Form perception is a cognitive correlate of the relation between subitizing ability and math performance.

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).

Verbalized arithmetic principles correlate with mathematics achievement.

BACKGROUND: When mathematical knowledge is expressed in general language, it is called verbalized mathematics. Previous studies on verbalized mathematics typically paid attention to mathematical vocabulary or educational practice. However, these studies did not exclude the role of symbolic mathematics ability, and almost no research has focused on verbalized mathematical principles. AIMS: This study is aimed to investigate whether verbalized mathematics ability independently predicts mathematics achievement. The current study hypothesized that verbalized mathematics ability supports mathematics achievement independent of general language, related cognitive abilities and even symbolic mathematical ability. SAMPLE: A sample of 241 undergraduates (136 males, 105 females, mean age = 21.95, SD = 2.38) in Beijing, China. METHODS: A total of 12 tests were used, including a verbalized arithmetic principle test, a mathematics achievement test, and tests on general language (sentence completion test), symbolic mathematical ability (including symbolic arithmetic principles test, simple arithmetic computation and complex arithmetic computation), approximate number sense ability (numerosity comparison test) and several related cognitive covariates (including the non-verbal matrix reasoning, the syllogism reasoning, mental rotation, figure matching and choice reaction time). RESULTS: Results showed that the processing of verbalized arithmetic principles displayed a significant role in mathematics achievement after controlling for general language, related cognitive abilities, approximate number sense ability and symbolic mathematics ability. CONCLUSIONS: The results suggest that verbalized mathematics ability was an independent predictor and provided empirical evidence supporting the verbalized mathematics role on achievement as an independent component in three-component mathematics model.

The structure correspondence hypothesis predicts how word and sentence in language correlate with term and principle in mathematics.

The association between language and mathematics is an important debated topic. Here, we proposed a structure correspondence hypothesis to explain under what conditions language and mathematics are closely related. According to the hypothesis, there would be an association when they have equivalent structure. One hundred and fifty high school students were recruited to finish mathematical and language tests at the element level (i.e., geometric term processing and word analogy) and at the low-dimensional combination level (i.e., geometric principle processing and sentence completion) as well as the tests to measure cognitive covariates (general intelligence and spatial processing). After controlling for age, gender and cognitive covariates, geometric term processing and word analogy were closely correlated, and geometric principle processing and sentence completion were significantly correlated. No other correlations were found. The results support the structure correspondence hypothesis and provide a new perspective of structure of language and verbalized mathematics for the relation between language and mathematics.

Different cognitive mechanisms used for solving open and closed math problems.

Problem-solving skills are very important in our daily life. Almost all problem-solving studies have addressed the cognitive correlates of solving closed problems, but only limited studies have investigated the cognitive mechanisms of solving open problems. The current study aimed to systematically examine differences between the cognitive mechanisms used for solving open and closed problems. In total, the abilities of 142 high school students to solve open and closed problems were assessed, as were a series of general cognitive abilities as controlled variates. Analogical reasoning uniquely contributed to solving both open and closed math problems, after controlling for age, gender, and inductive reasoning. Reactive cognitive flexibility (measured using the Wisconsin card sorting test) and spatial working memory uniquely correlated only with solving open and closed math problems, respectively. These findings suggest that the cognitive processes used to solve open and closed math problems differ. Open and closed math problems appear to require more reactive cognitive flexibility for generation and more memory for retrieval, respectively.

High-definition transcranial direct current stimulation (HD-tDCS) of the left middle temporal gyrus (LMTG) improves mathematical reasoning.

The role of the visuospatial network in mathematical processing has been established, but the role of the semantic neural network in mathematical processing is still poorly understood. The current study used high-definition transcranial direct current stimulation (HD-tDCS) to examine whether the semantic network supports mathematical processing. Using a single-blind, randomized, sham-controlled experimental design, 48 participants were randomly assigned to receive either anodal or sham HD-tDCS on the left middle temporal gyrus (LMTG), a core region of the semantic network. A number series completion task was used to measure mathematical reasoning and an arithmetical computation task was used as a control condition. Both tasks were administered before and after the 20 min HD-tDCS. The results showed that anodal HD-tDCS on the LMTG enhanced performance on the number series completion task, but not on the arithmetical computation task. Trial-level analysis further showed greater improvement at the more difficult problems of the number series completion task. These results demonstrate that the semantic network plays an important role in mathematical processing.

Verbal but not visual-spatial working memory contributes to complex arithmetic calculation.

The contribution of working memory to mathematics has been extensively studied. It has been proposed that verbal working memory (VWM) and visual-spatial working memory (VSWM) have distinct contributions, but results have been inconclusive. Here, we hypothesized that VWM and VSWM contribute differentially to separate sub-domains of mathematics. To test this hypothesis, we enrolled 199 primary school students and measured their VWM and VSWM with number/letter/matrix backward span tasks, and tested mathematics performance with simple subtraction, complex subtraction, multi-step calculation and number series completion, while controlling for several aspects of cognition. We found that while letter backward span had a significant contribution to complex subtraction, multi-step computation and number series completion, number backward span only had a significant contribution to multi-step computation, and matrix span had no effect on any math task. These results suggest that only VWM associated with complex mathematics, which might reflect verbal rehearsal. In contrast, VSWM does not appear to associated with mathematics.

The involvement of the semantic neural network in rule identification of mathematical processing.

The role of the visuospatial network in mathematical processing has been established, but the involvement of the semantic network in mathematical processing is still poorly understood. The current study utilized a number series completion paradigm with the event-related potential (ERP) technique to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. In total, 32 right-handed undergraduate students were recruited and asked to complete the number series completion as well as the arithmetical computation task in which numbers were presented in sequence. The event-related potential and multi-voxel pattern analysis showed that the rule identification process involves more semantic processing when compared with the arithmetical computation processes, and it elicited higher amplitudes for the late negative component (LNC) in left frontal and temporal lobes. These results demonstrated that the semantic network supports the rule identification in mathematical processing, with the LNC acting as the neural marker.

The developmental relationship between nonsymbolic and symbolic fraction abilities.

A fundamental research question in quantitative cognition concerns the developmental relationship between nonsymbolic and symbolic quantitative abilities. This study examined this developmental relationship in abilities to process nonsymbolic and symbolic fractions. There were 99 6th graders (Mage = 11.86 years), 101 10th graders (Mage = 15.71 years), and 102 undergraduate and graduate students (Mage = 21.97 years) participating in this study, and their nonsymbolic and symbolic fraction abilities were measured with nonsymbolic and symbolic fraction comparison tasks, respectively. Nonsymbolic and symbolic fraction abilities were significantly correlated in all age groups even after controlling for the ability to process nonsymbolic absolute quantity and general cognitive abilities, including working memory and inhibitory control. Moreover, the strength of nonsymbolic-symbolic correlations was higher in 6th graders than in 10th graders and adults. These findings suggest a weakened association between nonsymbolic and symbolic fraction abilities during development, and this developmental pattern may be related with participants' increasing proficiency in symbolic fractions.

Academic achievement is more closely associated with student-peer relationships than with student-parent relationships or student-teacher relationships.

Introduction: Personal relationships have long been a concern in education. Most studies indicate that good personal relationships are generally positively correlated with academic performance. However, few studies have compared how different types of personal relationships correlate with academic performance, and the conclusions of existing studies are inconsistent. Based on a large sample, the current study compared how the three closest types of personal relationships among students (with parents, teachers, and their peers) compared with their academic performance. Methods: Cluster sampling was used to issue questionnaires to students in Qingdao City, Shandong Province, China in 2018 (Study 1) and in 2019 (Study 2). The actual sample size included 28168 students in Study 1 and 29869 students in Study 2 (both studies, Grades 4 and 8), thus totaling 58037 students. All students completed a personal relationship questionnaire and several academic tests. Results: The results showed that: (1) the quality of personal relationships significantly and positively correlated with academic performance; (2) Among the three types of relationships tested, the quality of student-peer relationships was the most closely associated with academic achievement. Discussion: This study gives insights into future research directions in this field and also reminds educators to pay attention to the personal relationships among their students, especially peer relationships.

Altered resting-state functional connectivity in the prefrontal cortex is related to the development of dyscalculia in patients with Turner syndrome.

AIM: Patients with Turner syndrome have a high rate of developmental dyscalculia, but the underlying neurocognitive mechanisms are not well-understood. Some studies have implicated visuospatial impairments in patients with Turner syndrome, but others have focused on poor procedural skills in patients with Turner syndrome. This study used brain imaging data to test these two alternative views. METHODS: This study recruited 44 girls with Turner syndrome (mean age, 12.91 years; SD, 2.02), with 13 (29.5%) of them meeting the criterion for developmental dyscalculia, and 14 normally developing girls (mean age, 14.26 years; SD, 2.18) as a comparison group. All participants were given basic mathematical ability tests and an intelligence test and were scanned using magnetic resonance imaging. We compared patients with Turner syndrome who had dyscalculia, patients with Turner syndrome who did not have dyscalculia, and the normal controls in terms of brain structures and resting-state functional activity. RESULTS: Compared with normal controls, both groups of patients with Turner syndrome (with or without dyscalculia) showed similarly altered functional connectivity in the occipitoparietal dorsal stream. Importantly, compared with patients with Turner syndrome without dyscalculia and normal controls, patients with Turner syndrome with dyscalculia showed decreased functional connectivity between the prefrontal and the lateral occipital cortex. CONCLUSION: We concluded that both groups of patients with Turner syndrome shared visual deficits, and patients with Turner syndrome with dyscalculia had a deficit in frontal cortex-based higher cognitive processing. It is not their visuospatial deficits but rather their deficits in higher cognitive processing that are responsible for the development of dyscalculia in patients with Turner syndrome.

The database for extracting numerical and visual properties of numerosity processing in the Chinese population.

The ability to handle non-symbolic numerosity has been recurrently linked to mathematical abilities. The accumulated data provide a rich resource that can reflect the underlying properties (i.e., dot ratio, area, convex hull, perimeters, distance, and hash) of numerosity processing. This article reports a database of numerosity processing in the Chinese population. The database contains five independent datasets with 7459, 4902, 415, 671, 414 participants respectively. For each dataset, all data were collected in the same online computerized test, examination room, professorial tester, and using the same protocols. Computational modeling method could be used to extract the dot ratio and visual properties of numerosity from five types of dot stimuli. This database enables researchers to test the theoretical hypotheses regarding numerosity processing using a large sample population. The database can also indicate the individual difference of non-symbolic numerosity in mathematical abilities.

Differential associations between scale-free neural dynamics and different levels of cognitive ability.

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.

Early neural markers for individual difference in mathematical achievement determined from rational number processing.

The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.

How are different math knowledge presentations associated with math anxiety?

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.

The association between experience-based risky choice and mathematical ability.

Mathematical ability has always been considered an important influencing factor in description-based risky choices. Experience-based risky choices, which occur frequently in daily life, are very different from description-based risky choices. The association between experience-based risky choice and mathematical ability remains unknown. This study adopts the feedback paradigm for experience-based risky choice to explore the association between multiple mathematical abilities and experience-based risky choice. The results show that, in experience-based risky choice, mathematical ability did not influence the decision to pursue higher expected value, but it did influence preference for risky. Thus, our study contributes to a more comprehensive view of mathematical ability and risky choice.

Phonological activation improves semantic access provided by Arabic digits and number words.

Arabic digits (e.g., "6") and number words (e.g., "", "six", " ") are the two main formats in which numbers can be represented. Although phonology plays a crucial role in the semantic accessing of alphabetic words and Chinese characters, whether it is involved in the processing of different numerical notations, which have been shown to be dissociable from characters, is still unknown. Using a parity judgment task, two experiments were performed by manipulating the phonological relationship between a prime and a target. The primes were Tibetan or Chinese characters and the targets were presented either as number words (Experiment 1) or as Arabic digits (Experiment 2). The results revealed that phonology affected semantic access for both number words and Arabic digits. Additionally, semantic access for Tibetan number words was more susceptible to phonological information. The results for Arabic digits followed the same pattern for Tibetan primes. Further, language proficiency also affected the role of phonology in number processing. Participants with low language proficiency relied more on phonological encoding when processing the numbers. The results suggest that phonology is crucial for semantic access of different numerical notations.

Math anxiety as an independent psychological construct among social-emotional attitudes: An exploratory factor analysis.

Math anxiety is a widespread problem for children and adolescents worldwide. However, the psychological trait of math anxiety is poorly understood. The present study aimed to examine the psychological construct of math anxiety among social-emotional attitudes. A total of 28,726 students, including 17,378 fourth graders and 11,348 eighth graders, were selected from the Qingdao Basic Education Quality Assessment database using multi-stage cluster random sampling. There were 10 questionnaires assessing social-emotional attitudes in the database. Pearson's correlation analyses were performed to examine the intercorrelations between social-emotional attitudes and mathematical performance. Exploratory factor analysis (EFA) was conducted to examine the psychological structure of these 10 social-emotional attitudes. After controlling for other social-emotional attitudes, math anxiety had a weak but significant correlation to mathematical performance in most subtests across grades. Among three-factor, four-factor, and five-factor EFA models, math anxiety was an independent factor that was separate from other social-emotional attitudes across six parallel subtests in grades four and eight. Math anxiety is a stable and independent psychological construct that is separate from other social-emotional attitudes. It suggests that math anxiety should be considered as a distinct anxiety disorder specific to mathematical learning in subsequent versions of the Diagnostic and Statistical Manual of Mental Disorders.

Language Ability Accounts for Ethnic Difference in Mathematics Achievement.

The mathematics achievement of minority students has always been a focal point of educators in China. This study investigated the differences in mathematics achievement between Han and minority pupils to determine if there is any cognitive mechanism that can account for the discrepancy. We recruited 236 Han students and 272 minority students (including Uygur and Kazak) from the same primary schools. They were tested on mathematics achievement, language abilities, and general cognitive abilities. The results showed that Han pupils had better mathematics achievement scores and better Chinese language ability than minority students. After controlling for age, gender, and general cognitive abilities, there were still significant differences in mathematics achievement between Han and minority students. However, these differences disappeared after controlling for language ability. These results suggest that the relatively poor levels of mathematics achievement observed in minority students is related to poor Chinese language skills.

Numerosity sense correlates with fluent mathematical abilities.

Although a great deal of research has shown a relationship between numerosity sense and mathematical ability, some studies have failed to do so. The main source of this inconsistency could be the varied ways of measuring mathematical abilities. The current investigation explored several types of mathematical ability, from basic number processing and arithmetic computation to numerical reasoning and arithmetic learning. We hypothesized that the correlation between numerosity sense and mathematical ability depends on mathematical fluency. A total of 415 college students (178 males and 237 females, mean age = 20.42 years, range = 18.58-22.92 years) were recruited to complete seven mathematical tasks and two numerosity tasks, as well as other tasks that measured cognitive covariates. The results showed that after controlling for age, gender, and related general cognitive factors, numerosity sense still predicted substantial variation in parity judgment, visual digit comparison, and computation, but it did not predict variation in numerosity estimation, auditory digit comparison, number series completion, or digit associate learning. The results suggest that numerosity sense correlates with mathematical abilities that accompany fluency.

The association between non-symbolic number comparison and mathematical abilities depends on fluency.

Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.