Cognitive Precursors to Mathematical Competence: A Meta-Analysis and Two Longitudinal Investigations

Abstract

Building on models of mathematical cognition postulating three pathways to mathematics, the aim of this doctoral work is to test predictors of mathematical competence in the years spanning from late preschool into the first years of formal schooling. Number, language and spatial ability, along with working memory, executive function and nonverbal reasoning skills, were assessed as potential precursors of early mathematics outcomes with an emphasis on arithmetic and word problem solving. Additionally, the aim was to assess which cognitive predictors might underlie the connection between reading and mathematical outcomes. A total of eight research questions relating to the above were answered through two longitudinal investigations of a sample with Norwegian children, as well as a systematic review and metaanalysis of a global sample of concurrent and longitudinal studies. Using structural equation models (SEM), meta-regression and meta-SEM, my colleagues and I tested the predictors with different levels of specificity; overall predictor constructs and subcomponents of each were assessed with regards to their relations to mathematical outcomes. Key results reveal that the numerical pathway consists of both non-symbolic and symbolic number skills, but with symbolic number skills as a significantly stronger predictor of mathematical outcomes. We also found that the language pathway consists of separate domains. Phonological awareness skills are not a strong predictor of maths outcomes, but language comprehension predicts complex and verbally demanding mathematical tasks. Rapid automatized naming skills predict arithmetic fluency and are found to underlie shared aspects of reading and arithmetic. Additionally, we found that the spatial pathway leads to success in word problem solving but is not strongly related to arithmetic outcomes. Among the background predictors, nonverbal reasoning stood out as a strong predictor of competence across mathematical domains. This doctoral work makes several important contributions to the field of mathematical cognition and learning. First, the results make contributions to theory development by refining previous models of mathematical cognition, as well as increasing our understanding of shared processes in efficient reading and maths. Second, the findings can inform causal hypotheses to be tested in educational interventions designed to support children with low maths competence. Third, the methodological aspects of the large systematic review of precursors to mathematics highlight the characteristics and challenges pertaining to studies of mathematical outcomes that can inspire better practices and improved coherence across the field of mathematical cognition and learning