Gender Differences in Arithmetic Strategy Use: A Function of Skill and Preference

Unpacking associations among children's spatial skills, mathematics, and arithmetic strategies: decomposition matters

Several studies revealed links between mental rotation and mathematical tasks, but the intervening processes in this connection remain rather unexplored. Here, we aimed to investigate whether children's mental rotation skills relate to their accuracy in solving arithmetic problems via their usage of decomposition strategies, thus probing one potential intervening process. To this end, we examined a sample of 6- to 8-year-olds (N = 183) with a chronometric mental rotation task, and asked children to solve several arithmetic problems while assessing their solution strategies. After each arithmetic problem, children were asked about their strategy to solve the respective arithmetic problem and these were classified as either counting, decomposition, or retrieval strategies. Analyses were controlled for age, sex, fluid and verbal reasoning. Results indicated that children's response times and accuracy in the mental rotation task were best explained by linear functions of rotation angle, suggesting the usage of dynamic mental transformation strategies. A multiple mediation model revealed that children with higher mental rotation skills were more inclined to use higher-level mental strategies such as decomposition which in turn increased their accuracy of solving arithmetic problems. None of the other arithmetic strategies revealed significant indirect effects. These findings suggest that children with higher mental rotation skills may profit from visualizing and flexibly transforming numerical magnitudes, increasing the frequency of decomposition strategies. Overall, decomposition may play a unique role in the connection between children's mental rotation and arithmetic skills, which is an essential information for planning future training and experimental studies.

Arithmetic problem size modulates brain activations in females but not in males

Numerous empirical studies have reported that males and females perform equally well in mathematical achievement. However, still to date, very limited is understood about the brain response profiles that are particularly characteristic of males and females when solving mathematical problems. The present study aimed to tackle this issue by manipulating arithmetic problem size to investigate functional significance using functional magnetic resonance imaging (fMRI) in young adults. Participants were instructed to complete two runs of simple calculation tasks with either large or small problem sizes. Behavioural results suggested that the performance did not differ between females and males. Neuroimaging data revealed that sex/gender-related patterns of problem size effect were found in the brain regions that are conventionally associated with arithmetic, including the left middle frontal gyrus (MFG), left intraparietal sulcus (IPS) and insula. Specifically, females demonstrated substantial brain responses of problem size effect in these regions, whereas males showed marginal effects. Moreover, the machine learning method implemented over the brain signal levels within these regions demonstrated that sex/gender is discriminable. These results showed sex/gender effects in the activating patterns varying as a function of the distinct math problem size, even in a simple calculation task. Accordingly, our findings suggested that females and males use two complementary brain resources to achieve equally successful performance levels and highlight the pivotal role of neuroimaging facilities in uncovering neural mechanisms that may not be behaviourally salient.

Spatial-Numerical Magnitude Estimation Mediates Early Sex Differences in the Use of Advanced Arithmetic Strategies

An accumulating body of literature points to a link between spatial reasoning and mathematics learning. The present study contributes to this line of research by investigating sex differences both in spatial representations of magnitude and in the use of arithmetic strategies, as well as the relation between the two. To test the hypothesis that sex differences in spatial-numerical magnitude knowledge mediate sex differences in the use of advanced strategies (retrieval and decomposition), two studies were conducted. Study 1 included 96 US first graders (53% girls); Study 2 included 210 Russian first graders (49% girls). All participants completed a number line estimation task (a spatially based measure of numerical magnitude knowledge) and an arithmetic strategy task (a measure of strategy choice). The studies showed parallel results: boys produced more accurate numerical magnitude estimates on the number line estimation task and used advanced strategies more frequently on the arithmetic task. Critically, both studies provide support for the mediation hypothesis (although there were some differences in the pattern obtained for the two strategies). The results are discussed in the context of broader research about the relation between spatial and mathematical skills.

Ordinal models to analyze strategy sophistication: Evidence from a learning trajectory efficacy study

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We leverage data from a randomized teaching experiment with a kindergarten sample whose details are outlined in Clements et al. (2020). First, we describe our problem-solving strategy data, including how strategies were coded in ways that are amenable to analysis. Second, we explore what kinds of ordinal statistical models best fit the nature of arithmetic strategies, describe what each model implies about problem-solving behavior, and how to interpret model parameters. Third, we discuss the effect of "treatment", operationalized as instruction aligned with an arithmetic Learning Trajectory (LT). We show that arithmetic strategy development is best described as a sequential stepwise process and that children who receive LT instruction use more sophisticated strategies at post-assessment, relative to their peers in a teach-to-target skill condition. We introduce latent strategy sophistication as an analogous metric to traditional Rasch factor scores and demonstrate a moderate correlation them (r = 0.58). Our work suggests strategy sophistication carries information that is unique from, but complimentary to traditional correctness-based Rasch scores, motivating its expanded use in intervention studies.

Association between motor and math skills in preschool children with typical development: Systematic review

Mathematics has been the subject in which many school-age children have revealed many difficulties. Research carried out in an attempt to understand the causes of failure in this area pointed to a positive association between mathematical performance and motor performance. Given the importance of math development in future school outcomes, knowing which specific motor components are most associated with math performance can help educators define better strategies for teaching mathematics. In this sense, the present systematic review study aimed to identify the components of motor skills most positively associated with mathematical performance in children with typical development who attend preschool. The PRISMA methodology (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) was used in this study. The databases searched were ERIC, PubMED, SciELO, Scopus and Web of Science. A total of 2,909 articles were identified, of which 18 were included in this systematic review. The main results showed positive associations between fine motor skills, namely fine motor coordination and visuomotor integration, and mathematical performance. The math skill of numerical counting was the most associated with FMS. The main characteristics of the instruments used showed that the tasks of copying figures or drawings are the most used to assess visuomotor integration and the tasks of handling objects with pinch-like movements are the most used to assess fine motor coordination. Given the importance of mathematical performance in future school results, identifying early children with difficulties in fine motor skills will help educators to design better strategies for teaching mathematical skills. In this sense, the need to identify instruments to assess fine motor skills in preschool children with characteristics that facilitate their administration by the educator in the classroom context, i.e., requiring little administration time, not requiring much experience or training, the possibility of being administered to the group/class, few material resources, and the results can be easily interpreted, classified, and associated with mathematical performance.

Sex differences in the association of math achievement with visual-spatial and verbal working memory: Does the type of math test matter?

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual‐spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual‐spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual‐spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual‐spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older.

Sources of measurement error in pediatric intelligence testing

Pediatric intelligence tests, such as the Wechsler Intelligence Scale for Children, are commonly used diagnostic tools used in the process of diagnosing learning and behavior disabilities. Decisions concerning treatment are made based on the results of these tests and they are frequently used in educational and vocational contexts for important decisions that impact persons’ academic or professional lives. Research has however shown that important errors may occur despite the application of validation processes and adherence to quality criteria for psychometric tests. At the same time this evidence seems not to be pervasively acknowledged in psychological practice and research. In this article, I will showcase research that places attention on sources of measurement error in pediatric intelligence testing, discuss a process-performance approach to measurement in intelligence testing, and propose the “pretest methods,” methods stemming from the field of survey methodology commonly used in questionnaire construction, as a method to help address the problem of sources of measurement error in pediatric intelligence testing and improve the development of these intelligence tests.

Aerobic fitness relates to superior exact and approximate arithmetic processing in college-aged adults

BACKGROUND

Aerobic fitness relates to superior math achievement, but the underlying reasons remain unclear. This study tested how more efficient processing (efficiency hypothesis) or enhanced allocation of cognitive resources (resources hypothesis) underly fitness-related differences in arithmetic cognition in a sample of 138 college-aged adults.

METHOD

Participants completed an arithmetic task while pupillary measures were recorded prior to an aerobic fitness test.

RESULTS

Higher aerobic fitness was associated with shorter reaction time for all problems and greater pupillary reactivity for problems requiring approximate and exact arithmetic.

CONCLUSIONS

Superior aerobic fitness relates to greater cognitive resources available to execute exact and approximate arithmetic faster. Fitness-related differences in math achievement may be driven by the cognitive resources underlying arithmetic strategy. These differences may extend beyond educational achievement and affect the motivation to engage in health behaviors based on quantitative information. Thus, improving cardiovascular fitness has the potential to also ameliorate health numeracy.

Effect of Finger Gnosis on Young Chinese Children's Addition Skills

Evidence has revealed an association between finger gnosis and arithmetic skills in young Western children, however, it is unknown whether such an association can be generalized to Chinese children and what mechanism may underlie this relationship. This study examines whether finger gnosis is associated with addition skills in young Chinese children and, if so, what numerical skills could explain this correlation. A total of 102 Chinese children aged 5–6 years were asked to complete finger gnosis and addition tasks in Study 1. Results showed that finger gnosis was significantly associated with addition performance. However, no significant correlation was found between finger gnosis and the use of finger counting in solving addition problems. Moreover, girls’ finger gnosis was better than boys’, and children with musical training demonstrated better finger gnosis than those without. In Study 2, 16 children with high finger gnosis and 20 children with low finger gnosis were selected from the children in Study 1 and asked to perform enumeration, order judgment, number sense, and number line estimation. Children with high finger gnosis performed better in number line estimation than their counterparts with low finger gnosis. Moreover, the number line estimation fully mediated the relationship between finger gnosis and addition performance. Together, these studies provide evidence of a correlation between finger gnosis and addition skills. They also highlight the importance of number line estimation in bridging this association.

Counting on fine motor skills: links between preschool finger dexterity and numerical skills

Finger counting is widely considered an important step in children's early mathematical development. Presumably, children's ability to move their fingers during early counting experiences to aid number representation depends in part on their early fine motor skills (FMS). Specifically, FMS should link to children's procedural counting skills through consistent repetition of finger-counting procedures. Accordingly, we hypothesized that (a) FMS are linked to early counting skills, and (b) greater FMS relate to conceptual counting knowledge (e.g., cardinality, abstraction, order irrelevance) via procedural counting skills (i.e., one-one correspondence and correctness of verbal counting). Preschool children (N = 177) were administered measures of procedural counting skills, conceptual counting knowledge, FMS, and general cognitive skills along with parent questionnaires on home mathematics and fine motor environment. FMS correlated with procedural counting skills and conceptual counting knowledge after controlling for cognitive skills, chronological age, home mathematics and FMS environments. Moreover, the relationship between FMS and conceptual counting knowledge was mediated by procedural counting skills. Findings suggest that FMS play a role in early counting and therewith conceptual counting knowledge.

The association between symbolic and nonsymbolic numerical magnitude processing and mental versus algorithmic subtraction in adults

There are two well-known computation methods for solving multi-digit subtraction items, namely mental and algorithmic computation. It has been contended that mental and algorithmic computation differentially rely on numerical magnitude processing, an assumption that has already been examined in children, but not yet in adults. Therefore, in this study, we examined how numerical magnitude processing was associated with mental and algorithmic computation, and whether this association with numerical magnitude processing was different for mental versus algorithmic computation. We also investigated whether the association between numerical magnitude processing and mental and algorithmic computation differed for measures of symbolic versus nonsymbolic numerical magnitude processing. Results showed that symbolic, and not nonsymbolic, numerical magnitude processing was associated with mental computation, but not with algorithmic computation. Additional analyses showed, however, that the size of this association with symbolic numerical magnitude processing was not significantly different for mental and algorithmic computation. We also tried to further clarify the association between numerical magnitude processing and complex calculation by also including relevant arithmetical subskills, i.e. arithmetic facts, needed for complex calculation that are also known to be dependent on numerical magnitude processing. Results showed that the associations between symbolic numerical magnitude processing and mental and algorithmic computation were fully explained by individual differences in elementary arithmetic fact knowledge.

Effects of reading picture books on kindergartners' mathematics performance

This article describes a field experiment with a pretest-posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine experimental classes were read picture books. Data analysis revealed that, when controlled for relevant covariates, the picture book reading programme had a positive effect (d = .13) on kindergartners' mathematics performance as measured by a project test containing items on number, measurement and geometry. Compared to the increase from pretest to posttest in the control group, the increase in the experimental group was 22% larger. No significant differential intervention effects were found between subgroups based on kindergarten year, age, home language, socio-economic status and mathematics and language ability, but a significant intervention effect was found for girls and not for boys.

Longitudinal associations between executive control and developing mathematical competence in preschool boys and girls

Executive control (EC) is related to mathematics performance in middle childhood. However, little is known regarding how EC and informal numeracy differentially support mathematics skill acquisition in preschoolers. A sample of preschoolers (115 girls, 113 boys), stratified by social risk, completed an EC task battery at 3 years, informal numeracy assessments at 3.75 and 4.5 years, and a broad mathematics assessment during kindergarten. Strong associations were observed between latent EC at age 3 and mathematics achievement in kindergarten, which remained robust after accounting for earlier informal numeracy, socioeconomic status, language and processing speed. Relations between EC and mathematics achievement were stronger in girls than in boys. Findings highlight the unique role of EC in predicting which children may have difficulty transitioning to formal mathematics instruction.

The codevelopment of skill at and preference for use of retrieval-based processes for solving addition problems: individual and sex differences from first to sixth grades

The ability to retrieve basic arithmetic facts from long-term memory contributes to individual and perhaps sex differences in mathematics achievement. The current study tracked the codevelopment of preference for using retrieval over other strategies to solve single-digit addition problems, independent of accuracy, and skilled use of retrieval (i.e., accuracy and reaction time [RT]) from first to sixth grades inclusive (N=311). Accurate retrieval in first grade was related to working memory capacity and intelligence, and it predicted a preference for retrieval in second grade. In later grades, the relation between skill and preference changed such that preference in one grade predicted accuracy and RT in the next grade as RT and accuracy continued to predict future gains in preference. In comparison with girls, boys had a consistent preference for retrieval over other strategies and had faster retrieval speeds, but the sex difference in retrieval accuracy varied across grades. Results indicate that ability influences early skilled retrieval, but both practice and skill influence each other in a feedback loop later in development and provide insights into the source of the sex difference in problem-solving approaches.

Independent contributions of the central executive, intelligence, and in-class attentive behavior to developmental change in the strategies used to solve addition problems

Children's (N=275) use of retrieval, decomposition (e.g., 7=4+3 and thus 6+7=6+4+3), and counting to solve additional problems was longitudinally assessed from first grade to fourth grade, and intelligence, working memory, and in-class attentive behavior was assessed in one or several grades. The goal was to assess the relation between capacity of the central executive component of working memory, controlling for intelligence and in-class attentive behavior, and grade-related changes in children's use of these strategies. The predictor on intercept effects from multilevel models revealed that children with higher central executive capacity correctly retrieved more facts and used the most sophisticated counting procedure more frequently and accurately than their lower capacity peers at the beginning of first grade, but the predictor on slope effects indicated that this advantage disappeared (retrieval) or declined in importance (counting) from first grade to fourth grade. The predictor on slope effects also revealed that from first grade to fourth grade, children with higher capacity adopted the decomposition strategy more quickly than other children. The results remained robust with controls for children's sex, race, school site, speed of encoding Arabic numerals and articulating number words, and mathematics achievement in kindergarten. The results also revealed that intelligence and in-class attentive behavior independently contributed to children's strategy development.

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement.

Strengths and Weaknesses of the Choice/No-Choice Method in Research on Strategy Use

About 10 years ago, Siegler and Lemaire (1997 ) introduced the choice/no-choice method as a means of obtaining unbiased estimates of performance characteristics of cognitive strategies. They also illustrated the possibilities of this method and discussed its potential extensions for cognitive (developmental) research. The present article provides a critical discussion of the strengths and weaknesses of the choice/no-choice method in research on strategy choice and strategy change, starting from an overview of the studies that have been done with this new method. We end with a general evaluation and some issues for further research.

The influence of problem features and individual differences on strategic performance in simple arithmetic

The present study examined the influence of features differing across problems (problem size and operation) and across individuals (gender, amount of daily arithmetic practice, calculator use, and arithmetic skill) on simple arithmetic performance. Regression analyses were used to investigate the role of these variables in both strategy selection and strategy efficiency. Results show that more skilled and highly practiced students used memory retrieval more often and executed their strategies more efficiently than did less skilled and practiced students. Furthermore, calculator use correlated with both retrieval and procedural strategy efficiency but not with strategy selection. Only very small associations with gender were observed, with boys retrieving slightly faster than girls. Implications of the present findings for models of mental arithmetic are discussed.

School-Based Physical Activity Does Not Compromise Children's Academic Performance

PURPOSE

The purpose of this study was twofold: 1) to evaluate the effectiveness of a school-based physical activity intervention, Action Schools! BC (AS! BC), for maintaining academic performance in a multiethnic group of elementary children, and 2) to determine whether boys and girls' academic performance changed similarly after participation in AS! BC.

METHODS

This was a 16-month cluster randomized controlled trial. Ten schools were randomized to intervention (INT) or usual practice (UP). One INT school administered the wrong final test, and one UP school graded their own test, so both were excluded. Thus, eight schools (six INT, two UP) were included in the final analysis. Children (143 boys, 144 girls) in grades 4 and 5 were recruited for the study. We used the Canadian Achievement Test (CAT-3) to evaluate academic performance (TotScore). Weekly teacher activity logs determined amounts of physical activity delivered by teachers to students. Physical activity was determined with the Physical Activity Questionnaire for Children (PAQ-C). Independent t-tests compared descriptive variables between groups and between boys and girls. We used a mixed linear model to evaluate differences in TotScore at follow-up between groups and between girls and boys.

RESULTS

Physical activity delivered by teachers to children in INT schools was increased by 47 min x wk(-1) (139 +/- 62 vs 92 +/- 45, P < 0.001). Participants attending UP schools had significantly higher baseline TotScores than those attending INT schools. Despite this, there was no significant difference in TotScore between groups at follow-up and between boys and girls at baseline and follow-up.

CONCLUSION

The AS! BC model is an attractive and feasible intervention to increase physical activity for students while maintaining levels of academic performance.

Working memory deficits in adults with ADHD: is there evidence for subtype differences?

BACKGROUND

Working memory performance is important for maintaining functioning in cognitive, academic and social activities. Previous research suggests there are prevalent working memory deficits in children with attention deficit hyperactivity disorder (ADHD). There is now a growing body of literature characterizing working memory functioning according to ADHD subtypes in children. The expression of working memory deficits in adults with ADHD and how they vary according to subtype, however, remains to be more fully documented.

METHODS

This study assessed differences in working memory functioning between Normal Control (NC) adults (N = 18); patients with ADHD, Combined (ADHD-CT) Type ADHD (N = 17); and ADHD, Inattentive (ADHD-IA) Type (N = 16) using subtests from the Wechsler Adult Intelligence Scale-III and Wechsler Memory Scale-III and the Paced Auditory Serial Addition Task (PASAT).

RESULTS

The ADHD groups displayed significant weaknesses in contrast to the NC group on working memory tests requiring rapid processing and active stimulus manipulation. This included the Letter-Number-Sequencing test of the Wechsler scales, PASAT omission errors and the longest sequence of consecutive correct answers on the PASAT. No overall ADHD group subtype differences emerged; however differences between the ADHD groups and the NC group varied depending on the measure and the gender of the participants. Gender differences in performance were evident on some measures of working memory, regardless of group, with males performing better than females.

CONCLUSION

In general, the data support a dimensional interpretation of working memory deficits experienced by the ADHD-CT and ADHD-IA subtypes, rather than an absolute difference between subtypes. Future studies should test the effects of processing speed and load on subtype performance and how those variables interact with gender in adults with ADHD.

The development of strategy use in elementary school children: working memory and individual differences

The current study tested the development of working memory involvement in children's arithmetic strategy selection and strategy efficiency. To this end, an experiment in which the dual-task method and the choice/no-choice method were combined was administered to 10- to 12-year-olds. Working memory was needed in retrieval, transformation, and counting strategies, but the ratio between available working memory resources and arithmetic task demands changed across development. More frequent retrieval use, more efficient memory retrieval, and more efficient counting processes reduced the working memory requirements. Strategy efficiency and strategy selection were also modified by individual differences such as processing speed, arithmetic skill, gender, and math anxiety. Short-term memory capacity, in contrast, was not related to children's strategy selection or strategy efficiency.

A longitudinal analysis of sex differences in math and spatial skills in primary school age children

We report on a longitudinal study designed to assess possible sex differences in math achievement, math ability, and math-related tasks during the primary school age years. Participants included over 200 children from one public school district. Annual assessments included measures of math ability, math calculation achievement scores, rapid naming and decoding tasks, visual perception tests, visual motor tasks, and reading skills. During select years of the study we also administered tests of counting and math facts skills. We examined whether girls or boys were overrepresented among the bottom or top performers on any of these tasks, relative to their peers, and whether growth rates or predictors of math-related skills differed for boys and girls. Our findings support the notion that sex differences in math are minimal or nonexistent on standardized psychometric tests routinely given in assessments of primary school age children. There was no persistent finding suggesting a male or female advantage in math performance overall, during any single year of the study, or in any one area of math or spatial skills. Growth rates for all skills, and early correlates of later math performance, were comparable for boys and girls. The findings fail to support either persistent or emerging sex differences on non-specialized math ability measures during the primary school age years.

On the functional role of human parietal cortex in number processing: How gender mediates the impact of a ‘virtual lesion’ induced by rTMS

Areas around the horizontal part of the intraparietal sulcus (hIPS) have repeatedly been reported to participate in processing numerical magnitude. Using transcranial magnetic stimulation (TMS), we investigated the functional role of the hIPS by examining two effects from the domain of numerical cognition: in magnitude comparison tasks response latencies are inversely related to the numerical distance between two numbers. This distance effect indexes access to the mental number representation. In magnitude comparison tasks responses are faster when decade and unit comparison would lead to the same decision (e.g. 42_57, 4 < 5 and 2 < 7) than when they would not (e.g. 47_62, 4 < 6 but 7 > 2). This compatibility effect reflects unit-decade integration processes. Differential susceptibility of (fe)male participants to TMS was examined. We applied repetitive TMS (rTMS; 1Hz for 10 min) over the left hIPS in 12 participants (6 female). No stimulation and vertex stimulation served as control conditions. The effect of rTMS was mediated by gender: in male participants, the distance effect decreased after TMS over hIPS. For female participants distance and compatibility effect both increased. This modulation of the compatibility effect was limited in duration to no more than 4 min. The hIPS seems to be functionally involved both in number magnitude processing and in integrating unit-decade magnitude information of two-digit numbers. Relative hemispheric specialization of the hIPS with respect to two-digit magnitude comparison is discussed.