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Test scoring procedures should align with the intended uses and interpretations of test results. In this paper, we examine three test scoring procedures for an operational assessment of early numeracy, the Early Grade Mathematics Assessment (EGMA). The EGMA is an assessment that tests young children's foundational mathematics knowledge and has been administered in more than 25 countries. Current test specifications call for subscores to be reported for each of the eight subtests on the EGMA; however, in practice, composite scores have also been reported. To provide users with empirically-based guidance on the appropriateness and usefulness of different test scoring procedures, we examine the psychometric properties--including the reliability and distinctiveness of the results--and usefulness of reporting test scores as (1) total scores, (2) subscores, and (3) composite scores. These test scoring procedures are compared using data from an actual administration of the EGMA. Conclusions and recommendations for test scoring procedures are made. Generalizations to other testing programs are proposed.

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.