Previous research has shown that females consistently outperform males in exact arithmetic, perhaps due to the former's advantage in language processing. Much less is known about gender difference in approximate arithmetic. Given that approximate arithmetic is closely associated with visuospatial processing, which shows a male advantage we hypothesized that males would perform better than females in approximate arithmetic. In two experiments (496 children in Experiment 1 and 554 college students in Experiment 2), we found that males showed better performance in approximate arithmetic, which was accounted for by gender differences in spatial ability.

Numerical processing has been demonstrated to be subserved typically by the brain regions around the bilateral intraparietal sulcus (IPS). The goal of the current study was to investigate whether the processing of mathematical terms shared the same brain regions with numerical processing. Healthy adult participants performed semantic distance judgment tasks on five types of materials, including geometric terms, algebraic terms, linguistic terms, words for tools and other common objects, and Arabic numbers. Brain activation was measured with functional magnetic resonance imaging (fMRI). The results showed that geometric terms had greater activation than algebraic terms, linguistic terms and tool words in the horizontal IPS, but algebraic terms did not have greater activation than linguistic terms and tool words in this region. Arabic numbers showed greater activation than non-number materials (including geometric terms, algebraic terms, linguistic terms and tool words) in the bilateral IPS, right inferior frontal gyrus and bilateral middle frontal gyrus, but the non-number materials showed stronger activation in the left inferior frontal gyrus and left middle temporal gyrus. These results suggest that the brain area for the processing of numbers (the left IPS) seems to be involved in semantic processing of geometric terms, but not that of other mathematical terms such as algebraic terms. Both algebraic and geometric terms share similar brain organization with basic semantic processing in the left temporal and frontal regions.

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0–11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers. Forty undergraduates were asked to judge whether two two-digit numbers (presented serially in Experiment 1 and simultaneously in Experiment 2) were the same or not. Results showed that, when numbers were presented serially, unit digits did not make unique contributions to the magnitude and distance effects, supporting the holistic model. When numbers were presented simultaneously, unit digits made unique contributions, supporting the compositional model. The SNARC (Spatial-Numerical Association of Response Codes) effect was evident for the whole numbers and the decade digits, but not for the unit digits in both experiments, which indicates that two-digit numbers are represented on one mental number line. Taken together, these results suggested that the representation of two-digit numbers is on a single mental number line, but it depends on the stage of processing whether they are processed holistically or compositionally.

Quantities can be represented using either mathematical language (i.e., numbers) or natural language (i.e., quantifiers). Previous studies have shown that numerical processing elicits greater activation in the brain regions around the intraparietal sulcus (IPS) relative to other semantic processes. However, little research has been conducted to investigate whether the IPS is also critical for the semantic processing of quantifiers in natural language. In this study, 20 adults were scanned with functional magnetic resonance imaging while they performed semantic distance judgment involving six types of materials (i.e., frequency adverbs, quantity pronouns and nouns, animal names, Arabic digits, number words, and dot arrays). Conjunction analyses of brain activation showed that numbers and dot arrays elicited greater activation in the right IPS than did words (i.e., animal names) or quantifiers (i.e., frequency adverbs and quantity pronouns and nouns). Quantifiers elicited more activation in left middle temporal gyrus and inferior frontal gyrus than did numbers and dot arrays. No differences were found between quantifiers and animal names. These findings suggest that, although quantity processing for numbers and dot arrays typically relies on the right IPS region, quantity processing for quantifiers typically relies on brain regions for general semantic processing. Thus, the IPS does not appear to be the only brain region for quantity processing.

Behavioral studies have reported that males perform better than females in 3-dimensional (3D) mental rotation. Given the important role of the hippocampus in spatial processing, the present study investigated whether structural differences in the hippocampus could explain the sex difference in 3D mental rotation. Results showed that after controlling for brain size, males had a larger anterior hippocampus, whereas females had a larger posterior hippocampus. Gray matter volume (GMV) of the right anterior hippocampus was significantly correlated with 3D mental rotation score. After controlling GMV of the right anterior hippocampus, sex difference in 3D mental rotation was no longer significant. These results suggest that the structural difference between males' and females' right anterior hippocampus was a neurobiological substrate for the sex difference in 3D mental rotation.

Background

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).

Aims

To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics.

Samples

We recruited 80 undergraduates from four universities in Beijing.

Methods

The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing.

Results

The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics.

Conclusions

Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications.

There are three main hypotheses about mental representations of arithmetic facts: the independent representation hypothesis, the operand-order-free single-representation hypothesis, and the operand-order-specific single-representation hypothesis. The current study used electrical recordings of eye movements to examine the organization of arithmetic facts in long-term memory. Subjects were presented single-digit addition and multiplication problems and were asked to report the solutions. Analyses of the horizontal electrooculograph (HEOG) showed an operand order effect for multiplication in the time windows 150-300 ms (larger negative potentials for smaller operand first problems than for larger operand first ones). The operand order effect was reversed in the time windows from 400 to 1,000 ms (i.e., larger operand first problems had larger negative potentials than smaller operand first problems). For addition, larger operand first problems had larger negative potentials than smaller operand first in the series of time windows from 300 to 1,000 ms, but the effect was smaller than that for multiplication. These results confirmed the dissociated representation of addition and multiplication facts and were consistent with the prediction of the preferred operand-order-specific representation hypothesis.

To test whether the retrieval of arithmetic facts is independent of numerical notations, this study investigated the event-related potentials elicited by single-digit addition and multiplication problems in Arabic digits and Chinese number words. The results showed that, in comparison with addition, multiplication elicited a greater N300-like component at the left anterior electrodes and greater late positive potentials at the right posterior electrodes, regardless of numerical notations. The operation effects lasted from 250 to 900 ms for Arabic digits, but from 250 to 1400 ms for Chinese number words when participants were asked to respond only to false arithmetic equations (experiment one), and lasted from 350 to 1400 ms for Arabic digits and Chinese number words when participants were asked to respond to both true and false arithmetic equations (experiment two). The consistency in the operation effects in ERPs (i.e., a dissociation of brain organization for different arithmetic operations) for different number notations suggests that mental representation and retrieval of arithmetic facts may be relatively independent of numerical notations.

This study compared the patterns of brain activation elicited by single-digit addition and multiplication problems. 20 Chinese undergraduates were asked to verify whether arithmetic equations were true or false during functional magnetic resonance imaging. Results showed that both addition and multiplication were supported by a broad neural system that involved regions within SMA, precentral gyrus, intraparietal sulcus, occipital gyri, superior temporal gyrus, and middle frontal gyrus, as well as some subcortical structures. Nevertheless, addition problems elicited more activation in the intraparietal sulcus and middle occipital gyri at the right hemisphere, and superior occipital gyri at both hemispheres, whereas multiplication had more activation in precentral gyrus, supplementary motor areas, and posterior and anterior superior temporal gyrus at the left hemisphere. This pattern of dissociated activation supports our hypothesis that addition has greater reliance on visuospatial processing and multiplication on verbal processing.