As indicators of cognitive function, scale‐free neural dynamics are gaining increasing attention in cognitive neuroscience. Although the functional relevance of scale‐free dynamics has been extensively reported, one fundamental question about its association with cognitive ability remains unanswered: is the association universal across a wide spectrum of cognitive abilities or confined to specific domains? Based on dual‐process theory, we designed two categories of tasks to analyze two types of cognitive processes—automatic and controlled—and examined their associations with scale‐free neural dynamics characterized from resting‐state electroencephalography (EEG) recordings obtained from a large sample of human adults (N = 102). Our results showed that resting‐state scale‐free neural dynamics did not predict individuals' behavioral performance in tasks that primarily engaged the automatic process but did so in tasks that primarily engaged the controlled process. In addition, by fitting the scale‐free parameters separately in different frequency bands, we found that the cognitive association of scale‐free dynamics was more strongly manifested in higher‐band EEG spectrum. Our findings indicate that resting‐state scale‐free dynamics are not universal neural indicators for all cognitive abilities but are mainly associated with high‐level cognition that entails controlled processes. This finding is compatible with the widely claimed role of scale‐free dynamics in reflecting properties of complex dynamic systems.

Open math problem solving is critical to help students deepen the understanding and promote transfer of mathematics knowledge. However, the cognitive mechanism for open math problem solving, particularly the role of spatial abilities, has not been paid enough attention. This study recruited 192 junior middle school students (14.30 ± 0.48 years old). Results showed that both spatial visualisation (measured by paper folding) and spatial working memory (measured by spatial 2‐back) significantly associated with open math problem solving with controlled variables including age, sex, nonverbal matrix reasoning, and arithmetic principles. Moreover, spatial working memory was more associated with easy open math problem solving, while spatial visualisation more associated with difficult open math problem solving. These findings suggested that as the difficulty of open math problems increased, the construction of problem space mattered more than retaining and updating problem space in open math problem solving.

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A close relationship between math performance and math anxiety has been demonstrated, but how different presentations of mathematics are associated with math anxiety has not been investigated. This study recruited 826 elementary school students in grades 5 and 6. All students were given math trait and state anxiety questionnaires; a nonverbal matrix reasoning task; and verbalized, symbolic, and situational fraction problem-solving tasks. After data cleaning, 475 boys and 323 girls (798 in total) were included in the analysis (mean age = 11.79, SD = 0.82). Partial correlation analysis showed that students' math traits and state anxiety were more closely related to symbolic fraction problem-solving than to verbalized and situational fraction problem-solving. Mixed linear model analysis showed that math state anxiety for symbolic problem-solving was significantly greater than that for verbalized and situational problem-solving. Based on these findings, we concluded that the presentation of symbolic math is more likely to induce math anxiety than verbalized or situational math. This finding has potential practical applications in math anxiety interventions and education.