Unraveling the role of math anxiety in students’ math performance

Math anxiety (MA; i.e., feelings of anxiety experienced when being confronted with mathematics) can have negative implications on the mental health and well-being of individuals and is moderately negatively correlated with math achievement. Nevertheless, ambiguity about some aspects related to MA may prevent a fathomed understanding of this systematically observed relationship. The current study set out to bring these aspects together in a comprehensive study. Our first focus of interest was the multi-component structure of MA, whereby we investigated the relationship between state- and trait-MA and math performance (MP) and whether this relation depends on the complexity of a math task. Second, the domain-specificity of MA was considered by examining the contribution of general anxiety (GA) and MA on MP and whether MA also influences the performance in non-math tasks. In this study, 181 secondary school students aged between 16 and 18 years old were randomly presented with four tasks (varying in topic [math/non-math] and complexity [easy/difficult]). The math task was a fraction comparison task and the non-math task was a color comparison task, in which specific indicators were manipulated to develop an easy and difficult version of the tasks. For the first research question, results showed a moderate correlation between state- and trait-MA, which is independent of the complexity of the math task. Regression analyses showed that while state-MA affects MP in the easy math task, it is trait-MA that affects MP in the difficult math task. For the second research question, a high correlation was observed between GA and MA, but regression analyses showed that GA is not related to MP and MA has no predictive value for performance in non-math tasks. Taken together, this study underscores the importance of distinguishing between state and trait-MA in further research and suggests that MA is domain-specific.


Difficult
This trial will be solved incorrectly if the natural number bias or benchmarking strategy is used. Only when relying on the gap thinking strategy, this item will be solved correctly. This trial is difficult because it consists of double digits, without common components and the distance effect is small.

Mathematical indicators
(1) Natural number bias A major cause of students' difficulties with fractions is due to natural number bias, meaning that students tend to rely on natural number principles when reasoning about fractions, even when this is not justified (Ni & Zhou, 2005;Obersteiner et al., 2013;Reinhold et al., 2020;Vamvakoussi et al., 2012). Accordingly, students perform better on items where the largest fraction also has the largest numerator and denominator (i.e. congruent items, for example, 2/4 vs 1/3). Moreover, evidence for the natural number bias was found in that correct answers to incongruent items (i.e. where the natural number bias leads to the incorrect solution) took longer than giving a correct answer to congruent items (i.e. where the natural number bias leads to the correct solution) (Vamvakoussi et al., 2012;Van Hoof et al., 2013).
(2) Distance effect It was shown that the mean reaction time for fraction comparison tasks was predicted by the numerical distance between fractions. In other words, as two fractions are further apart, the median time to respond on the fraction comparison task decreases (Faulkenberry & Pierce, 2011). In this sense, fractions whose magnitude are closer together may be perceived as more difficult than fractions that are further apart. We distinguished between a small (≤ 0.15), medium (>0.15 -<0.35), and large distance (≥ 0.35).
(3) Gap thinking When responding to a fraction comparison task, many individuals apply the so-called gap thinking strategy, which consists of relying on which fraction has the smallest difference between the numerator and denominator to determine which fraction is the largest (González-Forte et al., 2020). For example, when comparing 2/7 versus 2/3, the gap between 2 and 7 is 5 which is more than the gap of 1 between 2 and 3, from which, according to this strategy, one concludes that 2/3 is larger than 2/7. For this indicator, it is considered whether applying the gap thinking strategy results in a correct answer or not. An additional neutral category was added because some items have the same gap (e.g. 6/7 vs 1/2).
(4) Benchmarking Some fractions, such as 1/2, are very prevalent so they can act as so-called benchmarks because their numerical value is instantly known (Obersteiner et al., 2020). When one of the two to be compared fractions in a fraction comparison task is a benchmark, the task proved to be easier. For a fraction comparison task, benchmarks may also be helpful when the two fractions to be compared are located on either side of a benchmark, for example, 7/9 is larger dan 1/2 and 3/8 is smaller than 1/2. We selected 9 benchmark fractions, so when one of the fractions of the comparison task was one of the 9 benchmarks, this indicator was categorized as easy. Furthermore, we made a distinction if the task contains no benchmark, but the two fractures to be compared were on either side of 1/2, the category was coded as medium and otherwise as difficult.
(5) Components Research on fraction comparison tasks has shown that fractions with a common component lead to more correct answers than fractions without a common component (González-Forte et al., 2020). In addition, it has been found that a common denominator (e.g. 1/4 vs 3/4), in particular, results in more correct fracture equations compared to common numerators (e.g. 2/4 vs 2/6). This indicator was coded as easy for fractions with a common component and difficult for fractions without a common component.
(6) Digits It is hypothesized that fractions consisting of double-digit numbers are more difficult than fractions consisting of single-digit numbers. A study focused on the natural number bias showed that for congruent fraction comparisons, 60% of the errors occurred when the fractions contained double-digit numbers (DeWolf & Vosniadou, 2011). Therefore, fractions with only single-digit numbers were coded as easy, fractions with only double-digits were coded as difficult and fractions containing a mix of single-and double digits were coded as medium.

Easy
This item is easy because there is a large distance effect, large brightness differences, congruency and there is no need to mix. There are no common components in this trial, but in this case it does not affect the difficulty of this trial.
Difficult This is a difficult item because of the small distance effect, small differences in brightness of the colours, no possible benchmarks, no congruency between lightest and darkest colour, no common components and the need to mix.

Figure 3
Phased Progress of the Trials (Example for the Easy Math Task) Table 1 Linear