Math-Fact Retrieval as the Cognitive Mechanism Underlying Gender Differences in Math Test Performance

Predicting Risk for Comorbid Reading and Mathematics Disability Using Fluency-Based Screening Assessments

The first purpose of this study was to examine the prevalence of risk for comorbid reading and mathematics disabilities (RMD) at start of first grade, when measured in a representative sample of 3,062 students with first-grade fluency measures (word reading; computation). The second purpose was to examine the utility of these measures for predicting RMD status within a sample of 577 students when RMD status was assessed at the end of second grade in terms of reading and math accuracy. When set at or below the 16^th percentile, first-grade risk for RMD was two times more common than chance; at or below the 7^th percentile, it was five times more common. Logistic regression showed that the two first-grade fluency measures accurately distinguished students with and without RMD in second grade; however, when cut scores were set to capture 85% of students with RMD, false positives were high. Overall, the results provide support for the use of fluency measures as an initial gating procedure in first grade, but additional gating steps appear necessary in the screening process to reduce false positives.

Math Fluency during Primary School

Math fluency is the ability to solve arithmetic facts quickly and accurately (i.e., addition and subtraction problems up to 20, and multiplication and division problems from the multiplication table). Curricula in primary school devote a significant period of time for learning and retrieval of arithmetic facts. Recently, a new computerized tool to assess math fluency—the BGU-MF (Ben-Gurion University Math Fluency) test—was developed and found to be a reliable and valid tool for adults. In the current study, we examine the performance of first to sixth-grade children in math fluency using the BGU-MF. The results present the performance of MF during childhood and emphasize that it continues to develop during primary school. Importantly, proficiency of MF differed by operations, and the automaticity of math facts was acquired in different grades. Moreover, we found that the BGU-MF is a reliable and valid tool not only for adults but also for children during primary school. Our study has educational implications for the teaching, practice, and retrieval of arithmetic facts.

Examining the Differential Role of General and Specific Processing Speed in Predicting Mathematical Achievement in Junior High School

Processing speed is divided into general (including perceptual speed and decision speed) and specific processing speed (including reading fluency and arithmetic fluency). Despite several study findings reporting the association between processing speed and children's mathematical achievement, it is still unclear whether general or specific processing speed differentially predicts mathematical achievement. The current study aimed to examine the role of general and specific processing speed in predicting mathematical achievements of junior high school students. Cognitive testing was performed in 212 junior school students at the beginning of the 7th grade year, along with assessment of general and specific processing speed. Relevant academic achievement scores were also recorded at the end of the 7th and 9th grade years. Hierarchical regression analyses showed that specific processing speed made a significant unique contribution in mathematical achievement by the end of the 7th grade and could significantly predict mathematical achievements in the high school entrance examinations by end of the 9th grade after controlling for age, gender, and general cognitive abilities. However, general processing speed could not predict mathematical achievements. Moreover, specific processing speed could significantly predict all academic achievements for both the 7th and 9th grade. These results demonstrated that specific processing speed, rather than general processing speed, was able to predict mathematical achievement and made a generalised contribution to all academic achievements in junior school. These findings suggest that specific processing speed could be a reflection of academic fluency and is therefore critical for long-term academic development.

Inattention, hyperactivity/impulsivity, and mathematics: Exploring gender differences in a nonclinical sample

In this study, we considered two subscales of attention problem (AP) behaviour, inattentiveness and hyperactivity/impulsivity, as latent traits, extreme values of which indicate attention deficit hyperactivity disorder (ADHD). We examined gender differences in these traits in a community sample of Russian schoolchildren and estimated the extent to which the association of AP behaviour and math achievement varied for boys and girls. The data from a three-wave longitudinal study of math achievement of 958 children (49 % girls) were used, and growth in math achievement was estimated. The levels of inattentiveness and hyperactivity/impulsivity of each child were measured based on teachers' responses using the Behaviour Rating Scale (BRS). The results demonstrated that inattentiveness had a negative association with math achievement, while hyperactivity/impulsivity was positively associated with math achievement when inattentiveness was controlled for. Inattentiveness was negatively associated with math achievement in both boys and girls. However, the size of this association decreased over time for boys, so the gap between boys with high inattentiveness and low inattentiveness decreased from grade 1 to grade 2. Meanwhile, for girls, the association between inattentiveness and math remained stable, so the gap between girls with high inattentiveness and girls with low inattentiveness did not change.

Gender-Based Performance in Mathematical Facts and Calculations in Two Elementary School Samples From Chile and Spain: An Exploratory Study

Gender differences in mathematical performance are not conclusive according to the scientific literature, although such differences are supported by international studies such as the Trends in International Mathematics and Science Study (TIMSS). According to TIMSS 2019, fourth-grade male students outperformed female students in Spanish-speaking countries, among others. This work approaches the study on gender difference by examining the basic calculation skills needed to handle more complex problems. Two international samples of second and third graders from Chile and Spain were selected for this exploratory study. Tests on basic mathematical knowledge (symbolic and non-symbolic magnitude comparisons, fluency, and calculation) were administered. The tests did not show significant difference or size effect between genders for mean performance, variance in the distribution of performance, or percentiles. As noted in the existing literature on this topic and reiterated by these findings, great care should be exercised when reporting on possible gender differences in mathematical performance, as these can contribute to low self-concept among female students.

Language-Related Longitudinal Predictors of Arithmetic Word Problem Solving: A Structural Equation Modeling Approach

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10 to 9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children's later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed.

A Pilot Study of a Self-voicing Computer Program for Prealgebra Math Problems

Fourteen students with visual impairments in Grades 5–12 participated in the field-testing of AnimalWatch-VI-Beta. This computer program delivered 12 prealgebra math problems and hints through a self-voicing audio feature. The students provided feedback about how the computer program can be improved and expanded to make it accessible to all users.

The Effect of Metacognitive Knowledge on Mathematics Performance in Self-Regulated Learning Framework-Multiple Mediation of Self-Efficacy and Motivation

Metacognition, self-efficacy, and motivation are important components of interaction in self-regulated learning (SRL). However, the psychological mechanism underlying the association among them in mathematical learning remained ambiguous. The present study investigated whether the relationship between metacognitive knowledge (MK) and mathematics performance can be mediated by self-efficacy and motivation. The sample comprised 569 students (245 male, Mage = 16.39, SD = 0.63) of Grade 10 in China. The MK in mathematics questionnaire, the self-efficacy questionnaire, the academic motivation scale, Raven advanced progressive matrix, and mathematics tests were used for data collection. Our results suggested that the mathematics performance could be predicted by MK, self-efficacy and intrinsic motivation. Moreover, the association between MK and mathematics performance was mediated by self-efficacy and intrinsic motivation, as revealed by a multiple mediation analysis. Additionally, there were sex differences in MK, self-efficacy and intrinsic motivation. The findings highlight the psychological mechanism in the mathematics of Chinese students and will help teachers to improve students’ mathematical learning in SRL framework more effectively. Implications for education and further studies are discussed.

Sex differences in number processing: Differential systems for subtraction and multiplication were confirmed in men, but not in women

Neuroimaging studies suggest segregated neuronal systems underlying number magnitude processing (e.g. subtraction) and arithmetic fact retrieval (e.g. multiplication). While number magnitude processing is thought to rely on the intraparietal sulcus (IPS) bilaterally, arithmetic fact retrieval is thought to rely on the left angular gyrus (AG). However, evidence from brain damaged patients and brain stimulation challenges this view and suggests considerable overlap between the systems underlying number magnitude processing and arithmetic fact retrieval. This study investigates, whether sex differences in number processing can account for these conflicting findings. A subtraction and a multiplication task were administered to 40 men and 34 women in their luteal phase during functional MRI. Replicating previous studies in men, we found the IPS to be more strongly activated during subtraction than multiplication, and the AG to be more strongly activated during multiplication than subtraction. However, no differences between the two tasks were observed in women.

A longitudinal study on predictors of early calculation development among young children at risk for learning difficulties

The purpose of this study was to explore domain-general cognitive skills, domain-specific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical competence, incoming calculations, socioeconomic status, and gender at the beginning of first grade and on calculation performance at four time points: the beginning of first grade, the end of first grade, the end of second grade, and the end of third grade. Latent growth modeling analysis showed that numerical competence, incoming calculation, processing speed, and decoding skills significantly explained the variance in calculation performance at the beginning of first grade. Numerical competence and processing speed significantly explained the variance in calculation performance at the end of third grade. However, numerical competence was the only significant predictor of calculation development from the beginning of first grade to the end of third grade. Implications of these findings for early calculation instructions among young at-risk children are discussed.

Performance of Mini-Mental State Examination (MMSE) in long-stay patients with schizophrenia or schizoaffective disorders in a psychiatric institute

Studies have found that age and education were associated with cognition in older adults. However, little is known how clinical factors (e.g. age of illness onset, length of hospital stay, type of antipsychotic medications, and duration of illness) are associated with cognitive functioning in patients with schizophrenia. This study aimed to examine the influence of socio-demographic and clinical factors on cognitive domains measured using Mini-Mental State Examination (MMSE) among patients with schizophrenia or schizoaffective disorders residing in a psychiatric institute in Singapore. A single-phase interview was conducted at the Institute of Mental Health (IMH) in patients diagnosed with schizophrenia or schizoaffective disorders (n=110). MMSE was administered to all participants. Data on socio-demographic characteristics, smoking, alcohol consumption, and medical history were collected. Age, gender, and level of education were significantly associated with MMSE scores. After adjusting for all socio-demographic correlates, longer length of hospital stay remained significant in predicting lower MMSE scores. Length of hospital stay was independently associated with cognitive functioning. Early interventions for cognition such as physical and mental exercises should be implemented for better prognosis.

Behavioural evidence for sex differences in the overlap between subtraction and multiplication

The present study aims to identify factors that may influence the dissociability of number magnitude processing and arithmetic fact retrieval at the behavioural level. To that end, we assessed both subtraction and multiplication performance in a within-subject approach and evaluated the interdependence of unit-decade integration measures on the one hand as well as sex differences in the interdependence of performance measures on the other hand. We found that subtraction items requiring borrowing (e.g. 53-29 = 24, 3 < 9) are more error prone than subtraction items not requiring borrowing (e.g. 59-23 = 34, 9 > 3), thereby demonstrating a borrowing effect, which has been suggested as a measure of unit-decade integration in subtraction. Furthermore, we observed that multiplication items with decade-consistent distractors (e.g. 6 × 4 = 28 instead of 24) are more error prone that multiplication items with decade-inconsistent distractors (e.g. 6 × 4 = 30 instead of 24), thereby demonstrating a decade-consistency effect, which has been suggested as a measure of unit-decade integration in simple multiplication. However, the borrowing effect in subtraction was not correlated with the effect of decade consistency in simple multiplication in either men or women. This indicates that unit-decade integration arises from different systems in subtraction and multiplication. Nevertheless, men outperformed women not only in subtraction, but also in multiplication. Furthermore, subtraction and multiplication performance on correct solution probes were correlated in women, but unrelated in men. Thus, the view of differential systems for number magnitude processing and arithmetic fact retrieval may not be universal across sexes.

Examining Gender Differences in Written Assessment Tasks in Biology: A Case Study of Evolutionary Explanations

Understanding sources of performance bias in science assessment provides important insights into whether science curricula and/or assessments are valid representations of student abilities. Research investigating assessment bias due to factors such as instrument structure, participant characteristics, and item types are well documented across a variety of disciplines. However, the relationships among these factors are unclear for tasks evaluating understanding through performance on scientific practices, such as explanation. Using item-response theory (Rasch analysis), we evaluated differences in performance by gender on a constructed-response (CR) assessment about natural selection (ACORNS). Three isomorphic item strands of the instrument were administered to a sample of undergraduate biology majors and nonmajors (Group 1: n = 662 [female = 51.6%]; G2: n = 184 [female = 55.9%]; G3: n = 642 [female = 55.1%]). Overall, our results identify relationships between item features and performance by gender; however, the effect is small in the majority of cases, suggesting that males and females tend to incorporate similar concepts into their CR explanations. These results highlight the importance of examining gender effects on performance in written assessment tasks in biology.

When problem size matters: differential effects of brain stimulation on arithmetic problem solving and neural oscillations

The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG) oscillations over the left posterior parietal cortex (LPPC). In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS). Participants underwent anodal (30min, 1.5 mA, LPPC) and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes.

The Academic Diligence Task (ADT): Assessing Individual Differences in Effort on Tedious but Important Schoolwork

The current study reports on the development and validation of the Academic Diligence Task (ADT), designed to assess the tendency to expend effort on academic tasks which are tedious in the moment but valued in the long-term. In this novel online task, students allocate their time between solving simple math problems (framed as beneficial for problem solving skills) and, alternatively, playing Tetris or watching entertaining videos. Using a large sample of high school seniors (N = 921), the ADT demonstrated convergent validity with self-report ratings of Big Five conscientiousness and its facets, self-control and grit, as well as discriminant validity from theoretically unrelated constructs, such as Big Five extraversion, openness, and emotional stability, test anxiety, life satisfaction, and positive and negative affect. The ADT also demonstrated incremental predictive validity for objectively measured GPA, standardized math and reading achievement test scores, high school graduation, and college enrollment, over and beyond demographics and intelligence. Collectively, findings suggest the feasibility of online behavioral measures to assess noncognitive individual differences that predict academic outcomes.

Exploring the relationship between math anxiety and gender through implicit measurement

Math anxiety, defined as a negative affective response to mathematics, is suggested as a strong antecedent for the low visibility of women in the science and engineering workforce. However, the assumption of gender differences in math anxiety is still being studied and results are inconclusive, probably due to the use of explicit measures such as direct questionnaires. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in males and females by using a novel affective priming task as an indirect measure. Specifically, university students (23 males and 30 females) completed a priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative, or related to mathematics). Participants were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication, or division) was true or false. People are typically found to respond to target stimuli more rapidly after presentation of an affectively related prime than after an affectively unrelated one. In the current study, shorter response latencies for positive as compared to negative affective primes were found in the male group. An affective priming effect was found in the female group as well, but with a reversed pattern. That is, significantly shorter response latencies were observed in the female group for negative as compared to positive targets. That is, for females, negative affective primes act as affectively related to simple arithmetic problems. In contrast, males associated positive affect with simple arithmetic. In addition, only females with lower or insignificant negative affect toward arithmetic study at faculties of mathematics and science. We discuss the advantages of examining pure anxiety factors with implicit measures which are free of response factors. In addition it is suggested that environmental factors may enhance the association between math achievements and math anxiety in females.

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.

Menstrual cycle variations in the BOLD-response to a number bisection task: implications for research on sex differences

Numerical processing involves either number magnitude processing, which has been related to spatial abilities and relies on superior parietal regions, or arithmetic fact retrieval, which has been related to verbal abilities and involves the inferior parietal lobule. Since men score better in spatial and women in verbal tasks, we assume that women have advantages in fact retrieval, while men have benefits in number magnitude processing. According to findings on menstrual cycle variations in spatial and verbal abilities, fact retrieval should improve during the luteal phase and magnitude processing during the follicular phase. To dissociate sex- and menstrual cycle-dependent effects on fact retrieval and number magnitude processing, we applied a number bisection task in 15 men and 15 naturally cycling women. Multiplicative items (e.g. 12_15_18) are part of a multiplication series and can be solved by fact retrieval, while non-multiplicative items (e.g. 11_14_17) are not part of a multiplication series and require number magnitude processing. In men and women in their luteal phase, error rates were higher and deactivation of the medial prefrontal cortex and the bilateral inferior parietal lobules was stronger for non-multiplicative compared to multiplicative items (positive multiplicativity effect), while in the follicular phase women showed higher error rates and stronger deactivation in multiplicative compared to non-multiplicative items (negative multiplicativity effect). Thus, number magnitude processing improves, while arithmetic fact retrieval impairs during the follicular phase. While a female superiority in arithmetic fact retrieval could not be confirmed, we observed that sex differences are significantly modulated by menstrual cycle phase.

Gender differences in the functional and structural neuroanatomy of mathematical cognition

Despite ongoing debate about the nature of gender differences in mathematics achievement, little is known about gender similarities and differences in mathematical cognition at the neural level. We used fMRI to compare brain responses in 25 females and 24 males during a mental arithmetic task involving 3-operand addition and subtraction. We also used voxel-based morphometry (VBM) to examine gender differences in brain structure. Although females and males did not differ in accuracy or response times (effect size d<0.3), significant gender differences in functional brain activation were observed in the right dorsal and ventral visuospatial information processing streams (d>1.1). Males showed greater dorsal stream activation in the right intra-parietal sulcus areas important for numerical cognition, and angular gyrus regions of the default mode network that are typically deactivated during complex cognitive tasks, as well as greater ventral stream activation in the right lingual and parahippocampal gyri. VBM revealed an opposite pattern of gender differences-compared to males, females had greater regional density and greater regional volume in dorsal and ventral stream regions where males showed greater fMRI activation. There were no brain areas where females showed greater functional activation than males, and no brain areas where males showed greater structural density or volume than females. Our findings provide evidence for gender differences in the functional and structural organization of the right hemisphere brain areas involved in mathematical cognition. Together with the lack of behavioral differences, our results point to more efficient use of neural processing resources in females.

Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

Two experiments were conducted to investigate the effects of practice on strategy selection and strategy efficiency in mental arithmetic. Participants had to solve simple addition or multiplication problems, after having received 0, 3, or 6 practice sessions (Experiment 1), and before and after having received 3 practice sessions (Experiment 2). Strategy selection was measured by means of trial-by-trial strategy reports, whereas strategy efficiency was measured by means of response latencies. Results showed significant practice effects on retrieval frequency, procedural frequency, retrieval efficiency, and procedural efficiency. However, practice effects on strategy efficiency appeared to be both strategy-specific (i.e., only for procedural strategies) and operation-specific (i.e., only for multiplication problems). Implications of the present results for mathematic cognition and its modeling are discussed.

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.

The Science of Sex Differences in Science and Mathematics

Amid ongoing public speculation about the reasons for sex differences in careers in science and mathematics, we present a consensus statement that is based on the best available scientific evidence. Sex differences in science and math achievement and ability are smaller for the mid-range of the abilities distribution than they are for those with the highest levels of achievement and ability. Males are more variable on most measures of quantitative and visuospatial ability, which necessarily results in more males at both high- and low-ability extremes; the reasons why males are often more variable remain elusive. Successful careers in math and science require many types of cognitive abilities. Females tend to excel in verbal abilities, with large differences between females and males found when assessments include writing samples. High-level achievement in science and math requires the ability to communicate effectively and comprehend abstract ideas, so the female advantage in writing should be helpful in all academic domains. Males outperform females on most measures of visuospatial abilities, which have been implicated as contributing to sex differences on standardized exams in mathematics and science. An evolutionary account of sex differences in mathematics and science supports the conclusion that, although sex differences in math and science performance have not directly evolved, they could be indirectly related to differences in interests and specific brain and cognitive systems. We review the brain basis for sex differences in science and mathematics, describe consistent effects, and identify numerous possible correlates. Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and ability-including the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There are no single or simple answers to the complex questions about sex differences in science and mathematics.

Gender-specific movement strategies using a computer-pointing task

Females typically demonstrate a movement time advantage for tasks requiring high levels of manual dexterity, whereas males are notably better at targeting activities. According to D. Kimura (2000), the hunter-gatherer hypothesis primarily accounts for those performance advantages; that dichotomy fails, however, when one makes movement outcome predictions for tasks that are not clearly fine-motor or interceptive in nature. Investigators have recently proposed that time constraints (M. Peters, 2005) and gender-specific response style differences (M. Peters & P. Campagnaro, 1996; L. E. Rohr, 2006) affect motor performance. Here, the author used a computer-pointing task measuring both movement error and movement time in 16 participants to further investigate response style differences. Kinematic and linear regression analyses between resultant error and both movement time and task difficulty reinforced the notion that gender-specific movement biases emphasize speed and accuracy, respectively, for men and women.

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.

Number Sense Growth in Kindergarten: A Longitudinal Investigation of Children at Risk for Mathematics Difficulties

Number sense development of 411 middle- and low-income kindergartners (mean age 5.8 years) was examined over 4 time points while controlling for gender, age, and reading skill. Although low-income children performed significantly worse than middle-income children at the end of kindergarten on all tasks, both groups progressed at about the same rate. An exception was story problems, on which the low-income group achieved at a slower rate; both income groups made comparable progress when the same problems were presented nonverbally with visual referents. Holding other predictors constant, there were small but reliable gender effects favoring boys on overall number sense performance as well as on nonverbal calculation. Using growth mixture modeling, 3 classes of growth trajectories in number sense emerged.

Brain mappings of the arithmetic processing in children and adults

Despite the increasing number of experimental mapping showing that human arithmetic cognition is supported by widely spread neural circuits; the theoretical reasoning about these data remains mostly metaphorical and guided by a connectionist approach. Although neurons at distinct areas in the brain are assumed to take charge of different duties in the solution of the experimental task, the results are always discussed by hypothesizing some association between the different areas without questioning any difference of behavior at the level of the neurons at each of these areas. Here, the brain is assumed as Distributed Intelligent Processing System (DIPS) formed by collections of loosely interacting specialized agents (neurons), each agent specializing, for example, in data collection (sensors), problem solving (associative neurons), data communication (interneuronal systems) and in acting upon the surrounding environment (motorneurons). A new technique for EEG brain mapping is proposed and used to study arithmetic cognition in elementary school aged children and adults. Factor analysis showed three distinct patterns of neuronal recruitment for arithmetic calculations in all experimental groups which varied according to the type of calculation, age and sex.

Adaptive User Displays for Intelligent Tutoring Software

Intelligent tutoring software (ITS) holds great promise for K-12 instruction. Yet it is difficult to obtain rich information about users that can be used in realistic educational delivery settings--public school classrooms--in which eye tracking and other user sensing technologies are not suitable. We are pursuing three "cheap and cheerful" strategies to meet this challenge in the context of an ITS for high school math instruction. First, we use detailed representations of student cognitive skills, including tasks to assess individual users' proficiency with abstract reasoning, proficiency with simple math facts and computational skill, and spatial ability. Second, we are using data mining and machine learning algorithms to identify instructional sequences that have been effective with previous students, and to use these patterns to make decisions about current students. Third, we are integrating a simple focus-of-attention tracking system into the software, using inexpensive, web cameras. This coarse-grained information can be used to time the display of multimedia hints, explanations, and examples when the user is actually looking at the screen, and to diagnose causes of problem-solving errors. The ultimate goal is to create non-intrusive software that can adapt the display of instructional information in real time to the user's cognitive strengths, motivation, and attention.

The early education of socioeconomically disadvantaged children

This chapter reviews selected research on the education of low-socioeconomic status (SES) children from birth through the first years of elementary school. Themes include the importance of early academic skills and interest to later achievement; the benefits of integrating knowledge from research on mental health and other areas; the need to utilize and build children's strengths as well as address their weaknesses; and a call to connect research to practice and policy. Relevant research on race and culture is reviewed because ethnic minority low-SES children are at great risk of poverty. Gender is discussed because low-SES boys have poorer general achievement than girls, while very few low-SES girls pursue careers in math- and science-related fields.