HRV indicates the variation in time between successive heartbeats and represents vagal withdrawal, i.e., the inhibition of the parasympathetic branch of the ANS. This inhibition results in the activation of the cardiac system to induce rapid adaptation and prepare the body for external demands [21,22]. Therefore, increased salivary cortisol, increased SCL and decreased HRV can be considered as signs of physiological arousal.

Changes in these physiological measures are traditionally linked to changes in affective states, including those in the mathematical domain. When performing a mental arithmetic test in a “high stress condition”, i.e. when negative feedback was given on a trial-by-trail basis, a significant decrease in HRV were observed in primary school children, suggesting that negative math-related experiences can increase arousal [23]. Higher physiological arousal, when associated with negative affective states such as math anxiety, can in turn have an impact on math performance. Low HRV was found to mediate the relationship between trait math anxiety and math performance in middle school students, with higher trait math anxiety being associated with lower HRV and, in turn, with longer response times in an arithmetic task [24]. Furthermore, in young adults with low HRV, the negative effect of trait math anxiety on performance was explained by their feelings of anxiety experienced during the task [25]. Similarly, increased skin conductance has been associated with poorer mental arithmetic performance in university students [26,27], particularly in participants with high trait math anxiety [26]. These findings suggest that individuals with high math anxiety are likely to be more sensitive to physiological arousal and may tend to focus their attention on these reactions, reducing the cognitive resources available for the task [28]. Indeed, when participants with higher math anxiety are instructed to reappraise the situation and interpret the test and their bodily responses in a more positive light (an emotion regulation strategy known as cognitive reappraisal), the negative association between physiological arousal and performance is reduced [26].

It should be noted, however, that studies investigating associations between physiological measures and scores on math anxiety questionnaires are inconclusive and sometimes conflicting. For example, a significant positive association was found between trait math anxiety and skin conductance responses, recorded in university students while they performed a fraction comparison task in the laboratory [29]. Conversely, in high school students taking a math exam at school, a negative correlation was found between math anxiety scores and SCL recorded before the start of the exam, whereas no significant association was found between math anxiety and SCL during the exam [30]. However, no correlations were found between trait math anxiety and either SCL or HRV during task execution or the anticipation period in young adults judging the correctness of equations [25]. These discrepancies highlight the divergent findings regarding the relationship between math anxiety and physiological activation during or in anticipation of numerical tasks. Therefore, physiological responses should be interpreted with caution as indicators of math anxiety [29,31], as contextual and individual differences may play a critical role in shaping these responses.

On the other hand, an increased physiological response may support better performance, and trait math anxiety appears to moderate this association. For example, higher salivary cortisol was found to be positively associated with math performance in individuals with low math anxiety but negatively associated with math performance in individuals with high math anxiety [32]. These findings challenge the view that increased physiological arousal only represents negative affect experienced during the task. Physiological arousal can indicate mental effort that supports test performance [33]. In this case, physiological arousal cannot be identified as a proxy for trait math anxiety. Instead, individual differences in trait math anxiety may account for the differential impact of physiological responses.

The biopsychosocial model accounts for individual differences in arousal regulation processes and their relationship to motivation and behaviour. Activation of the ANS and HPA systems is not uniquely representative of a particular psychological state, as physiological responses interact with intrapersonal and interpersonal variables in a context-specific manner. In particular, individual differences in the context and task appraisals play a crucial role [33,34]. When individuals are confronted with a goal-relevant situation, their appraisal of this situation as a challenge (i.e., when individual resources are perceived as adequate for the demands) or as a threat (i.e., when demands are perceived as exceeding the individual resources) leads to different interpretations of physiological arousal, with different consequences for behaviour. Feeling challenged may lead to approach behaviour, actively responding to the situation or stimulus to achieve a goal, whereas feeling threatened may lead to avoidance behaviour, moving away from or ignoring the situation or stimulus.

Whether an individual evaluates a situation as challenging or threatening can be influenced by dispositional and affective factors, such as trait math anxiety. It has been argued that math anxiety and its negative impact on performance is due to students’ negative interpretation of their math-related experiences [35]. Experiencing sweaty palms or an accelerated heartbeat is commonly understood as a sign of likely failure. Interpreting these reactions as indicative of a challenging situation could improve performance, whereas interpreting them as a math-related distress could instead lead to worrying thoughts and impair performance. The findings of Mattarella-Micke and colleagues [32] are consistent with this account, where different interpretations of physiological cues are captured by different levels of trait math anxiety.

Math anxiety may not be the only factor influencing situation appraisal. Individuals predisposed to a low sense of control and lack of resilience may be more prone to negative appraisals in general [36], and consequently in the context of a mathematics test. Individual differences in the tendency to feel threatened, out of control and emotionally unstable are captured by neuroticism. It is a core personality trait that appears in several personality frameworks, including the widely recognized Big Five model [[37], [38], [39]]. In this model, personality is conceptualized as a configuration of stable interindividual differences, described along five key dimensions: neuroticism, agreeableness, conscientiousness, extraversion, and openness to experience. Like math anxiety, neuroticism has traditionally been assessed using self-report questionnaires. Therefore, scores on neuroticism represent conscious and retrospective appraisals of one’s emotional experiences in different situations.

Recent evidence shows associations between neuroticism and math ability. Among undergraduate students, neuroticism showed a negative association with math ability only among students enrolled in humanities programmes, which are characterised by the absence of mathematics teaching [40]. On the other hand, among women enrolled in STEM programs a significant positive association was found between math ability and neuroticism, which was stronger at higher levels of math anxiety [41]. Different levels of neuroticism may lead to different appraisals of the same math-related situation. However, neuroticism alone may not determine how the situation is evaluated. Therefore, differences in neuroticism should be considered alongside students’ field of study and gender.

The choice of a particular degree programme is influenced by a variety of personal and affective factors, which may contribute differentially to math ability in different fields [42]. People who choose a humanities programme may be driven by the desire to avoid mathematics, likely influenced by math anxiety [[5], [6], [7]]. Therefore, humanities students with high neuroticism may be particularly prone to evaluating a mathematics test situation as a threat, given that mathematics does not appeal to them and they are likely less familiar with numerical content compared to STEM students.

Gender2 differences in attitudes towards mathematics are often reported. Women typically report higher levels of math anxiety and lower levels of confidence in their math abilities compared to men [8,44,45]. Women are also less represented in STEM programmes [46] and are subject to the stereotype that mathematics is a male domain [47], which can lead to greater physiological arousal in women rather than in men during a numerical task [48]. In the case of women, those high in neuroticism may pay more attention to physiological arousal, which in the context of a math-related situation may be interpreted as a challenge rather than a threat, as they may be accustomed to these feelings in this particular context.

The primary aim of the present study is to examine individual differences in the physiological correlates of math ability in a sample of university students.

We measured physiological changes using salivary cortisol concentration, SCL and HRV, all of which have been used in previous research on math anxiety [[23], [24], [25], [26], [27],29,30]. We chose these measures because they are known to reflect the activity of neural systems involved in emotion regulation. Salivary cortisol concentration reflects the activity of the HPA axis, while SCL, which represents the tonic component of skin conductance, captures cognitively driven sympathetic arousal. HRV, on the other hand, reflects parasympathetic activity, which counterbalances sympathetic activation. By integrating these complementary measures, our approach provides a comprehensive assessment of physiological reactivity and a thorough understanding of the body’s responses.3

First, we investigated the relationship between physiological indices and math ability, using a variable-centred approach. If physiological responses represent a negative affective state, we expected that a decrease in physiological responses (increase in salivary cortisol concentration, increase in SCL and decrease in HRV) would correspond to better performance, like the effect of trait math anxiety. However, we cannot exclude the possibility that increases in physiological response are associated with better performance, reflecting effective task engagement. In addition, we examined whether the associations between physiological responses and performance were influenced by trait math anxiety and neuroticism (collectively referred to as “trait variables”), where trait math anxiety indicates negative emotions towards mathematics and neuroticism indicates a general tendency towards negative emotions. These trait variables affect how likely an individual is to perceive a situation as threatening — either specifically for math in the case of math anxiety, or generally across situations in the case of neuroticism. In line with the biopsychosocial model, we expected that an increase in physiological response would be associated with a decrease in math ability in individuals with higher levels of the trait variables. Conversely, for individuals with lower levels of these variables, better performance might be associated with an increase in physiological response, suggesting that they perceive the mathematics test as challenging and exert mental effort to support effective test performance. We also investigated whether these effects varied by field of study, particularly between STEM and humanities university programmes, and by gender, as these factors were observed to moderate the association between math ability and the trait variables, particularly neuroticism.

Second, using the person-centred approach, we investigated the existence of different student profiles based on physiological responses and trait variables, and whether these profiles differed in their mathematical performance. Given that there is no clear relationship between physiological responses and psychological states, we expected to find heterogeneous profiles. For example, we might find a group of participants with higher levels of physiological responses and trait variables, including those more threatened by the mathematics test and therefore performed lower. We might also find participants with a profile characterised by low trait variables and high physiological responses, who are mentally engaged in the task and therefore perform better on the mathematics task. We did not exclude the possibility that other profiles might emerge, as this is the first time such analysis is applied with multiple physiological data in the mathematical domain. We then investigated whether these profiles were distributed differently across fields of study and gender, and whether, within these groups, the association between profiles and mathematical performance varied within these groups.

Applying these two approaches to the same dataset can provide a comprehensive view of the physiological correlates of math ability and how they differ across individuals.