This study examined the effects of training involving spatial versus nonspatial representations of numerical magnitude for promoting arithmetic fluency. The key goal was to advance theoretical understanding of the relation between spatial and math learning, while simultaneously laying the groundwork for the development of future educational interventions. Toward this goal, the study tested the hypothesis that the use of spatial representations during training facilitates arithmetic fluency via improvements in numerical magnitude knowledge. Participants (first graders from low-income racially/ethnically diverse backgrounds, N = 205) were randomly assigned to one of four experimental conditions: spatial-continuous, spatial-discrete, nonspatial-verbal cues, and nonspatial-no verbal cues. All conditions involved eight 30-min training sessions, in which children received instruction on addition/subtraction problems with totals within 10. The key difference between conditions was the type of materials utilized during training-specifically, the type of magnitude cues they contained. The results showed that children's arithmetic skills increased from pre- to posttest in all conditions and that the increase was significantly larger in the spatial, compared to nonspatial, conditions. However, there was no effect of condition on numerical magnitude knowledge, which leaves open the question about the underlying mechanism. The findings demonstrating a causal relation between spatial and mathematical domains have both theoretical significance and practical implications for the choice of instructional materials. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

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.

Using data from 12 studies, we meta-analyze correlations between parent number talk during interactions with their young children (mean sample age ranging from 22 to 79 months) and two aspects of family socioeconomics, parent education, and family income. Potential variations in correlation sizes as a function of study characteristics were explored. Statistically significant positive correlations were found between the amount of number talk in parent-child interactions and both parent education and family income (i.e., r = 0.12 for education and 0.14 for income). Exploratory moderator analyses provided some preliminary evidence that child age, as well as the average level of and variability in socioeconomic status, may moderate effect sizes. The implications of these findings are discussed with special attention to interpreting the practical importance of the effect sizes in light of family strengths and debate surrounding "word gaps".

Click to increase image sizeClick to decrease image size Notes1 https://stanford.io/3SBkAp02 Casey, B., Erkut, S., Ceder, I., & Young, J. M. (2008). Use of a storytelling context to improve girls’ and boys’ geometry skills in kindergarten. Journal of Applied Developmental Psychology, 29(1), 29-48.3 Dearing, E., Casey, B., & Young, C. (2019). Family card games that support early math skills: A research-practice partnership. Presentation at the Erikson Institute Math Conference, Chicago.4 https://stanford.io/3LLQBbV5 https://stanford.io/3faR2Ac6 https://stanford.io/3r7vpn17 https://stanford.io/3fjgh3p8 https://stanford.io/3LRIQkH9 https://stanford.io/3LZqdvr10 https://stanford.io/3flSqQK11 https://stanford.io/3UE8IEK12 https://stanford.io/3DZsGUr13 https://stanford.io/3SutYe014 Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.

This study used a person-centered approach to examine mother-daughter dyad behaviors when jointly solving addition problems during a card game. The goal was to identify maternal and child profile behaviors during the interaction as predictors of children’s autonomous addition accuracy and strategy use at the end of first grade. Videotaped observations of the dyads playing addition card games (N = 91) were coded by trained observers. Latent profile analysis identified three profiles: (1) the Independent profile (52% of sample) included children who often solved independently and received little maternal support; (2) the Supported profile (35%) had children who received greater maternal support; and (3) the Dependent profile (13%) included children who received the most help from mothers. The three mother-daughter profiles differed in terms of children’s: (1) independence level, (2) task mastery behaviors, and (3) strategy use. The mothers varied in terms of: (1) use of simplifying behaviors, (2) use of math fact hints, and (3) support of different types of addition strategies. OLS regression models (controlling for mother demographics and child cognitive skills) revealed that children in the Independent profile had higher addition skills at the end of first grade in comparison to children in the Dependent profile, with the Supported children in between. Children in the Independent and Supported profiles used advanced decomposition strategies more frequently in comparison to the Dependent profile children. Taken together, a person-centered approach revealed latent subgroups of maternal-child interactions that were associated with children’s later addition accuracy and strategy use.

There are extensive controversies about: (1) whether any gender differences in math exist, (2) what factors might contribute to any gender differences, and (3) whether gender differences in abilities and attitudes are likely to impact the substantially smaller number of women in math intensive Science, Technology, Engineering, and Mathematics (STEM) fields. We provide a review of gender differences in math, describing the inconsistencies and disagreements in the literature, which we propose can often be tied to the population being studied or to features relating to the math measures being used. Then we address two potential areas of gender differences (spatial skills and math attitudes), which may be critical in influencing gender differences in math within certain populations and types of math skills. Next, this article compares key gender-math theories, analyzing them from a bio-psycho-social framework. These findings are discussed within the context of our bio-psycho-social theory of gender differences in both math skills and STEM fields. In an overview of our bio-psycho-social theory, we propose that it is relative tilt in patterns of brain organization relating to spatial versus verbal abilities (rather than math versus verbal abilities tilt) that leads to gender differences in math behaviors and attitudes. This relative spatial-verbal tilt is likely a key player in influencing math skills/careers. At the end of the article, the educational implications are addressed including implications for interventions.

The aim of this study is to investigate whether maternal spatial support during two types of joint manipulative toy play tasks with 2-year-old children was longitudinally associated with math screening test scores in second grade. The interaction between spatial support and maternal education was explored as well. We also investigated predictions of a teacher rating of math performance at second grade, although these effects were less robust. Data were drawn from BONDS (The Behavior Outlook Norwegian Developmental Study), a longitudinal study of Norwegian children and their families. Participants were a subsample of 932 mothers and their 2-year-olds. Mothers were asked to help their children solve both a puzzle task and a shape-color sorting task. Mothers' spatial support included spatial language, gestures, and placement of objects. Results showed that higher levels of spatial support during mother-child interaction tasks at 2 years of age was significantly associated with fewer math difficulties in second grade. This was the case for a puzzle task (a task associated with spatial visualization skills), but not for a shape-color sorting task (a task associated with shape and color feature discriminations). Conclusions are drawn with respect to the importance of identifying optimal parental spatial strategies associated with better math outcomes. These findings on parental facilitation of spatial skills during joint early play may be useful for future training interventions directed at parents of children at risk for poor math skills.

This study addresses girls' (6-7-year-olds; N = 162) arithmetic skills within the context of learning environments provided by their mothers. Mothers and daughters were videotaped solving addition problems during card games. Maternal support was assessed through coding math fact hints and addition-strategy suggestions. Their first-grade daughters were then assessed on addition accuracy at end-of-year. Using regression analyses, results showed that maternal use of relevant math facts during the card games was associated with their child's later addition accuracy. Two types of math facts showed this association: (a) those relevant to the numbers to be added on the cards, and (b) novel math facts provided by mothers to scaffold decomposition arithmetic strategy-use. These findings suggest the importance of supportive mathematical interactions during informal games as a possible source of developing girls' early math skills. The study also identifies potentially valuable types of support for early arithmetic learning in informal contexts.

The goal of this study was to examine fathers' support of their children's spatial learning during a joint block-building task at the beginning of first grade as a predictor of their children's math achievement at the end of first grade. Observational measures of videotaped father-child interactions from the Boston site of the NICHD Study of Early Child Care and Youth Development (N = 105) were used to examine the effectiveness of spatial support during a block building task. Trained observers rated fathers' spatial support by applying two approaches: (a) a qualitative rating scale assessing level of paternal spatial concept support involving encouragement of child spatial learning and enriched spatial explanations, and (b) a measure assessing quantitative paternal spatial location language support. A significant sex by quality of spatial concept support interaction showed that for girls (but not for boys), fathers' qualitatively higher spatial concept support predicted superior math achievement scores by the end of first grade, even after controlling for a host of variables, including children's math achievement at age 4.5 years, family income, child intelligence and ratings of fathers' and mothers' general cognitive support (e.g., support for a range of perceptual, cognitive, and linguistic development) across all parent-child activities during the first grade home visit. The quantitative measure of frequency of paternal spatial location language support was not predictive of math, but children's independent accuracy on the block building task did predict math achievement. Though only correlational, findings suggest that fathers may have an important role to play in providing high-quality spatial concept support for their young daughters. (C) 2018 Elsevier Inc. All rights reserved.

The development of math reasoning and 3-d mental rotation skills are intertwined. However, it is currently not understood how these cognitive processes develop and interact longitudinally at the within-person level - either within or across genders. In this study, 553 students (52% girls) were assessed from fifth to seventh grades on 3-d mental rotation spatial skills (assessed each fall) and numerical and algebraic math reasoning skills (assessed each spring). Boys outperformed girls on mental rotation tests across all three grades, and on fifth and seventh grade math reasoning tests. Consistent with the literature on between-person comparisons, there was a positive correlation between mental rotation and math reasoning skills in the full sample and for both genders. A random intercept cross-lagged panel model was used to control for these confounding group-level differences in order to isolate within-person associations between earlier and later performance. Initially in fifth grade, math reasoning predicted subsequent sixth grade mental rotation skills. By seventh grade, more advanced mental rotation skills were associated with subsequent math reasoning skills while math reasoning skills were no longer predictive of mental rotation skills. An examination of gender differences revealed that this pattern was driven by boys while girls experienced less within-person change. These findings suggest that boys may initially rely in part on their math reasoning skills to solve 3-d mental rotation tasks. However, as their 3-d mental rotation skills mature, they begin to primarily depend upon these developing spatial skills to solve math reasoning problems rather than the reverse.

Researchers generally agree that spatial problem solving skills involve the ability to generate mental images as a strategy for solving mathematics problems, often in conjunction with maintaining and manipulating those images. Further, translating these mental images into physical representations/graphics through drawings or diagrams is advantageous for many mathematics problems. The chapters by Sinclair, Moss, Hawes, and Stephenson (this volume) and Lowrie and Logan (this volume), point out Polya's (1965) recommendation to "draw a diagram" as one of the first steps in understanding a mathematics problem. Students who use this heuristic may be more successful on a wide range of problems across mathematics content areas. Ho and Lowrie (2014) report that Singapore students are taught to use the model method, which is a visual problem-solving heuristic prevalently used in Singapore classrooms, and Murata (2008) reports on the use of the tape diagram approach as visual-spatial tool used to solve many types of mathematics problems in Japanese classrooms-both countries that score highly on standardized testing.

This chapter reviews the spatial literature from the perspective of potential mechanisms for widening the range of spatially-based strategies available when solving math problems. We propose that teaching generalized spatial skills, disconnected from specific math content, may not be the best direction to go in future spatial interventions. Students who do not start out with strong spatial skills may need to learn to develop different types of "spatial sense" specific to each content area. Thus, acquiring and applying spatial strategies may depend in part on developing spatial sense within these specific math domains. In this chapter, we present an overview of evidence for different types of spatial sense that may serve as a prerequisite for effectively applying spatial strategies within these math content areas. The chapter also provides examples of math activities designed to help children acquire spatial sense and apply spatial strategies when solving diverse types of math problems.

The goal of this study was to examine maternal support of spatial concept learning and planning at 36 months as predictors of children's math achievement at 4(1/2) years and first grade. Observational measures of videotaped mother-child interactions from the Boston site of the NICHD Study of Early Child Care and Youth Development (N = 140) were used to examine the effectiveness of support for spatial concept learning and planning during a block building play activity. Trained observers rated maternal support of children's learning of spatial concepts through spatial language and gestures, with higher ratings involving explanations and encouragement of children's use of spatial concepts. This measure was predictive of math achievement at 4(1/2) years when controlling for length of the parent-child observation, child gender, ethnicity, and IQ at 2 years, as well as maternal years of education, verbal intelligence, income-to-needs averaged from 1 to 36 months, parenting stress, general cognitive stimulation, and maternal support of numerical concepts during the same observation. Maternal support of children's planning skills, also rated by trained observers during the block building activity, involved identifying incremental steps to reach the block building goal, with higher ratings given for encouraging planning on the part of the child. This measure was predictive of math achievement at 4(1/2) years, as well as reading achievement at both 4(1/2) years and first grade, suggesting that maternal planning support has associations with the two key measures of school readiness, while maternal spatial support may be specific to mathematics.

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the addition/subtraction problems. In fifth grade, girls were given an arithmetic fluency test, a mental rotation spatial task, and a numeric and algebra math reasoning test. Using structural equation modeling, the estimated path model accounted for 87% of the variance in math reasoning. First-grade spatial skills had a direct pathway to fifth-grade math reasoning as well as an indirect pathway through first-grade decomposition strategy use. The total effect of first-grade spatial skills was significantly higher in predicting fifth-grade math reasoning than all other predictors. First-grade decomposition strategy use had the second strongest total effect, while retrieval strategy use did not predict fifth-grade math reasoning. It was first-grade spatial skills (not fifth-grade) that directly predicted fifth-grade math reasoning. Consequently, the results support the importance of early spatial skills in predicting later math. As expected, decomposition strategy use in first grade was linked to fifth-grade math reasoning indirectly through first-grade arithmetic accuracy and fifth-grade arithmetic fluency. However, frequency of first-grade decomposition use also showed a direct pathway to fifth-grade arithmetic reasoning, again stressing the importance of these early cognitive processes on later math reasoning.

This study investigated whether problem behaviors, typically associated with a clinical diagnosis of ADHD, would also be associated with subclinical ADHD symptoms within a non-clinical college sample. These are symptoms characteristic of ADHD, which are insufficient to warrant a DSM-IV diagnosis of ADHD. Self-ratings of behaviors known to be comorbid with ADHD (Oppositional-Defiant Disorder (ODD) behaviors, risk-taking, and Executive-Functioning (EF) problems) were examined as predictors of self-ratings of ADHD symptoms. Measures of ODD symptoms, risk-taking, and EF behavioral problems (related to poor management of time) significantly predicted ADHD symptoms, as measured by Barkley’s ADHD Combined Subscale. These predictors accounted for 26% of the variance. The same measures predicted symptoms of ADHD, Inattentive type, as measured by Barkley’s Inattentiveness (IA) Subscale, and accounted for 30% of the variance. For the Hyperactivity-Impulsivity Subscale (HI), the ODD measure significantly entered the equation, while the other two measures were borderline significant, accounting altogether for 10% of the variance. As hypothesized, the EF measure was the strongest predictor for IA, and the ODD measure was the strongest predictor for HI. In conclusion, problem behaviors comorbid with a formal clinical ADHD diagnosis were found to be significantly associated with subclinical ADHD symptoms within a non-clinical sample of college students, as indicated by the substantial proportion of the variance they accounted for in predicting the Barkley’s’ Combined and Inattentiveness Subscales, and to a lessor extent for the Hyperactivity/Impulsivity Subscale. This indicates that college students with ADHD symptoms may have substantial problems not only with their ADHD symptoms, but also with executive functioning and externalizing behaviors associated with these symptoms.

The primary goal in this study was to examine maternal support of numerical concepts at 36months as predictors of math achievement at 41/2 and 6-7 years. Observational measures of mother-child interactions (n=140) were used to examine type of support for numerical concepts. Maternal support that involved labeling the quantities of sets of objects was predictive of later child math achievement. This association was significant for preschool (d=.45) and first-grade math (d=.49), controlling for other forms of numerical support (identifying numerals, one-to-one counting) as well as potential confounding factors. The importance of maternal support of labeling set sizes at 36months is discussed as a precursor to children's eventual understanding of the cardinal principle.

This study was designed to examine early predictors of later math reasoning in girls. Specifically, girls' first-grade spatial skills were compared with first-grade verbal and arithmetic skills as predictors of spatial and verbal–analytical math reasoning in fifth grade (N=79). The first-grade girls were given assessments measuring: (1) spatial skills (WISC-IV Block-Design subtest, and 2-d and 3-d mental-rotation tasks), (2) verbal skills (Peabody Picture Vocabulary Test), and (3) arithmetic skills (addition/subtraction). In fifth grade, girls were given a math-reasoning test, assessing both math reasoning-spatial (geometry/measurement items) and math reasoning-analytical (number/algebra items). The estimated path model accounted for approximately half the variance in math reasoning. First-grade spatial skills were the strongest predictors of both types of fifth-grade math reasoning. First-grade arithmetic skills significantly predicted math reasoning-analytical. Early verbal skills were not directly related to fifth-grade math reasoning, although there was an indirect pathway connecting them through early spatial skills. Thus, spatial skills, assessed by first grade, already function as key long-term predictors of analytical as well as spatial math-reasoning skills as late as fifth grade.

The present study addresses girls' (6-7-year-olds; N = 162) early spatial and arithmetic skills within the context of learning environments provided by their mothers. The study was designed to determine the relationship between maternal supportive interactions on a joint origami spatial problem-solving task and their first grade daughters' spatial and arithmetic skills. During home visits the mothers and daughters were videotaped jointly solving origami tasks with maternal supportive interactions assessed through ratings of maternal stimulation of cognitive development and maternal quality of assistance; the girls were separately assessed in school on spatial and arithmetic skills. Using structural equation modeling, the main findings were (1) maternal supportive interactions on a mother-child origami task mediated the relation between mothers' spatial skills/educational level and their daughters' spatial skills and (2) their daughters' spatial skills in turn mediated the relation between quality of maternal supportive spatial interactions and the daughters' arithmetic achievement. The present findings indicate the importance of early maternal supportive interactions relating to spatial problem solving for girls' spatial and arithmetic achievement. Furthermore, all pathways linking girls' home environments and arithmetic skills were mediated through the girls' spatial skills, suggesting that for young girls, development of early spatial skills may be important for effective arithmetic learning. (C) 2014 Elsevier Inc. All rights reserved.