Working memory and literacy as predictors of performance on algebraic word problems

The interplay between ego-resiliency, math anxiety and working memory in math achievement

Previous research has suggested that math anxiety may contribute to poor math performance by interfering with working memory. However, only a limited number of studies investigated the mediating role of working memory in the math anxiety-math performance link in school-aged children. Unlike math anxiety, ego-resiliency is a personality resource that promotes the management of challenges and has been positively associated with math performance and negatively with anxiety. Nevertheless, there is still limited understanding regarding the specific role of ego-resiliency in math learning and how it relates to math anxiety. This study aimed to investigate conjunctly the interplay between primary school children's ego-resiliency, math anxiety, working memory, and performance on two different math tasks (i.e., arithmetic task and word problem-solving task), after controlling for general anxiety and age. The study involved 185 Italian children from grades 3 to 5. Serial multi-mediational analyses revealed that: (1) ego-resiliency has a positive indirect effect on math achievement through two paths - math anxiety, and math anxiety and working memory; (2) the study replicated previous findings showing that working memory partially mediated the relationship between math anxiety and math performance; (3) similar patterns of results were found for both math skills. The study identifies ego-resiliency as a possible protective factor in the development of math anxiety and suggests that ego-resiliency could be worth considering when designing interventions aimed at reducing negative emotions towards mathematics.

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.

The association between working memory and mathematical problem solving: A three-level meta-analysis

Although working memory (WM) is an important factor in mathematical problem solving (MPS), it remains unclear how well WM relates to MPS. Thus, we aimed to determine this relationship by using a meta-analysis. We searched electronic databases for studies published between 2000 and 2020 and established operational criteria. We conducted Egger’s regression tests and created funnel plots to test for publication bias. Finally, a three-level meta-analytic model analysis of data from 130 studies involving 43,938 participants and 1,355 effect sizes revealed a moderate relationship between WM and MPS (r = 0.280, 95% CI = [0.263, 0.314]). Moreover, moderator analyses showed that: (1) dressed-up word problems were more strongly tied to WM than to intra-mathematical problems; (2) the central executive function showed the strongest relation with MPS, whereas the phonological loop had the weakest; (3) gender ratio had significant moderating effects; and (4) some of the above-mentioned significant moderating effects were unique after controlling for other factors. Implications for research and practice were also discussed.

The underlying neural bases of the reversal error while solving algebraic word problems

Problem solving is a core element in mathematical learning. The reversal error in problem solving occurs when students are able to recognize the information in the statement of comparison word problems, but they reverse the relationship between two variables when building the equations. Functional magnetic resonance images were acquired to identify for the first time the neural bases associated with the reversal error. The neuronal bases linked to this error have been used as inputs in 13 classifiers to discriminate between reversal error and non-reversal error groups. We found brain activation in bilateral fronto-parietal areas in the participants who committed reversal errors, and only left fronto-parietal activation in those who did not, suggesting that the reversal error group needed a greater cognitive demand. Instead, the non-reversal error group seems to show that they have developed solid algebraic knowledge. Additionally, the results showed brain activation in the right middle temporal gyrus when comparing the reversal error vs non-reversal error groups. This activation would be associated with the semantic processing which is required to understand the statement and build the equation. Finally, the classifier results show that the brain areas activated could be considered good biomarkers to help us identify competent solvers.

The role of working memory updating, inhibition, fluid intelligence, and reading comprehension in explaining differences between consistent and inconsistent arithmetic word-problem-solving performance

Children's performance in arithmetic word problems (AWPs) predicts their academic success and their future employment and earnings in adulthood. Understanding the nature and difficulties of interpreting and solving AWPs is important for theoretical, educational, and social reasons. We investigated the relation between primary school children's performance in different types of AWPs and their basic cognitive abilities (reading comprehension, fluid intelligence, inhibition, and updating processes). The study involved 182 fourth- and fifth-graders. Participants were administered an AWP-solving task and other tasks assessing fluid intelligence, reading comprehension, inhibition, and updating. The AWP-solving task included comparison problems incorporating either the adverb more than or the adverb less than, which demand consistent or inconsistent operations of addition or subtraction. The results showed that consistent problems were easier than inconsistent problems. Efficiency in solving inconsistent problems is related to inhibition and updating. Moreover, our results seem to indicate that the consistency effect is related to updating processes' efficiency. Path analyses showed that reading comprehension was the most important predictor of AWP-solving accuracy. Moreover, both executive functions-updating and inhibition-had a distinct and significant effect on AWP accuracy. Fluid intelligence had both direct and indirect effects, mediated by reading comprehension, on the overall measure of AWP performance. These domain-general factors are important factors in explaining children's performance in solving consistent and inconsistent AWPs.

Closing the Word-Problem Achievement Gap in First Grade: Schema-Based Word-Problem Intervention with Embedded Language Comprehension Instruction

The main purpose of this study was to test the effects of word-problem intervention, with versus without embedded language comprehension instruction, on at-risk 1st graders' word-problem performance. We also isolated the need for a structured approach to word-problem intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n=391; mean age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based word-problem intervention with embedded language instruction, the same word-problem intervention but without language comprehension instruction, structured number knowledge intervention without a structured word-problem component, and a control group. Each intervention included 45 30-min sessions. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based word-problem intervention at 1st grade, with both word-problem conditions outperforming the number knowledge condition and the control group. Yet, word-problem performance was significantly stronger for the schema-based condition with embedded language comprehension instruction compared to the schema-based condition without language comprehension instruction. Number knowledge intervention conveyed no word-problem advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to word-problem intervention; the efficacy of schema-based instruction at 1st grade; and the added value of language comprehension instruction within word-problem intervention. Results also provide causal evidence on the role of language comprehension in word-problem solving.

Working memory growth predicts mathematical problem-solving growth among emergent bilingual children

An area of mathematics found to be difficult for emergent bilingual children whose first language (L1) is Spanish in the United States is solving mathematical word problems. The purpose of this study was to determine the relationship between growth in the executive component of working memory (WM) and growth in mathematical word-problem solving in children whose L1 is Spanish. Elementary school children (Grades 1, 2, and 3) were administered a battery of mathematical, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, and WM) in both Spanish (L1) and English (second language [L2]) in Year 1 and again 1 year later. Multilevel growth modeling showed that growth in WM significantly predicted growth in L1 and L2 mathematical word-problem solving. Furthermore, the contributions of WM to mathematical word-problem-solving growth in both L1 and L2 were independent of language skills in vocabulary, reading, estimation, naming speed, inhibition, STM, and calculation. Overall, the results suggest that the mental activities that underlie WM play a significant role in predictions of L1 and L2 mathematical word-problem-solving accuracy.

Transfer effects of mathematical literacy: an integrative longitudinal study

Mathematical literacy (ML) is considered central to the application of mathematical knowledge in everyday life and thus is found in many comparative international educational standards. However, there exists barely any evidence about predictors and outcomes of ML having a lasting effect on achievement in nonmathematical domains. We drew on a large longitudinal sample of N = 4001 secondary school students in Grades 5 to 9 and tested for effects of ML on later academic achievement. We took prior achievement in different domains (information and communication technology literacy, scientific literacy, reading comprehension, and listening comprehension), socioeconomic status, and gender into account and investigated predictive effects of math grade, mathematical self-concept, reasoning, and prior achievement on ML. Using structural equation models, we found support for the importance of integrating multiple predictors and revealed a transfer effect of ML on achievement in different school domains. The findings highlight the importance of ML for school curricula and lasting educational decisions.

Do the Processes Engaged During Mathematical Word-Problem Solving Differ Along the Distribution of Word-Problem Competence?

Conventional research methods for understanding sources of individual differences in word-problem solving (WPS) only permit estimation of average relations between component processes and outcomes. The purpose of the present study was instead to examine whether and if so how the component processes engaged in WPS differ along the spectrum of WPS performance. Second graders (N = 1,130) from 126 classrooms in 17 schools were assessed on component processes (reasoning, in-class attentive behavior, working memory, language comprehension, calculation fluency, word reading) and WPS. Multilevel, unconditional quantile multiple regression indicated that 3 component processes, calculation fluency, language comprehension, and working memory, are engaged in WPS differentially depending on students' overall word-problem skill. The role of calculation fluency and language comprehension was stronger with more competent word-problem solving ability. By contrast, the role of working memory was stronger with intermediate-level than for strong problem solving. Results deepen insight into the role of these processes in WPS and provide the basis for hypothesizing how instructional strategies may be differentiated depending on students' overall level of WPS competence.

Math problem-solving and cognition among emerging bilingual children at risk and not at risk for math difficulties

Cognitive processes that underlie individual differences in mathematical problem-solution accuracy in elementary emerging bilingual children (English Learners) at risk and not at risk for math problem-solving difficulties (MD) were examined. A battery of tests was administered in both English and Spanish that assessed problem-solving, achievement, and cognitive processing in children in first (N = 155/MD N = 23), second (N = 129/MD N = 44) and third grades (N = 110/MD N = 39). The results were that (a) the executive component of working memory (WM) predicted MD status independent of measures of fluid intelligence, reading, calculation, knowledge of algorithms, processing speed, short-term memory, and inhibition, (b) low performance on Spanish measures of numeracy and executive component of WM were major predictors of the odds of being classified as MD and (c) bilingual proficiency primarily moderated English rather than Spanish measures of cognition. The results support the notion that the executive system of WM is an important predictor of emerging bilingual children's math problem-solving difficulties.

Individual differences in math problem solving and executive processing among emerging bilingual children

This study identified cognitive processes that underlie individual differences in working memory (WM) and mathematical problem-solving accuracy in emerging bilingual children (English learners). A battery of tests was administered in both English and Spanish that assessed problem solving, achievement, and cognitive processing in children in first grade (n = 155), second grade (n = 129), and third grade (n = 110). The results were that (a) the executive component of WM predicted solution accuracy of word problems independent of first language and second language measures of vocabulary, reading, domain-specific knowledge (e.g., calculation, estimation), and short-term memory and (b) first language (Spanish) measures of the executive component of WM and magnitude comparisons were major predictors of math problem-solving accuracy in both languages. The results support the notion that the executive system of WM is a unique predictor of emerging bilingual children's math problem-solving accuracy in both languages.

Fronto-insular-parietal network engagement underlying arithmetic word problem solving

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real-world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one-step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto-insular-parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task-dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out-of-scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto-insular-parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.

Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

The purpose of this study was to assess whether the differential effects of working memory (WM) components (the central executive, phonological loop, and visual-spatial sketchpad) on math word problem-solving accuracy in children (N = 413, ages 6-10) are completely mediated by reading, calculation, and fluid intelligence. The results indicated that all three WM components predicted word problem solving in the nonmediated model, but only the storage component of WM yielded a significant direct path to word problem-solving accuracy in the fully mediated model. Fluid intelligence was found to moderate the relationship between WM and word problem solving, whereas reading, calculation, and related skills (naming speed, domain-specific knowledge) completely mediated the influence of the executive system on problem-solving accuracy. Our results are consistent with findings suggesting that storage eliminates the predictive contribution of executive WM to various measures Colom, Rebollo, Abad, & Shih (Memory & Cognition, 34: 158-171, 2006). The findings suggest that the storage component of WM, rather than the executive component, has a direct path to higher-order processing in children.

Numbers in action: individual differences and interactivity in mental arithmetic

Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.

Can Touch Screen Tablets be Used to Assess Cognitive and Motor Skills in Early Years Primary School Children? A Cross-Cultural Study

Assessment of cognitive and motor functions is fundamental for developmental and neuropsychological profiling. Assessments are usually conducted on an individual basis, with a trained examiner, using standardized paper and pencil tests, and can take up to an hour or more to complete, depending on the nature of the test. This makes traditional standardized assessments of child development largely unsuitable for use in low-income countries. Touch screen tablets afford the opportunity to assess cognitive functions in groups of participants, with untrained administrators, with precision recording of responses, thus automating the assessment process. In turn, this enables cognitive profiling to be conducted in contexts where access to qualified examiners and standardized assessments are rarely available. As such, touch screen assessments could provide a means of assessing child development in both low- and high-income countries, which would afford cross-cultural comparisons to be made with the same assessment tool. However, before touch screen tablet assessments can be used for cognitive profiling in low-to-high-income countries they need to be shown to provide reliable and valid measures of performance. We report the development of a new touch screen tablet assessment of basic cognitive and motor functions for use with early years primary school children in low- and high-income countries. Measures of spatial intelligence, visual attention, short-term memory, working memory, manual processing speed, and manual coordination are included as well as mathematical knowledge. To investigate if this new touch screen assessment tool can be used for cross-cultural comparisons we administered it to a sample of children (N = 283) spanning standards 1–3 in a low-income country, Malawi, and a smaller sample of children (N = 70) from first year of formal schooling from a high-income country, the UK. Split-half reliability, test-retest reliability, face validity, convergent construct validity, predictive criterion validity, and concurrent criterion validity were investigated. Results demonstrate “proof of concept” that touch screen tablet technology can provide reliable and valid psychometric measures of performance in the early years, highlighting its potential to be used in cross-cultural comparisons and research.

Untangling the Contribution of the Subcomponents of Working Memory to Mathematical Proficiency as Measured by the National Tests: A Study among Swedish Third Graders

The aim with the present study was to examine the relationship between the subcomponents in working memory (WM) and mathematical performance, as measured by the National tests in a sample of 597 Swedish third-grade pupils. In line with compelling evidence of other studies, individual differences in WM capacity significantly predicted mathematical performance. Dividing the sample into four groups, based on their mathematical performance, revealed that mathematical ability can be conceptualized in terms of different WM profiles. Pupils categorized as High-math performers particularly differed from the other three groups in having a significant higher phonological ability. In contrast, pupils categorized as Low-math performers were particularly characterized by having a significant lower visuo-spatial ability. Findings suggest that it is important for educators to recognize and acknowledge individual differences in WM to support mathematical achievement at an individual level.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing.

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

Word problems: a review of linguistic and numerical factors contributing to their difficulty

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group.

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children's mathematical abilities

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability.

Working memory and executive functions: effects of training on academic achievement

The aim of this review is to illustrate the role of working memory and executive functions for scholastic achievement as an introduction to the question of whether and how working memory and executive control training may improve academic abilities. The review of current research showed limited but converging evidence for positive effects of process-based complex working-memory training on academic abilities, particularly in the domain of reading. These benefits occurred in children suffering from cognitive and academic deficits as well as in healthy students. Transfer of training to mathematical abilities seemed to be very limited and to depend on the training regime and the characteristics of the study sample. A core issue in training research is whether high- or low-achieving children benefit more from cognitive training. Individual differences in terms of training-related benefits suggested that process-based working memory and executive control training often induced compensation effects with larger benefits in low performing individuals. Finally, we discuss the effects of process-based training in relation to other types of interventions aimed at improving academic achievement.

Entwicklung von Handkoordination, exekutiven Funktionen und Schulleistungen bei Kindern mit Auffälligkeiten in der Handgeschicklichkeit

In der vorliegenden Studie wurden die Handgeschicklichkeit, exekutive Funktionen und Schulleistungen bei Vorschulkindern mit und ohne Problemen in der Handgeschicklichkeit über einen 3-Jahres-Zeitraum untersucht. Insgesamt wurden N = 94 Kinder, die zu Beginn 5- oder 6-jährig waren, untersucht, davon 47 Risikokinder mit sehr niedrigen Leistungen in der Handgeschicklichkeit und 47 Vergleichskinder. Diese wurden anhand der Variablen Alter, sozioökonomischer Status und nonverbale Intelligenz bestimmt. Die Risikokinder zeigten persistierende Defizite in der Handkoordination über den gesamten Untersuchungszeitraum hinweg. Obwohl sich alle Kinder insgesamt deutlich in den exekutiven Funktionen verbesserten, zeigten die Risikokinder ferner eine bedeutsam schlechtere Interferenzkontrolle und kognitive Flexibilität als die Vergleichskinder. Auch die schulischen Leistungen in den Bereichen Lesen, Schreiben und Mathematik zu Beginn der Beschulung waren bei den Risikokindern niedriger als bei den Vergleichskindern. Diese Befunde deuten auf domänübergreifende Probleme bei inhibitorischen und/oder Automatisierungsprozessen bei Kindern mit Auffälligkeiten in der Handgeschicklichkeit hin und geben wichtige Hinweise auf notwendige Interventionsmaßnahmen.

Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across Grades 2-3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems.

Working memory components as predictors of children's mathematical word problem solving

This study determined the working memory (WM) components (executive, phonological loop, and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N=310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM, reading, and math calculation. Structural equation modeling analyses indicated that (a) all three WM components significantly predicted problem-solving accuracy, (b) reading skills and calculation proficiency mediated the predictive effects of the central executive system and the phonological loop on solution accuracy, and (c) academic mediators failed to moderate the relationship between the visual-spatial sketchpad and solution accuracy. The results support the notion that all components of WM play a major role in predicting problem-solving accuracy, but basic skills acquired in specific academic domains (reading and math) can compensate for some of the influence of WM on children's mathematical word problem solving.

Motorische Koordinationsdefizite im Kindesalter

In vorliegender Studie wurden kognitive Basisfunktionen bei Kindern mit niedrigen motorisch-koordinativen Leistungen und mit Risiko für motorische Entwicklungsstörungen untersucht. Insgesamt 179 Kinder im Alter von 7 Jahren wurden mit einer motorischen Testbatterie (M-ABC-2) getestet; 34 wiesen unterdurchschnittliche koordinative Fähigkeiten auf, 8 wurden als Risikokinder identifiziert. Alle Kinder absolvierten kognitiv-exekutive Aufgaben zu Aufmerksamkeits- und Arbeitsgedächtnisfunktionen. Die Ergebnisse zeigen, dass koordinativ unterdurchschnittliche Kinder in kognitiv-exekutiven Bereichen der Aufmerksamkeit zwar aufgabenübergreifend langsamer waren, die Leistungsgenauigkeit aber vergleichbar mit koordinativ unauffälligen Kindern ist. Dagegen zeigen Kinder mit Risiko für eine motorische Entwicklungsstörung qualitativ schlechtere Genauigkeitsleistungen. Die Arbeitsgedächtnisleistungen sind von den koordinativen Leistungen weitgehend unabhängig. Die Ergebnisse werden hinsichtlich möglicher Prozesse diskutiert, die kognitiven Problemen bei motorischen Entwicklungsstörungen zugrunde liegen können.

Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions

BACKGROUND

The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children.

AIM

The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills.

SAMPLE AND METHOD

A total of 141 third- and fourth-graders were administered arithmetical tasks and measures of working memory, fluid IQ and reading. Regression analysis was used to examine the relationship between working memory and written arithmetical skills.

RESULTS

Three central executive measures (counting span, trail making and verbal fluency) and one phonological loop measure (Digit Span) were significant and predictors of arithmetical performance when the influence of reading, age and IQ was controlled for in the analysis.

CONCLUSIONS

The present findings demonstrate that working memory, in general, and the central executive, in particular, contribute to children's arithmetical skills. It was hypothesized that monitoring and coordinating multiple processes, and accessing arithmetical knowledge from long-term memory, are important central executive functions during arithmetical performance. The contribution of the phonological loop and the central executive (concurrent processing and storage of numerical information) indicates that children aged 9-10 years primarily utilize verbal coding strategies during written arithmetical performance.