Capturing Children’s Mathematical Knowledge: An Assessment Framework

Abstract

This paper explores an innovative assessment framework for measuring children’s formal and informal mathematical knowledge. Many existing standardized measures, such as the Early Grade Mathematics Assessment, measure children’s performance in early primary grade skills that have been identified by researchers and policy makers as foundational and predictive of later academic achievement (Platas, Ketterlin-Geller, & Sitabkhan, 2016; RTI International, 2014). However, these standardized assessments only provide information on children’s mathematical ability as it pertains to skills and concepts that are a focus of school instruction, referred to as formal mathematics. While valuable, they leave unmeasured the mathematics that children use and develop as part of their everyday life, such as the strategies they use to solve simple arithmetical problems that arise as they move through their day (Khan, 1999; Saxe, 1991; Taylor, 2009).  In this article, we draw from mixed methods studies which focus on capturing the informal mathematical skills that children develop outside of school in various contexts (Guberman, 1996; Nasir, 2000; Sitabkhan, 2009; Sitabkhan, 2015). We describe how the use of observations of children’s mathematical activities in natural settings and subsequent cognitive interviews using mathematical tasks derived from those observations can illuminate mathematical knowledge and skills that may otherwise remain hidden. We found that an assessment framework that focuses on both standardized measures of formal mathematical learning and contextualized measures of children’s everyday mathematics can provide a more complete and nuanced picture of children’s knowledge, and taken together can inform the development of curricular materials and teacher training focused on early learning.