When is working memory important for arithmetic?: the impact of strategy and age

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition

Counting and number line trainings in kindergarten: Effects on arithmetic performance and number sense

Contains fulltext : 192025.pdf (publisher's version ) (Open Access)Children's early numerical capacities form the building blocks for later arithmetic proficiency. Linear number placements and counting skills are indicative of mapping, as an important precursor to arithmetic skills, and have been suggested to be of vital importance to arithmetic development. The current study investigated whether fostering mapping skills is more efficient through a counting or a number line training programme. Effects of both programmes were compared through a quasi-experimental design, and moderation effects of age and SES were investigated. Ninety kindergartners were divided into three conditions: a counting, a number line, and a control condition. Pretests and posttests included an arithmetic (addition) task and a battery of number sense tasks (comparison, number lines and counting). Results showed significantly greater gains in arithmetic, counting, and symbolic number lines in the counting training group than in the control group. The number line training group did not make significantly greater gains than the control group. Training gains were moderated by age, but not SES. We concluded that counting training improved numerical capacities effectively, whereas no such improvements could be found for the number line training. This suggests that only a counting approach is effective for fostering number sense and early arithmetic skills in kindergarten. Future research should elaborate on the parameters of training programmes and the consequences of variation in these parameters.11 p

A meta-analysis on the differences in mathematical and cognitive skills between individuals with and without mathematical learning disabilities

Types of mathematical learning disability (MLD) are very heterogeneous. Lower scores on mathematics and several cognitive skills have been revealed in samples with MLD compared with those with typical development (TD), but these studies vary in sample selection, making it difficult to generalize conclusions. Furthermore, many studies have investigated only one or few cognitive skills, making it difficult to compare their relative discrepancies. The current meta-analysis (k = 145) was conducted to (a) give a state-of-the-art overview of the mathematical and cognitive skills associated with MLD and (b) investigate how selection criteria influence conclusions regarding this topic. Results indicated that people with MLD display lower scores not only on mathematics but also on number sense, working memory, and rapid automatized naming compared with those with TD, in general independently of the criteria used to define MLD. A profile that distinguishes people with more serious, persistent, or specific MLD from those with less severe MLD was not detected

Number sense in kindergarten children: Factor structure and working memory predictors

Contains fulltext : 178272.pdf (publisher's version ) (Closed access)In the current study, the factor structure of number sense, or the ability to understand, use, and manipulate numbers, was investigated. Previous analyses yielded little consensus concerning number sense factors, other than a distinction between nonsymbolic and symbolic processing. Furthermore, associations between number sense factors and working memory components were investigated to gain insight into working memory involvement in number sense. A total of 441 Dutch kindergartners took part in the study. The factor structure of number sense and associations with working memory were tested using structural equation modelling. Results indicated that there was a distinction between nonsymbolic and symbolic number processing. Nonsymbolic processing was predicted by central executive performance, and symbolic processing was predicted by both central executive and visuospatial sketchpad performance. This implies that symbolic and nonsymbolic processing are distinguishable at this age, and that working memory involvement in symbolic processing is different from that in nonsymbolic processing.7 p

The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4–6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development

Explaining variability: Numerical representations in 4- to 8-year-old children

Contains fulltext : 178269.pdf (publisher's version ) (Closed access)The present study aims to examine relations between number representations and various sources of individual differences within early stages of development of number representations. The mental number line has been found to develop from a logarithmic to a more linear representation. Sources under investigation are counting skills and executive functions and are set out against mental number lines from 0 to 10 and 0 to 100 in a sample of 4- to 8-year-old children (N = 80). Findings indicate that counting skills, inhibition, and updating are the most important predictors of the shape of the mental number line over and above age-related developmental differences, with number lines from 0 to 10 being linear to a large extent and number lines from 0 to 100 developing from a random pattern toward logarithmic representations. The shape of the mental number line was found to predict scores on the number comparison task only on the smaller-scale comparison task.20 p

Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school

Contains fulltext : 178264.pdf (publisher's version ) (Open Access)The relative importance of visual-spatial and verbal working memory for mathematics performance and learning seems to vary with age, the novelty of the material, and the specific math domain that is investigated. In this study, the relations between verbal and visual-spatial working memory and performance in four math domains (i.e., addition, subtraction, multiplication, and division) at different ages during primary school are investigated. Children (N = 4337) from grades 2 through 6 participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed at the start, middle, and end of the school year using a speeded arithmetic test. Multilevel Multigroup Latent Growth Modeling was used to model individual differences in level and growth in math performance, and examine the predictive value of working memory per grade, while controlling for effects of classroom membership. The results showed that as grade level progressed, the predictive value of visual-spatial working memory for individual differences in level of mathematics performance waned, while the predictive value of verbal working memory increased. Working memory did not predict individual differences between children in their rate of performance growth throughout the school year. These findings are discussed in relation to three, not mutually exclusive, explanations for such age-related findings.12 p