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 in 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.