Cognitive predictors of children’s development in mathematics achievement: a latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children’s individual differences in mathematics achievement. However, research into the predictors of children’s individual growth rates, i.e., between-person differences in within-person change, in mathematics achievement is scarce. We assessed 334 children’s domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the 1st and 2nd grade of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children’s starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children’s initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children’s individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one’s mathematical success. We argue the need for more research focus on explaining children’s individual growth rates in mathematics achievement

Making sense of numbers : early mathematics achievement and working memory in primary school children

This dissertation aimed to investigate symbolic and non-symbolic number sense in relation to each other, to working memory, and to mathematics performance through the testing of (longitudinal) associations and training effects. These aims were achieved through a series of eight studies, with four different methodologies: meta-analyses aggregated previously reported associations between constructs and explored sources of variation. Short studies indexed the factor structure of number sense and the predictive role of working memory for number sense. Longitudinal studies were used to model development of number sense and mathematics performance, and explore the dynamic pattern of reciprocal associations. Training studies, finally, were used to investigate which assets of number sense and working memory could be trained, and how this impacted related constructs. The dissertation allows three main conclusions to be drawn. First, working memory capacity can be used to predict both number sense and formal mathematical skill, as evident from the reported meta-analyses, but the contribution of various working memory components differs depending on the domain of numerical skills assessed, the way in which working memory is assessed, and various other methodological decisions. Second, number sense can be divided into symbolic number sense (working with verbal and written number symbols) and non-symbolic number sense (working with quantities such as dots and line lengths), both of which are predictive of skill growth in number sense at a later age. Both factors can be predicted using concurrent working memory measures, but not by the same sets of working memory components. Symbolic and non-symbolic number sense are affected by training activities in discordant ways: symbolic number sense can be trained effectively in kindergarten, but there is only limited support for the notion that non-symbolic number sense van be trained in a similar way. Third, number sense is a consistent predictor of mathematical skill, but this relation is bidirectional: although number sense measures at one point in time can predict mathematics performance at a later point in time, mathematics performance can also predict number sense longitudinally. This indicated that insights associated with mathematics performance can be used to fine-tune a child’s understanding of number. Recommendations for future research include in increased focus on the dynamic relations between number sense, mathematics achievement, and working memory, more specific scrutiny of the roles of non-symbolic and symbolic number sense as latent constructs, and investigation of the relative merits of training specific assets of number sense, rather than the overarching skill. In sum, this dissertation contributes in an important way to current understandings of children’s number sense, its relations to mathematics and working memory, and the possibilities to facilitate these skills at an early age

Classroom versus individual working memory assessment: predicting academic achievement and the role of attention and response inhibition

Working memory (WM) is an important predictor for academic learning and achievement. Typically, children’s WM is assessed in controlled testing situations, which might not reflect functioning in typical classroom learning situations with natural distractions. In this study, we compared WM performance in controlled and classroom situations and their predictive value for academic achievement. Also, we examined whether performance differences between situations were moderated by attention or response inhibition. In a within-subjects design, primary school children completed visuospatial and verbal WM tasks in two settings (classroom versus controlled individual setting). First, WM functioning was lower in the classroom setting. Second, attention moderated individual differences in this discrepancy between settings, but response inhibition did not. Third, classroom obtained verbal WM scores were the strongest predictors of academic achievement. Our results indicate that classroom assessment of verbal WM provides a more ecologically valid measurement of WM abilities in a real-life learning situation

Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense

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 program. Effects of both programs were compared through a quasi-experimental design, and moderation effects of age and socio-economic status (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 programs and the consequences of variation in these parameters

Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense

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 program. Effects of both programs were compared through a quasi-experimental design, and moderation effects of age and socio-economic status (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 programs and the consequences of variation in these parameters