Pathways to Third-Grade Calculation Versus Word-Reading Competence: Are They More Alike or Different?

The structure correspondence hypothesis predicts how word and sentence in language correlate with term and principle in mathematics

The association between language and mathematics is an important debated topic. Here, we proposed a structure correspondence hypothesis to explain under what conditions language and mathematics are closely related. According to the hypothesis, there would be an association when they have equivalent structure. One hundred and fifty high school students were recruited to finish mathematical and language tests at the element level (i.e., geometric term processing and word analogy) and at the low-dimensional combination level (i.e., geometric principle processing and sentence completion) as well as the tests to measure cognitive covariates (general intelligence and spatial processing). After controlling for age, gender and cognitive covariates, geometric term processing and word analogy were closely correlated, and geometric principle processing and sentence completion were significantly correlated. No other correlations were found. The results support the structure correspondence hypothesis and provide a new perspective of structure of language and verbalized mathematics for the relation between language and mathematics.

Comorbid Word Reading and Mathematics Computation Difficulty at Start of First Grade

The purpose of this analysis was to describe cognitive processes associated with comorbid difficulty between word reading (WR) and mathematics computation (MC) at the start of first grade among children selected for WR and MC delays. A sample of 234 children (mean age 6.50 years, SD = 0.31) was assessed on WR, MC, core cognitive processes (phonological processing, rapid automatized naming, verbal counting [VC]), and domain-general cognitive processes (working memory, oral language, nonverbal reasoning, attentive behavior). Structural equation modeling was used to predict a latent Comorbidity factor, which modeled shared variance between WR and MC, and to identify processes associated with that Comorbidity factor. Results identified each of the core cognitive processes, especially VC, and each of the domain-general cognitive processes, especially working memory, as explaining shared variance between WR and MC. Implications for understanding comorbid difficulty at the start of first grade and designing coordinated first-grade interventions are discussed.

Cognitive Predictors of the Overlap of Reading and Math in Middle School

Math and reading skills are known to be related, and predictors of each are well researched. What is less understood is the extent to which these predictors, uniquely and collectively, overlap with one another, are differentially important for different academic skills, and account for the overlap of math and reading. We examined 20 potential predictors from four domains (working memory, processing speed, attention, and language) using latent variables and both timed and untimed achievement skill, in a sample (N=212) of at-risk middle schoolers, half of whom were English learners. The predictors accounted for about half of the overlap among achievement skills, suggesting that other factors (e.g., domain specific skills) might also be relevant for the overlap. We also found some differential prediction (language for reading, working memory for math). The present results extend and refine our understanding of the contribution of these cognitive predictors for reading and math.

Relative Contributions of g and Basic Domain-Specific Mathematics Skills to Complex Mathematics Competencies

Meta-analytic structural equation modeling was used to estimate the relative contributions of general cognitive ability or g (defined by executive functions, short-term memory, and intelligence) and basic domain-specific mathematical abilities to performance in more complex mathematics domains. The domain-specific abilities included mathematics fluency (e.g., speed of retrieving basic facts), computational skills (i.e., accuracy at solving multi-step arithmetic, algebra, or geometry problems), and word problems (i.e., mathematics problems presented in narrative form). The core analysis included 448 independent samples and 431,344 participants and revealed that g predicted performance in all three mathematics domains. Mathematics fluency contributed to the prediction of computational skills, and both mathematics fluency and computational skills predicted word problem performance, controlling g. The relative contribution of g was consistently larger than basic domain-specific abilities, although the latter may be underestimated. The patterns were similar across younger and older individuals, individuals with and without a disability (e.g., learning disability), concurrent and longitudinal assessments, and family socioeconomic status, and have implications for fostering mathematical development.

Severe Pandemic Learning Loss and the Promise of Remotely Delivered Intervention in Students With Comorbid Reading and Mathematics Learning Difficulty

Analyses were conducted with second graders, drawn from an ongoing multi-cohort randomized controlled trial (RCT), who had been identified for RCT entry based on comorbid reading comprehension and word-problem solving difficulty. To estimate pandemic learning loss, we contrasted fall performance for 3 cohorts: fall of 2019 (pre-pandemic; n = 47), 2020 (early pandemic, when performance was affected by the truncated preceding school year; n = 35), and 2021 (later pandemic, when performance was affected by the truncated 2019 to 2020 school year plus the subsequent year's ongoing interruptions; n = 75). Across the 2 years, declines (standard deviations below expected growth) were approximately 3 times larger than those reported for the general population and for students in high-poverty schools. To estimate the promise of structured remote intervention for addressing such learning loss during extended school closures, we contrasted effects in the RCT's 2018 to 2019 cohort (entirely in-person intervention delivery; n = 66) against the same intervention's effects in the 2020 to 2021 cohort (alternating periods of remote and in-person delivery; n = 29). Large intervention effects were not moderated by pandemic status, suggesting potential for structured remote intervention to address student needs during extended school closures.

Early rapid naming longitudinally predicts shared variance in reading and arithmetic fluency

A number of cognitive factors have been suggested to underlie development in reading and arithmetic skills. Although the two domains are strongly linked, only a few studies have investigated the processes that are shared between them during the early school years. Rapid automatized naming (RAN) has been identified as a strong predictor of a common fluency factor in reading and arithmetic. In the current study with 232 Norwegian children, we examined how RAN in preschool and Grade 1 relates to the shared and nonshared variance in arithmetic fluency and reading fluency in Grade 3. Furthermore, we examined whether related processing skills (phoneme awareness, working memory, speed of processing, and symbol knowledge) can account for the relationship between RAN and shared fluency-or if they predict variance that is unique to each domain. Our results show that RAN in both preschool and Grade 1 is a strong predictor of shared variance between reading fluency and arithmetic fluency measured several years later, whereas other predictors mainly relate to the nonshared parts of variance in the fluency outcomes. That is, control variables with the theoretical potential to explain some of RAN's relation to the overlap between reading and arithmetic fluency do not in fact account for this relationship. Our findings provide a starting point for future investigations of the mechanisms of rapid naming.

A-B-3-Associations and dissociations of reading and arithmetic: Is domain-specific prediction outdated?

Reading and arithmetic are core domains of academic achievement with marked impact on career opportunities and socioeconomic status. While associations between reading and arithmetic are well established, evidence on underlying mechanisms is inconclusive. The main goal of this study was to reevaluate the domain-specificity of established predictors and to enhance our understanding of the (co-)development of reading and arithmetic. In a sample of 885 German-speaking children, standard domain-specific predictors of reading and arithmetic were assessed before and/or at the onset of formal schooling. Reading and arithmetic skills were measured at the beginning and end of second grade. Latent variables were extracted for all relevant constructs: Grapheme-phoneme processing (phonological awareness, letter identification), RAN (RAN-objects, RAN-digits), number system knowledge (number identification, successor knowledge), and magnitude processing (non-symbolic and symbolic magnitude comparison), as well as the criterion measures reading and arithmetic. Four structural equation models tested distinct research questions. Grapheme-phoneme processing was a specific predictor of reading, and magnitude processing explained variance specific to arithmetic. RAN explained variance in both domains, and it explained variance in reading even after controlling for arithmetic. RAN and number system knowledge further explained variance in skills shared between reading and arithmetic. Reading and arithmetic entail domain-specific cognitive components, and they both require tight networks of visual, verbal, and semantic information, as reflected by RAN. This perspective provides a useful background to explain associations and dissociations between reading and arithmetic performance.

Taking a Closer Look: The Relationship between Pre-School Domain General Cognition and School Mathematics Achievement When Controlling for Intelligence

Intelligence, as well as working memory and attention, affect the acquisition of mathematical competencies. This paper aimed to examine the influence of working memory and attention when taking different mathematical skills into account as a function of children’s intellectual ability. Overall, intelligence, working memory, attention and numerical skills were assessed twice in 1868 German pre-school children (t1, t2) and again at 2nd grade (t3). We defined three intellectual ability groups based on the results of intellectual assessment at t1 and t2. Group comparisons revealed significant differences between the three intellectual ability groups. Over time, children with low intellectual ability showed the lowest achievement in domain-general and numerical and mathematical skills compared to children of average intellectual ability. The highest achievement on the aforementioned variables was found for children of high intellectual ability. Additionally, path modelling revealed that, depending on the intellectual ability, different models of varying complexity could be generated. These models differed with regard to the relevance of the predictors (t2) and the future mathematical skills (t3). Causes and conclusions of these findings are discussed.

Developmental changes in episodic memory across early- to mid-childhood: insights from a latent longitudinal approach

Episodic memory is a cornerstone ability that allows one to recall past events and the spatiotemporal context in which they occur. In an effort to characterise the development of this critical ability, many different tasks have been used independently to assess age-related variations in episodic memory. However, performance on memory tasks is multiply determined, and the extent to which different tasks with varying features relate to each other and represent episodic memory as a latent cognitive construct across childhood is unclear. The present study sought to address this question by exploring the feasibility of using four different laboratory-based tasks to characterise changes in episodic memory ability during early- to mid-childhood in 200 typically developing children (4-8 years). Using longitudinal data and a structural equation modeling framework, results suggest that multiple tests of episodic memory can be utilised to indicate a comparable latent construct of episodic memory ability over this period of development, and that this ability improves consistently between 4 to 8 years. Overall, results highlight that episodic memory measured as a construct increases at a similar rate over early- to mid-childhood and demonstrate the benefits of using multiple laboratory tasks to characterise developmental changes in episodic memory.

Connections between Mathematics and Reading Development: Numerical Cognition Mediates Relations between Foundational Competencies and Later Academic Outcomes

We examined longitudinal relations between 1^st-grade cognitive predictors (early nonverbal reasoning, processing speed, listening comprehension, working memory, calculation skill, word-problem solving, word-reading fluency, attentive behavior, and numerical cognition) and 2^nd-grade academic outcomes (calculations, word-problem solving, and word reading) in 370 children (M _age = 6.55 years, SD _age = 0.33 years at the start of the study) who were identified as at-risk or not-at-risk for mathematics disability. Path analysis mediation models revealed that numerical cognition, assessed at an intermediary timepoint, mediated the effects of processing speed, working memory, calculation skill, word-problem solving, and attentive behavior on all 3 outcomes. Findings indicate that multiple early domain-general cognitive abilities are related to later mathematics and reading outcomes and that numerical cognition processes, which may track ease of forming symbol-concept associations, predict later performance across both academic domains.

Inferencing Skill and Attentional Control Account for the Connection Between Reading Comprehension and Mathematics

We examined the relations of inference, vocabulary, decoding, short-term memory, and attentional control to reading comprehension and mathematics performance for first-grade students in the US (N = 83). The students were composed of 75% Hispanics, 15% Whites, and 6% Asian Americans. Students' performance on mathematics and reading comprehension were very strongly related (r = 0.88). Results from path analysis showed that inference (0.27 ≤ s ≤ 0.38) was independently and positively related to both reading comprehension and mathematics performance after accounting for short-term memory, attentional control, decoding, and vocabulary. Decoding was independently related to reading comprehension, but not mathematics, whereas vocabulary was independently related to mathematics, but not to reading comprehension. Attentional control was directly related to mathematics, and indirectly related to reading comprehension and mathematics via inference, vocabulary, and decoding, with a substantial total effect on reading comprehension and mathematics (0.56 respectively). Short-term memory was not directly nor indirectly related to reading comprehension and mathematics. Overall these results show that language and cognitive skills are shared resources of reading comprehension and mathematics, and highlight the roles of attentional control and inference skill in reading comprehension and mathematics.

Do Reading and Arithmetic Fluency Share the Same Cognitive Base?

We examined the role of different cognitive-linguistic skills in reading and arithmetic fluency, and whether the effects of these skills are mediated by reading and arithmetic accuracy. One hundred twenty-six English-speaking Grade 1 children (67 females, 59 males; M _age = 6.41 years) were followed from the beginning of Grade 1 (Time 1) to the end of Grade 1 (Time 2). At Time 1, they were assessed on measures of non-verbal IQ, speed of processing, working memory, phonological awareness, rapid automatized naming (RAN), and number sense. At Time 2, they were assessed on measures of reading and arithmetic accuracy as well as on measures of reading and arithmetic fluency. Results of path analysis showed first that when reading and arithmetic fluency were included in the model as separate outcomes, RAN was predictive of both and that speed of processing and working memory were predictive of only arithmetic fluency. Second, RAN, speed of processing, and working memory had both direct and indirect effects (via reading and arithmetic accuracy) on the covariation of reading and arithmetic fluency. Irrespective of how reading and arithmetic fluency were treated in the analyses, the effects of non-verbal IQ, phonological awareness, and number sense were all indirect. Taken together, these findings suggest that reading and arithmetic fluency draw on a broader network of cognitive-linguistic skills, whose effects can sometimes be indirect through reading and arithmetic accuracy.

Learning a new geometric concept: The role of working memory and of domain-specific abilities

It has been suggested that not only domain‐specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain‐specific factors and of verbal versus visuospatial WM on geometric learning of a new geometrical figure (trapezoid), never presented previously by the teachers participating to the study, after a lecture also involving manipulatives. Results on 105 children in their Year 4 indicated that not only some domain‐specific components (geometric declarative knowledge and calculation) but also visuospatial working memory had a significant specific impact on the ability of solving geometric problems requiring to calculate the perimeter and the area of the new figure. On the contrary, verbal WM and geometrical mental imagery did not offer a specific contribution. These findings could have important educational implications, stressing the importance of taking into account the main different aspects supporting the acquisition of geometry.

The Relationship of Reading Abilities With the Underlying Cognitive Skills of Math: A Dimensional Approach

Math and reading are related, and math problems are often accompanied by problems in reading. In the present study, we used a dimensional approach and we aimed to assess the relationship of reading and math with the cognitive skills assumed to underlie the development of math. The sample included 97 children from 4th and 5th grades of a primary school. Children were administered measures of reading and math, non-verbal IQ, and various underlying cognitive abilities of math (counting, number sense, and number system knowledge). We also included measures of phonological awareness and working memory (WM). Two approaches were undertaken to elucidate the relations of the cognitive skills with math and reading. In the first approach, we examined the unique contributions of math and reading ability, as well as their interaction, to each cognitive ability. In the second approach, the cognitive abilities were taken to predict math and reading. Results from the first set of analyses showed specific effects of math on number sense and number system knowledge, whereas counting was affected by both math and reading. No math-by-reading interactions were observed. In contrast, for phonological awareness, an interaction of math and reading was found. Lower performing children on both math and reading performed disproportionately lower. Results with respect to the second approach confirmed the specific relation of counting, number sense, and number system knowledge to math and the relation of counting to reading but added that each math-related marker contributed independently to math. Following this approach, no unique effects of phonological awareness on math and reading were found. In all, the results show that math is specifically related to counting, number sense, and number system knowledge. The results also highlight what each approach can contribute to an understanding of the relations of the various cognitive correlates with reading and math.

Developmental dynamics between reading and math in elementary school

Reading and math attainment develop during elementary grades. Questions remain, though, about the co-developmental nature of the relation between reading and math. This study examined dynamic, longitudinal pathways between reading and math in first through fourth grades. Participants of the study were 554 academically at-risk children (Mage at the first assessment point = 6.57 years; SD = 0.38) from Texas Project Achieve. Children were assessed utilizing the Woodcock-Johnson-III reading and math measures. Results from dynamic bivariate latent change score models indicated unidirectional longitudinal coupling effects from reading to math. Specifically, average and high levels of reading performance were associated with subsequent gains in math growth, in particular for below average performing children in math. In contrast, low levels of reading performance had negligible or no amplifying influences on change in math growth. The nature of the dynamics was replicated even when controlling for nonverbal cognitive abilities. Results demonstrated that good reading skills pave the way for children to develop their math skills. Such findings underscore the importance of considering reading performance in treating math difficulties.

Comorbid Learning Difficulties in Reading and Mathematics: The Role of Intelligence and In-Class Attentive Behavior

The goal was to identify the domain-general cognitive abilities and academic attitudes that are common and unique to reading and mathematics learning difficulties that in turn will have implications for intervention development. Across seventh and eighth grade, 315 (155 boys) adolescents (M age = 12.75 years) were administered intelligence, verbal short-term and working memory, and visuospatial memory, attention, and ability measures, along with measures of English and mathematics attitudes and mathematics anxiety. Teachers reported on students' in-class attentive behavior. A combination of Bayesian and multi-level models revealed that intelligence and in-class attentive behavior were common predictors of reading accuracy, reading fluency, and mathematics achievement. Verbal short-term memory was more critical for reading accuracy and fluency, whereas spatial ability and mathematics self-efficacy were more critical for mathematics achievement. The combination of intelligence and in-class attentive behavior discriminated typically achieving students from students with comorbid (D = 2.44) or mathematics (D = 1.59) learning difficulties, whereas intelligence, visuospatial attention, and verbal short-term memory discriminated typically achieving students from students with reading disability (D = 1.08). The combination of in-class attentive behavior, verbal short-term memory, and mathematics self-efficacy discriminated students with mathematics difficulties from their peers with reading difficulties (D = 1.16). Given the consistent importance of in-class attentive behavior, we conducted post hoc follow-up analyses. The results suggested that students with poor in-class attentive behavior were disengaging from academic learning which in turn contributed to their risk of learning difficulties.

Dynamic Assessment for Identifying Spanish-Speaking English Learners' Risk for Mathematics Disabilities: Does Language of Administration Matter?

We examined dynamic assessment's (DA's) added value over traditional assessments for identifying Spanish-speaking English learners' (ELs) risk for developing mathematics disabilities, as a function of the language of test administration (English vs. Spanish), type of math outcome, and EL's language dominance. At the start of first grade, ELs (N = 368) were randomly assigned to English-DA or Spanish-DA conditions, were assessed on static mathematics measures and domain-general (language, reasoning) measures in English, and completed DA in their assigned language condition. At year's end, they were assessed on calculation and word-problem solving outcomes in English. Results from multigroup path models indicated that Spanish-DA mitigates the impact of ELs' language dominance on DA performance. Moreover, ELs' language dominance moderated DA's predictive validity differentially depending on DA language and type of outcome. Spanish-DA showed higher predictive validity in Spanish-dominant ELs than English-dominant ELs when predicting calculations but not word-problem solving. English-DA was predictive for both outcomes, regardless of ELs' language dominance.

The Critical Role of Word Reading as a Predictor of Response to Intervention

This study examines the initial word reading performance of fourth-grade struggling readers and the extent to which differing levels of word reading performance at pretest influenced their response to reading interventions. A large group of students with significant reading comprehension difficulties (N = 481) were classified into three clusters of word reading proficiency based on their pretest performance: (a) very low, (b) low, and (c) near adequate. We examined their performance on several academic, language, and executive functioning measures at the beginning of the year and their reading comprehension performance at the beginning of year and after 1 year of reading intervention to examine how each cluster responded to instruction. Results from a discriminant function analysis indicated that performance on five pretest variables were meaningful predictors of word reading proficiency cluster membership: phonological processing, writing fluency, math calculation, math fluency, and reading efficiency and comprehension. Results also demonstrated that word reading proficiency at pretest was related to response to intervention on reading comprehension measures. Students in the very low word reading proficiency cluster showed minimal response to intervention whereas the near-adequate word reading cluster demonstrated greatest response to intervention. These results suggest word reading is a critical predictor of response to intervention for students with significant comprehension problems in the upper elementary grades and that students with the most substantial word reading problems may require more intensive and specialized treatments than students with greater word reading performance to show meaningful progress in reading.

Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N = 200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing, number comparison, memory skills, and processing and articulation speed in the spring of Grade 1 and on reading and arithmetic fluency in the fall of Grade 2. RAN and verbal counting were strongly associated, and a constructed latent factor, serial retrieval fluency (SRF), was the strongest unique predictor of the shared variance. Other unique predictors were phonological awareness, number comparison, and processing speed. Findings highlight the importance of SRF in clarifying the relation between reading and arithmetic fluency.

The Relationship Between Reading Fluency and Arithmetic Fact Fluency and Their Shared Cognitive Skills: A Developmental Perspective

This study investigated the underlying cognitive abilities which are related to both fluency in reading and arithmetic across different developmental phases of their acquisition. An unselected sample of children in first (N = 83), second (N = 66), and third (N = 67) grades completed several reading and arithmetic fluency tasks, as well as rapid automatized naming (RAN), working memory (WM), and inhibition measures. The results of a stepwise regression analysis revealed differences in the predictive models of fluency in both academic domains in first grade. However, similar patterns were found in the second and third grades. Specifically, in first grade reading fluency was predicted by inhibition and WM, while arithmetic fact fluency was predicted by RAN and WM. In contrast, in second grade both types of fluency were predicted by RAN and WM, and in third grade only RAN was found to be a predictor. Alongside the gradual reduction in the cognitive components participating in reading and arithmetic fluency, the results of the present study suggest that both fluencies share the same underlying cognitive mechanisms. Practical implications of the current results are discussed.

Role of Neurocognitive Factors in Academic Fluency for Children and Adults With Spina Bifida Myelomeningocele

OBJECTIVES

Fluency is a major problem for individuals with neurodevelopmental disorders, including fluency deficits for academic skills. The aim of this study was to determine neurocognitive predictors of academic fluency within and across domains of reading, writing, and math, in children and adults, with and without spina bifida. In addition to group differences, we expected some neurocognitive predictors (reaction time, inattention) to have similar effects for each academic fluency outcome, and others (dexterity, vocabulary, nonverbal reasoning) to have differential effects across outcomes.

METHODS

Neurocognitive predictors were reaction time, inattention, dexterity, vocabulary, and nonverbal reasoning; other factors included group (individuals with spina bifida, n=180; and without, n=81), age, and demographic and untimed academic content skill covariates. Univariate and multivariate regressions evaluated hypotheses.

RESULTS

Univariate regressions were significant and robust (R 2 =.78, .70, .73, for reading, writing, and math fluency, respectively), with consistent effects of covariates, age, reaction time, and vocabulary; group and group moderation showed small effect sizes (<2%). Multivariate contrasts showed differential prediction across academic fluency outcomes for reaction time and vocabulary.

CONCLUSIONS

The novelty of the present work is determining neurocognitive predictors for an important outcome (academic fluency), within and across fluency domains, across population (spina bifida versus typical), over a large developmental span, in the context of well-known covariates. Results offer insight into similarities and differences regarding prediction of different domains of academic fluency, with implications for addressing academic weakness in spina bifida, and for evaluating similar questions in other neurodevelopmental disorders. (JINS, 2019, 25, 249-265).

Contributions of Basic Cognitive Processing to Chinese Reading: The Mediation Effect of Basic Language Processing

Prior research has mostly focused on either basic language or basic cognitive precursors of reading development, but relatively little is known about their relative importance for reading, especially for Chinese beginning readers. The present study examined whether and how basic cognitive processing (executive function, attention, and visual-spatial perception) and basic language processing (phonological awareness, morphological awareness, orthographic awareness, and RAN) measured at kindergarten influence Chinese character reading and reading comprehension in the first grade. Results showed that basic language abilities including morphological awareness and rapid automatized naming predicted later Chinese character reading. Only one basic cognitive skill, sustained attention, predicted later reading comprehension. Mediation analysis showed that the overall effects of basic cognitive skills on later character reading and reading comprehension were mediated by basic language skills. These findings supported an integration reading model for early Chinese reading and basic language processing at kindergarten plays an important role in explaining the relation between basic cognitive processing and grade one reading performance.

Longitudinal Predictors of the Overlap between Reading and Math Skills

The predictors of developing reading skill are well known, and there is increasing coherence around predictors of developing math as well. These achievement skills share strong relations. Less knowledge is available regarding the extent to which predictors overlap and predict one another, particularly longitudinally, and across different types of reading and math. We followed kindergarten students (n = 193) for one year, evaluating a range of relevant predictor skills in kindergarten, and a range of relevant achievement outcomes (core, fluency, complex) of reading and math in grade 1. Few predictors differentially predicted math versus reading with some exception (phonological awareness and rapid naming for reading; counting knowledge for math). The pattern was more similar for core and fluency outcomes relative to complex ones. A small set of predictors accounted for much of the overlap among math and reading outcomes, regardless of type (core, fluency, or complex). Results have the potential to inform the development of early screening tools to consider both achievement domains simultaneously, and support the importance of following students identified as at-risk in one domain for their performance in both domains.

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction.

The relationship between learning mathematics and general cognitive ability in primary school

Three relationships between learning mathematics and general cognitive ability have been hypothesized: The educational hypothesis that learning mathematics develops general cognitive skills, the psychometric hypothesis that differences in general cognitive ability cause differences in mathematical attainment, and the reciprocal influence hypothesis that developments in mathematical ability and general cognitive ability influence each other. These hypotheses are assessed with a sample of 948 children from the Twins Early Development Study who were assessed at 7, 9, and 10 years on mathematics, English, and general cognitive ability. A cross-lagged path analysis with mathematics and general cognitive ability measures supports the reciprocal influence hypothesis between 7 and 9 and between 9 and 10. A second analysis including English assessments only provides evidence of a reciprocal relationship between 7 and 9. Statement of Contribution What is already known on this subject? The correlations between mathematical attainment, literacy, and measures of general cognitive skills are well established. The role of literacy in developing general cognitive skills is emerging. What the present study adds? Mathematics contributes to the development of general cognitive skills. General cognitive ability contributes to mathematical development between 7 and 10. These findings support the hypothesis of reciprocal influence between mathematics and general cognitive ability, at least between 7 and 9.

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8^th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects and domain-specific effects were indexed by prior grade mathematics achievement and mathematical cognition measures of prior grade number knowledge, addition skills, and fraction knowledge. Use of functional data analysis enabled grade-by-grade estimation of overall domain-general and domain-specific effects on subsequent mathematics achievement, the relative importance of individual domain-general and domain-specific variables on this achievement, and linear and non-linear across-grade estimates of these effects. The overall importance of domain-general abilities for subsequent achievement was stable across grades, with working memory emerging as the most important domain-general ability in later grades. The importance of prior mathematical competencies on subsequent mathematics achievement increased across grades, with number knowledge and arithmetic skills critical in all grades and fraction knowledge in later grades. Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain-specific knowledge were equally important in later grades.

Executive Function Buffers the Association between Early Math and Later Academic Skills

Extensive evidence has suggested that early academic skills are a robust indicator of later academic achievement; however, there is mixed evidence of the effectiveness of intervention on academic skills in early years to improve later outcomes. As such, it is clear there are other contributing factors to the development of academic skills. The present study tests the role of executive function (EF) (a construct made up of skills complicit in the achievement of goal-directed tasks) in predicting 5th grade math and reading ability above and beyond math and reading ability prior to school entry, and net of other cognitive covariates including processing speed, vocabulary, and IQ. Using a longitudinal dataset of N = 1292 participants representative of rural areas in two distinctive geographical parts of the United States, the present investigation finds EF at age 5 strongly predicts 5th grade academic skills, as do cognitive covariates. Additionally, investigation of an interaction between early math ability and EF reveals the magnitude of the association between early math and later math varies as a function of early EF, such that participants who have high levels of EF can “catch up” to peers who perform better on assessments of early math ability. These results suggest EF is pivotal to the development of academic skills throughout elementary school. Implications for further research and practice are discussed.

Distinct influences of affective and cognitive factors on children's non-verbal and verbal mathematical abilities

Individual differences in children's math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children's math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving.

Children's visuospatial memory predicts mathematics achievement through early adolescence

A previous study showed that gains in visuospatial memory from first to fifth grade predicted end-of-fifth grade mathematics but not reading achievement, controlling other factors. In this follow up study, these relations were assessed from sixth to ninth grade, inclusive (n = 145). The results showed that growth in visuospatial memory across the elementary school years was related to growth in mathematics achievement after fifth grade, controlling intelligence, the central executive and phonological memory components of working memory, in-class attentive behavior, parental education, and fifth grade mathematics achievement. As found for fifth grade, this relation was not found for reading achievement after fifth grade. In total, the results suggest that visuospatial memory has a unique influence on ease of learning some types of mathematics and that this influence becomes more important across successive grades.

The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes. (PsycINFO Database Record

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.