Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of working memory. Concurrent analyses indicated that mathematics anxiety represents a unique source of individual differences in children’s calculation skills and mathematical applications, but not in children’s geometric reasoning. Furthermore, we found that higher levels of mathematics anxiety in second grade predicted lower gains in children’s mathematical applications between second and third grade, but only for children with higher levels of working memory. Overall, our results indicate that mathematics anxiety is an important construct to consider when examining sources of individual differences in young children’s mathematical performance. Furthermore, our findings suggest that mathematics anxiety may affect how some children use working memory resources to learn mathematical applications.     

Additive and multiplicative effects of working memory and test anxiety on mathematics performance in grade 3 students

The aim of this study was to investigate the interplay between test anxiety and working memory (WM) on mathematics performance in younger children. A sample of 624 grade 3 students completed a test battery consisting of a test anxiety scale, WM tasks and the Swedish national examination in mathematics for grade 3. The main effects of test anxiety and WM, and the two-way interaction between test anxiety and WM on mathematics performance, were modelled with structural equation modelling techniques. Additionally, the effects were also tested separately on tasks with high WM demands (mathematical problem-solving) versus low WM demands (basic arithmetic). As expected, WM positively predicted mathematics performance in all three models (overall mathematics performance, problem-solving tasks, and basic arithmetic). Test anxiety had a negative effect on problem-solving on the whole sample level but concerning basic arithmetic only students with lower WM were affected by the negative effects of test anxiety on performance. Thus, students with low WM are more vulnerable to the negative effects of test anxiety in low WM tasks like basic arithmetic. The results are discussed in relation to the early identification of test anxiety.     

Mathematical thinking in second-grade children with different forms of LD

Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving.     

Working memory and mathematics in primary school children: A meta-analysis

Working memory, including central executive functions (inhibition, shifting and updating) are factors thought to play a central role in mathematical skill development. However, results reported with regard to the associations between mathematics and working memory components are inconsistent. The aim of this meta-analysis is twofold: to investigate the strength of this relation, and to establish whether the variation in the association is caused by tests, sample characteristics and study and other methodological characteristics. Results indicate that all working memory components are associated with mathematical performance, with the highest correlation between mathematics and verbal updating. Variation in the strength of the associations can consistently be explained by the type of mathematics measure used: general tests yield stronger correlations than more specific tests. Furthermore, characteristics of working memory measures, age and sample explain variance in correlations in some analyses. Interpretations of the contribution of moderator variables to various models are discussed.     

Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit?

The relationship between verbal and visual-spatial working memory and mathematical computation skill was examined in children and adults with and without disabilities in mathematics. A hierarchical regression analysis showed that, when partialing for the influence of reading ability, age, and gender, mathematical computation was better predicted by verbal than by visual-spatial working memory. Furthermore, the results showed that the relationship between mathematics ability and working memory were not significantly moderated by age but were stable across a broad age span. We concluded that, regardless of age, deficits in mathematics are mediated by both a domain-general and a domain-specific working memory system.     

The association between working memory and educational attainment as measured in different mathematical subtopics in the Swedish national assessment: primary education

The aim of this study was to examine the relationship between working memory capacity and mathematical performance measured by the national curriculum assessment in third-grade children (n?=?40). The national tests concerned six subareas within mathematics. One-way ANOVA, two-tailed Pearson correlation and multiple regression analyses were conducted. The results showed that working memory could be deemed as a predictor for the overall mathematical ability. However, the significance of working memory contributions varied for the different mathematical domains assessed. Working memory contributed most to basic mathematical competencies. Algorithms were not explained significantly by working memory. The contributions of different working memory resources varied as a function of the mathematical domain, but in certain respects the variance was shared across the elements and both visuo-spatial and phonological abilities seem important for mathematic performance. We suggest that individuals’ working memory capacity is important to take into consideration in learning.     

From Parental Involvement to Children's Mathematical Performance: The Role of Mathematics Anxiety

This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping several domains of parental involvement, and children were assessed on mathematics anxiety, whole number arithmetic, word problems, and algebraic reasoning. Research Findings: The results indicated that parents influence children's mathematics achievement by reducing mathematics anxiety, particularly for more difficult kinds of mathematics. Specifically, the mediation analyses demonstrated that parental home support and expectations influenced children's performance on word problems and algebraic reasoning by reducing children's mathematics anxiety. Mathematics anxiety did not mediate the relationship between home support and expectations and whole number arithmetic. Practice or Policy: Policies and programs targeting parental involvement in mathematics should focus on home-based practices that do not require technical mathematical skills. Parents should receive training, resources, and support on culturally appropriate ways to create home learning environments that foster high expectations for children's success in mathematics.     

The Contribution of Memory and Anxiety to the Math Performance of College Students with Learning Disabilities

The impact of memory and anxiety on math performance was analyzed in a sample of 115 college undergraduates, all of whom had a diagnosed learning disability. The direct effects of memory and anxiety on math performance were first examined, followed by an examination of whether anxiety moderates the relationship between memory and math. Both memory and anxiety were found to directly affect math performance. Additionally, anxiety served as a moderator of the relationship between memory and math for most, but not all, measures of math achievement. The moderating effect of anxiety was stronger for long-term retrieval than for short-term memory. The relationships between memory, anxiety, and math were not significantly different for males and females. These findings suggest that, when working with individuals who have low anxiety but poor memory, enhancing memory strategies may be effective for remediating problems in math. However, for those with high levels of anxiety, it may be more efficacious to first ameliorate the anxiety, as working on memory may have a negligible effect on math performance for these individuals.     

Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children, failed spatial working memory tasks that had either low or high attentional demands but did not fail the visual tasks. In addition, children with MLD made more intrusion errors in the spatial working memory tasks requiring high attentional control than did their TD peers. Finally, as a post hoc analysis the sample of MLD was divided in two: children with severe MLD and children with low mathematical achievement. Results showed that only children with severe MLD failed in spatial working memory (WM) tasks if compared with children with low mathematical achievement and TD. The findings are discussed on the basis of their theoretical and clinical implications, in particular considering that children with MLD can benefit from spatial WM processes to solve arithmetic word problems, which involves the ability to both maintain and manipulate relevant information.     

Longitudinal contributions of executive functioning and visual-spatial skills to mathematics learning in young Chinese children

One hundred sixty-five Hong Kong Chinese children were administered measures of early mathematics, visual-spatial skills, and executive functioning (working memory, inhibition, shifting, updating) once in kindergarten (mean age?=?62.80 months, SD?=?3.74) and again in first grade (mean age?=?77.25 months, SD?=?4.60). In kindergarten, visual-spatial skills, inhibition, shifting, and working memory were all uniquely associated with concurrent mathematics performance; in first grade, only working memory and visual-spatial skills were significantly related to concurrent mathematics abilities. Furthermore, working memory and visual-spatial skills in kindergarten predicted 19% of the variance in children’s mathematics performance in first grade, beyond the autoregressive effects of mathematics performance in kindergarten as well as demographic variables. Findings highlight the importance of working memory and visual-spatial skills for young Chinese children in mastering mathematics.     

Construction play and cognitive skills associated with the development of mathematical abilities in 7-year-old children

Construction play is thought to develop logico-mathematical skills, however the underlying mechanisms have not been defined. In order to fill this gap, this study looks at the relationship between Lego construction ability, cognitive abilities and mathematical performance in 7-year-old, Year 2 primary school children (N = 66). While studies have focused on the relationship between mathematics performance and verbal memory, there are limited studies focussing on visuospatial memory. We tested both visuospatial and verbal working memory and short term memory, as well as non-verbal intelligence. Mathematical performance was measured through the WIAT-II numerical operations, and the word reading subtest was used as a control variable. We used a Lego construction task paradigm based on four task variables found to systematically increase construction task difficulty. The results suggest that Lego construction ability is positively related to mathematics performance, and visuospatial memory fully mediates this relationship. Future work of an intervention study using Lego construction training to develop visuospatial memory, which in turn may improve mathematics performance, is suggested.     

A working memory model applied to mathematical word problem solving

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.     

“I think I can,but I'm afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for mathematics, before completing an operation span task to measure working memory capacity, rating self-efficacy for mental multiplication, and then solved computer-based multiplication problems at two complexity levels. A simultaneous regression design was used to assess the unique variance associated with each variable. There were two new findings; the differential role of self-efficacy on response time and efficiency, and the potential compensatory relationship between self-efficacy and mathematics anxiety related to efficiency outcomes. Educational implications and suggestions for future research were proposed.     

Cognitive processes and math performance: a study with children at third grade of basic education

The present study aims to examine the relationship between cognitive factors and mathematical achievement in primary education. Participants were 103 Portuguese third grade students, aged 8 and 9. All participants completed a battery for working memory (WMTB-C), a test of general intelligence (Raven's Progressive Color Matrices), a selective attention test (d2), and mathematical exercises (arithmetic story problems and measurement skills). Data suggested significant correlations between math performance, executive, visuospatial sketchpad and g factor. Our findings suggest the importance of the cognitive factors in two mathematical domains considered. In consonance with the research in this area, we conclude that working memory (WM) assumes an important role in different math curricular achievements.     

Working Memory and Children’s Mathematical Skills: Implications for mathematical development and mathematics curricula

This study examined the contributions of the different components of the working memory (WM) model to a range of mathematical skills in children, using measures of WM function that did not involve numerical stimuli. A sample of 148 children (78 Year 3, mean age 8 years and 1 month, and 70 Year 5 pupils, mean age 9 years and 10 months) completed WM measures and age‐appropriate mathematics tests designed to assess four mathematical skills defined by the National Curriculum for England. Visuo‐spatial sketchpad and central executive, but not phonological loop, scores predicted unique variance in children’s curriculum‐based mathematical attainment but the relative contributions of each component did not vary much across the different skills. Subsequently, the mathematics data were re‐analysed using cluster analysis and new performance‐related mathematics factors were derived. All three components of WM predicted unique variance in these performance‐related skills, but revealed a markedly distinct pattern of associations across the two age groups. In particular, the data indicated a stronger role for the visuo‐spatial sketchpad in the younger children’s mathematics performance. We discuss our findings in terms of the importance of WM in the development of early mathematical ability.     

Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities

The purpose of this study was to describe the mathematical problem-solving profiles of students with mathematics disabilities (MD) with and without comorbid reading disabilities (RD). The disability status of fourth-grade students was verified through testing (n = 18 MD; n = 22 MD + RD). Then a hierarchy of mathematics problem-solving tasks was administered. The results demonstrated large deficits for both groups; however, the differences between students with MD and those with MD + RD were mediated by the level of problem solving (arithmetic story problems vs. complex story problems vs. real-world problem solving) and by performance dimension (operations vs. problem solving). On arithmetic story problems, the differences between the disability subtypes were similar for operations and problem solving. By contrast, on complex story problems and real-world problem solving, the differences between the subtypes were larger for problem solving than for operations.     

The Development of Young Pupils’ Self‐Representation and Mathematical Performance in Relation to Processing Efficiency and Working Memory

The present study outlines a specific three‐level hierarchy of the cognitive system, in particular the relationship between cognitive and metacognitive processes in mathematics. The emphasis is on the impact of processing efficiency and working memory ability on the development of self‐representation and mathematical performance. We developed and used instruments measuring pupils' self‐representation, mathematical performance, working memory, and information processing and administered them to 126 pupils (8–11 years old) three times, with breaks of three to four months between testing. Results indicated that the development of each of the abilities was affected by the state of the others. In particular, processing efficiency had a coordinator role on the growth of mathematical performance, while self‐image, as a specific dimension of self‐representation, depended mainly on previous working memory ability.     

Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability

Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n=15) and low achieving (LA, n=44) were identified. These groups and a group of typically achieving (TA, n=46) children were administered a battery of mathematical cognition, working memory, and speed of processing measures (M=6 years). The children with MLD showed deficits across all math cognition tasks, many of which were partially or fully mediated by working memory or speed of processing. Compared with the TA group, the LA children were less fluent in processing numerical information and knew fewer addition facts. Implications for defining MLD and identifying underlying cognitive deficits are discussed.     

Metacognition, General Ability, and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.     

Metacognition,General Ability,and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.