Both non-symbolic and symbolic quantity processing are important for arithmetical computation but not for mathematical reasoning

The interconnection of orthographic, phonetic, and semantic skills with arithmetic fluency

Arithmetic fluency is considered considers highly rely on language processing, encompassing essential skills. However, the independent predictive power of phonetic, semantic, or orthographic skills in relation to arithmetic fluency remains an unresolved query. This study introduces the common component hypothesis to elucidate the inconsistent findings in previous research. The hypothesis posits that significant correlations between language and mathematics hinge on whether the language and mathematics utilized in a given task share a common component. According to this hypothesis, processing skills for each of the three fundamental language elements (i.e., phonetic, semantic, orthographic) should correlate with arithmetic fluency, as these elements are also integral to simple arithmetic processing. A cohort of one hundred and ninety-eight primary school students participated in the study, undertaking a battery of tests assessing general cognitive abilities, psycholinguistic elements, and arithmetic fluency. The results showed that orthographic, phonetic, and semantic abilities independently predicted arithmetic fluency, even after accounting for all other cognitive predictors. These findings substantiate the common component hypothesis, providing empirical support for explaining the association between language and mathematics. This evidence contributes to addressing the interplay between language and mathematics in educational contexts.

Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency

BACKGROUND

Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'.

AIMS

The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels.

SAMPLE

Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later).

METHODS

Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured.

RESULTS

Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2.

CONCLUSION

Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.

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 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.

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.

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.

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.

Visual Perception Supports Adults in Numerosity Processing and Arithmetical Performance

Previous studies have found a correlation between numerosity processing and arithmetical performance. Visual perception has already been indicated as the shared cognitive mechanism between these two; however, these studies mostly focused on children. It is not clear whether the association between numerosity processing and arithmetical performance still existed following the development of individual arithmetical performance. Consequently, the underlying role of visual perception in numerosity processing and arithmetical performance has not been sufficiently studied in adults. For this study, researchers selected a total of 205 adult participants with an average age of 22years. The adults were administered arithmetic tests, numerosity comparison, and visual figure matching. Mental rotation, choice reaction time, and nonverbal intelligence were used as cognitive covariates. Results showed that numerosity comparison of adults correlated with their arithmetical performance, even after controlling for age and gender differences as well as general cognitive processing. However, after controlled for visual figure matching, the well-established association between numerosity comparison and arithmetic performance disappeared. These results supported the visual perception hypothesis, that visual perception measured by visual figure matching can account for the correlation between numerosity comparison and arithmetic performance. This indicated that even for adult populations, visual perceptual ability was the underlying component of numerosity processing and arithmetic performance.

Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.

Visual form perception predicts 3-year longitudinal development of mathematical achievement

Numerous studies have demonstrated an association between approximate number system (ANS) acuity and mathematical performance. Studies have also shown that ANS acuity can predict the longitudinal development of mathematical achievement. Visual form perception in the current investigation was proposed to account for the predictive role of ANS acuity in the development of mathematical achievement. One hundred and eighty-eight school children (100 males, 88 females; mean age = 12.2 ± 0.3 years) participated in the study by completing five tests: numerosity comparison, figure matching, mental rotation, nonverbal matrix reasoning, and choice reaction time. Three years later, they took a mathematical achievement test. We assessed whether the early tests predicted mathematical achievement at the later date. Analysis showed that the ANS acuity measured via numerosity comparison significantly predicted mathematical achievement 3 years later, even when controlling for individual differences in mental rotation, nonverbal matrix reasoning, and choice reaction time, as well as age and gender differences. Hierarchical regression and mediation analyses further showed that the longitudinal predictive role of ANS acuity in mathematical achievement was interpreted by visual form perception measured with a figure-matching test. Together, these results indicate that visual form perception may be the underlying cognitive mechanism that links ANS acuity to mathematical achievement in terms of longitudinal development.

Visual form perception is fundamental for both reading comprehension and arithmetic computation

Visual perception has been found to be a critical factor for reading comprehension and arithmetic computation in separate lines of research with different measures of visual form perception. The current study of 1099 Chinese elementary school students investigated whether the same visual form perception (assessed by a geometric figure matching task) underlies both reading comprehension and arithmetic computation. The results showed that visual form perception had close relations with both reading comprehension and arithmetic computation, even after controlling for age, gender, and cognitive factors such as processing speed, attention, working memory, visuo-spatial processing, and general intelligence. Results also showed that numerosity comparison's relations with reading comprehension and arithmetic computation were fully accounted for by visual form perception. These results suggest that reading comprehension and arithmetic computation might share a similar visual form processing mechanism.

The Role of Approximate Number System in Different Mathematics Skills Across Grades

Although approximate number system (ANS) has been found to predict mathematics ability, it remains unclear if both aspects of ANS (symbolic and non-symbolic estimation) contribute equally well to mathematics performance and if their contribution varies as a function of the mathematics outcome and grade level. Thus, in this study, we examined the effects of both aspects of ANS on different mathematics skills across three grade levels. Three hundred eleven children (100 children from kindergarten, 107 children from Grade 2, and 104 children from Grade 4) from two kindergartens and three elementary schools in Shanghai, China, were assessed on measures of ANS (dot estimation and number line estimation), general cognitive ability (nonverbal intelligence, inhibition, and working memory), and mathematics abilities (numerical operations and mathematical problem solving in all grades, early mathematical skills in kindergarten, and calculation fluency in Grades 2 and 4). Results of hierarchical regression analyses showed that, in kindergarten, non-symbolic estimation predicted all mathematics skills even after controlling for age, gender, and general cognitive ability. In Grades 2 and 4, symbolic estimation accounted for unique variance in mathematical problem solving, but not in calculation fluency. Symbolic estimation also predicted numerical operations in Grade 4. Taken together, these findings suggest that in the early phases of mathematics development different aspects of ANS contribute to different mathematics skills.

Bogdanova O, Kovas Y. Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

Relation between Approximate Number System Acuity and Mathematical Achievement: The Influence of Fluency

Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants' performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement.