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Using a longitudinal data set, this paper examines to what extent school-entry (N = 553; mean age 6.32 years) early mathematics and literacy skills predict students' later achievement in a lower-middle-income country, Kenya. Controlling for socioeconomic status, intervention status, rural versus urban settings and parental literacy, the findings reveal that school-entry mathematics skills were significantly predictive of students' end of Grade 2 mathematics and reading achievement in English and Kiswahili. Likewise, school-entry English early literacy skills predicted students' end of Grade 2 mathematics and reading achievement in English and Kiswahili. This article extends earlier research on links between elements of school readiness and later achievement in high-income countries.

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.

This paper describes the development and intended uses of the Early Grades Mathematics Assessment (EGMA), which measures essential early mathematical knowledge and skills that are foundational to more sophisticated mathematical abilities, predictive of later achievement, and teachable. Administering the EGMA can provide policy makers, practitioners, and researchers with information about whether existing educational policies, curricular reforms or programs, and instructional interventions are supporting students in reaching important goals in mathematics. We highlight the utility of the EGMA results in three abbreviated illustrations of implementation studies in low-income countries. Recommendations for policy makers, practitioners, and researchers are provided.

The Mathematical Development Beliefs Survey was developed to measure early childhood teachers' beliefs about mathematics teaching and learning in the preschool classroom. This instrument was designed to measure beliefs concerning (a) age-appropriateness of mathematics instruction, (b) classroom locus of generation of mathematical knowledge (teacher vs child), (c) mathematical development as a primary goal of preschool education, and (d) confidence level in providing mathematics instruction. The reliability and validity of the instrument was examined through multiple phases of development, including two pilot studies and a final study with 346 pre- and in-service preschool teachers across three states. Methods included cognitive interviews with participants, literature reviews, and interviews with experts in the field, as well as statistical procedures such as analyses of variance between well-defined groups of in- and preservice teachers, correlations between measures of knowledge and beliefs, and confirmatory factor analysis. Reliability of the instrument was examined through the use of Cronbach's alpha and item-total correlations. These statistical procedures provided very good to excellent support for both validity and reliability. Potential applications include informing development and evaluation of early childhood education teacher preparation programs and professional development interventions.

Over the past 20 years, research on the role of mathematical proficiency in academic and economic success has proliferated. Understanding how mathematical development and learning can be fostered in both in- and out-of-school settings is key to ensuring widespread numerical literacy. Much of what is known about how children develop mathematical knowledge and the educational practices that support such development come out of high-income countries. Widening the lens of research to include children and youth across languages, cultures, and contexts is essential to informing practices and policies across the globe. From pre-primary through primary grades, this chapter examines the increasing emphasis on supporting mathematical development in early childhood, efforts to move away from memorization-based instruction toward support of conceptual understanding, out-of-school influences on mathematical learning, and promising instructional practices. [ABSTRACT FROM AUTHOR]

The article discusses role of educators in supporting social, emotional and mathematical development in early childhood. Topics discussed include engaging children with physical features such as student-created number walls, "The Intentional Teacher" book by Ann S. Epstein and opportunity for learning with outdoor play.