Early Understanding of Conceptual and Procedural Mathematics Relate to Later Mathematical Skills

• In Event: 2-138 - Moderators of the Development of Mathematical Skills

Integrative Statement

Though commonly considered as a unitary construct in educational contexts, early mathematics may be better represented by two or more related constructs (Dowker, 2008; LeFevre et al., 2010). Indeed, decades of research has suggested math may be effectively represented by conceptual and procedural aspects of mathematics (e.g., Bisanz & LeFevre, 1992; Hiebert, 2013; Rittle-Johnson, Siegler, & Alibali, 2001; Star, 2005). However, additional research is needed to better understand the relations between early conceptual and procedural skills and later math. As well, there is evidence from some small-scale studies that suggest an interaction between each conceptual and procedural mathematical skills and executive functions such that children who had high levels of conceptual skills benefitted more from procedural understanding than did peers who had worse conceptual understanding (e.g., Gilmore, Keeble, Richardson, & Cragg, 2017). Further investigation is needed to better understand the relations between conceptual skills, procedural skills, and executive functions in the prediction of later mathematical skills.
Analyses were conducted using data from the Family Life Project, a large-scale, longitudinal, prospective study of child development with children from areas of non-urban Pennsylvania and North Carolina. The Family Life Project consists of 1,292 participants who were enrolled at 2 months of age and who took part in regular data collection visits at their homes and in their schools. For the present analysis, data were collected when children were approximately 5 years of age and enrolled in PreKindergarten, and again one year later when children were enrolled in Kindergarten. Executive function was assessed using a battery of six notebook-based assessments (Willoughby, Blair, Wirth, and Greenberg, 2012). Math skills were assessed using the assessment developed by the Early Childhood Longitudinal Study, Kindergarten Cohort: 1998-1999. Prior confirmatory factor analysis (REDACTED) established the presence of two unique, correlated domains of mathematics in PreK: conceptual and procedural understanding of math (r = .48, p < .001).
Math skills in kindergarten were regressed conceptual and procedural skills from PreK, as well as executive function and a host of covariates (i.e., child IQ, processing speed, receptive vocabulary, family income-to-needs ratio, and mom education; Table 1). Both conceptual and procedural skills in PreKindergarten were related to kindergarten math at a similar magnitude (β = .15, p < .001; β = .18, p < .001, respectively), as was PreK executive function (β = .16, p < .001). A second regression was then run to test the additive value of interactions between conceptual and procedural skills and each conceptual and procedural skills with executive function. The interaction between conceptual skills and executive function was related to kindergarten math (β = -.18, p = .011), such that students with high levels of executive function in PreKindergarten, but low levels of conceptual knowledge were able to catch up to their peers who had higher levels of conceptual knowledge. In contrast the interactions between conceptual and procedural skills and between procedural skills and executive function were not (p’s > .05). Implications will be discussed.

Group Authors

The Family Life Project Key Investigators

Authors

• Camilla Gilmore, Loughborough University
  Presenting Author

• Andrew Ribner, New York University
  Non-Presenting Author

• Korbinian Moeller, University of Tuebingen
  Non-Presenting Author

• Clancy Blair, New York University
  Non-Presenting Author