Children skilled in mental abacus show enhanced non-symbolic number sense

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.

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.

How does working memory matter in young children's arithmetic skills: The mediating role of basic number processing

The current study investigated whether and how each component of the working memory model was associated with kindergarten children's arithmetic performance. A total of 103 Chinese kindergarten children were administered tests of the visuospatial sketchpad, the phonological loop, the central executive, and basic number processing (i.e., number line estimation, nonverbal numerosity estimation and numerical magnitude comparison). The results showed that among the three working memory components, the central executive accounted for a significant proportion of the variance in young children's arithmetic performance. In terms of basic number processing, number line estimation and numerical magnitude comparison had significant influences on young children's arithmetic performance. Furthermore, numerical magnitude comparison played a mediating role between the visuospatial sketchpad and early arithmetic skills. These findings highlight the importance of working memory and basic number processing in early arithmetic skills and reveal different pathways through which the three working memory components influence young children's arithmetic performance.

Non-symbolic and symbolic number lines are dissociated

People use mental number lines for both symbolic numerals and numerosity, but little is known about how these two mental number lines are related. The current study investigated the association in effect size, directionality of the mental number line, and development between symbolic and non-symbolic mental number lines to determine if they were related to or independent from each other. We collected data from numerosity- and digit-matching tasks that used the following numbers: 11, 14, 17, 20, 23, 26, and 29. Tasks were performed by college undergraduates and the fifth-grade primary school students. The results showed that none of the effects for non-symbolic numbers was related to any of the effects for symbolic numbers, and vice versa, in both adults and children. Another notable finding was that the correlation between the SNARC (spatial-numerical association of response code) effect size and mathematical ability was negative in the adult group. These results are consistent with the dissociated processes hypothesis and suggest that mental number lines are notation-dependent. As shown by the SNARC effect, the mental number line might result in interference in the current task by an automatically activated spatial notation-dependent representation of numbers.

A Review of the Effects of Abacus Training on Cognitive Functions and Neural Systems in Humans

Abacus, which represents numbers via a visuospatial format, is a traditional device to facilitate arithmetic operations. Skilled abacus users, who have acquired the ability of abacus-based mental calculation (AMC), can perform fast and accurate calculations by manipulating an imaginary abacus in mind. Due to this extraordinary calculation ability in AMC users, there is an expanding literature investigating the effects of AMC training on cognition and brain systems. This review study aims to provide an updated overview of important findings in this fast-growing research field. Here, findings from previous behavioral and neuroimaging studies about AMC experts as well as children and adults receiving AMC training are reviewed and discussed. Taken together, our review of the existing literature suggests that AMC training has the potential to enhance various cognitive skills including mathematics, working memory and numerical magnitude processing. Besides, the training can result in functional and anatomical neural changes that are largely located within the frontal-parietal and occipital-temporal brain regions. Some of the neural changes can explain the training-induced cognitive enhancements. Still, caution is needed when extend the conclusions to a more general situation. Implications for future research are provided.