The structure of executive functions and relations with early math learning

In this dissertation, the relation between executive functions and mathematical skills in children was investigated. Two main aims were addressed: (1) unraveling the structure of executive functions, and (2) investigating the nature of the relations between executive functions and mathematics. Concerning the factor structure of executive functions, in the past a distinction in inhibition (the ability to suppress a dominant response), shifting (the ability to switch between tasks or rules), and updating (the ability to store items in working memory and to update these items when new, relevant information is presented) has been found, but not all studies confirmed this structure. We hypothesized that the task choices and scoring methods might be responsible for these contradictory findings. Therefore we selected tasks in which input modality was varied, baseline speed was controlled for and scores were obtained in various ways. We then investigated whether the distinction in inhibition, shifting, and updating could be replicated in a group of 211 children, who were tested at the beginning of grade 1 (6 years old) and again 18 months later. Confirmatory factor analysis showed that the best model did not contain the three expected executive function factors, but instead an updating factor and a combined inhibition/shifting factor, besides two baseline speed factors (verbal and motor speed). These results might indicate a difference in structural organization of executive functions in children and adults, but there may also be an alternative explanation: the distinction in three executive functions might be a methodological artifact. To address the second aim of the project, the development of the updating factor and the combined inhibition/shifting factor was modeled and relations with the development of mathematics during the first two years of primary education were analyzed. Latent growth curve models showed that the development of updating and mathematics task scores was linear. Moreover, development in both domains was strongly interrelated: the overall level of updating was related to the overall level in mathematics (an intercept-intercept correlation) and children who developed more in updating also developed more in mathematics (a slope-slope correlation). In the final study, we investigated how the strategies that children choose to solve multiplication problems changed during a period of eight weeks. Using latent growth modeling for categorical data, we were able to show that strategies gradually come and go during development, a phenomenon described as Overlapping Waves (Siegler, 1996). Moreover, children who used mature strategies also solved more problems correctly, and development in strategy selection and accuracy were also interrelated. Finally, we expected that the strategies children select and their success in the execution of the selected strategy are partially determined by their updating abilities: children with poor updating abilities are limited in their possibilities to make the connections that are necessary to progress to more mature strategies. As expected, updating abilities were related to both strategy selection and accuracy, showing that children with poor updating abilities suffer from a double deficit: they choose immature strategies that are error-prone and make more procedural mistakes carrying out these strategies.