REL Midwest Ask A REL Response

Math

March 2021

Assel, M. A., Montroy, J. J., Williams, J. M., Foster, M., Landry, S. H., Zucker, T., Crawford, A., Hyatt, H., & Bhavsar, V. (2020). Initial validation of a math progress monitoring measure for prekindergarten students. Journal of Psychoeducational Assessment, 38(8), 1014–1032. https://eric.ed.gov/?id=EJ1277499

From the ERIC abstract: “Given the importance of math in today’s society, it is critical that children who are at risk for math difficulty are identified early. We developed and validated a prekindergarten math subtest (i.e., CIRCLE Progress Monitoring [CPM] Math Subtest). This teacher-completed measure evaluates domains considered important for later math development. Evaluation of validity was undertaken in a longitudinal sample of 383 children (M[subscript age] = 4.9 years), and a follow-up sample of 3,691 children (M[subscript age] = 4.4 years). The measure demonstrated adequate psychometric properties, including strong internal consistency reliability ([alpha] = 0.94) and test-retest reliability (r = 0.78). Evaluation of concurrent and predictive validity demonstrated scores on the CPM Math Subtest were correlated with scores on other assessments at high levels (rs from 0.55-0.65). Exploratory and confirmatory factor analyses revealed that the subtest conforms to a well-defined five-factor model that parallels areas considered to be important in the math literature.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Brendefur, J. L., Johnson, E. S., Thiede, K. W., Strother, S., & Severson, H. H. (2018). Developing a multi-dimensional early elementary mathematics screener and diagnostic tool: The Primary Mathematics Assessment. Early Childhood Education Journal, 46(2), 153–157. https://eric.ed.gov/?id=EJ1171173

From the ERIC abstract: “There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students at risk for poor math outcomes and a diagnostic tool to provide a more in-depth profile of children’s specific strengths and weaknesses in mathematics. The PMA allows teachers and school personnel to make better instructional decisions by providing more targeted analyses.”

Clarke, B., Strand Cary, M. G., Shanley, L., & Sutherland, M. (2020). Exploring the promise of a number line assessment to help identify students at-risk in mathematics. Assessment for Effective Intervention, 45(2), 151–160. https://eric.ed.gov/?id=EJ1243106

From the ERIC abstract: “This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0-20 and NLA 0-100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test-retest reliability. The NLA 0-20 had low and the NLA 0-100 had low to moderate correlations with math achievement. Results indicated that the NLA 0-100 explained a small, but unique portion of the variance in first grade mathematics performance when controlling for performance on the Assessing Student Proficiency in Early Number Sense (ASPENS) a set of early numeracy screening measures. We discuss study results related to the utility of adding number line assessment tasks to mathematics screening batteries and propose additional areas of research.”

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Clemens, N. H., Keller-Margulis, M. A., Scholten, T., & Yoon, M. (2016). Screening assessment within a multi-tiered system of support: Current practices, advances, and next steps. In S. R. Jimerson, M. K. Burns, & A. M. VanDerHeyden (Eds.), Handbook of Response to Intervention (pp. 187–213). Springer. https://eric.ed.gov/?id=ED566739

From the ERIC abstract: “Within multi-tiered systems of support (MTSS), screening assessments play an important role in identifying students who are in need of supplemental support strategies. In this chapter, the authors review the tools and methods commonly used in MTSS for academic skills screening, identify limitations with these practices, and highlight potential areas of improvement regarding assessment methods and content of screening tools, decision-making processes used to identify students in need of support, and methods used for evaluating screening tools. A set of recommendations and directions for future work are offered for advancing screening assessment and improving decision-making processes in schools with MTSS.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance (NCEE). https://eric.ed.gov/?id=ED544376

From the ERIC abstract: “The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide is organized around five recommendations: (1) Teach number and operations using a developmental progression; (2) Teach geometry, patterns, measurement, and data analysis using a developmental progression; (3) Use progress monitoring to ensure that math instruction builds on what each child knows; (4) Teach children to view and describe their world mathematically; and (5) Dedicate time each day to teaching math, and integrate math instruction throughout the school day.”

Hampton, D. D., Lembke, E. S., Lee, Y.-S., Pappas, S., Chiong, C., & Ginsburg, H. P. (2012). Technical adequacy of early numeracy curriculum-based progress monitoring measures for kindergarten and first-grade students. Assessment for Effective Intervention, 37(2), 118–126. https://eric.ed.gov/?id=EJ955539

From the ERIC abstract: “The purpose of this study was to examine six early numeracy measures used to monitor the mathematics progress of kindergarten and first-grade students. Seventy-one kindergarten students and 75 first-grade students were administered the measures each week. Delayed-alternate form reliability was adequate for instructional decision making on some measures, and low reliability was reported for quantity discrimination, as well as for the next number and number facts measures. Concurrent criterion validity coefficients comparing the measures with student performance on the ‘Woodcock-Johnson Tests of Achievement—Third Edition’ (WJ III) resulted in weaker coefficients as compared to previous studies that have compared similar measures with the WJ III. Hierarchical linear modeling was used at each grade level to ascertain the ability of the six measures to model weekly growth trajectories over 13 weeks. All measures produced growth rates that were significant across time, for both kindergarten and first grade, with linear growth observed for all measures.”

Lee, Y.-S., Lembke, E., Moore, D., Ginsburg, H. P., & Pappas, S. (2012). Item-level and construct evaluation of early numeracy curriculum-based measures. Assessment for Effective Intervention, 37(2), 107–117. https://eric.ed.gov/?id=EJ955507

From the ERIC abstract: “The present study examined the technical adequacy of curriculum-based measures (CBMs) of early numeracy. Six 1-min early mathematics tasks were administered to 137 kindergarten and first-grade students, along with an omnibus test of early mathematics. The CBM measures included Count Out Loud, Quantity Discrimination, Number Identification, Missing Number, Next Number, and Number Facts. Alpha and split-half reliabilities were assessed, and construct validity and criterion validity (both concurrent and predictive) were examined. In addition, an item analysis was conducted for each measure using classical test theory and item response theory approaches, specifically using a Rasch model. Results indicated that the measures produced moderately strong reliability coefficients, satisfactory item difficulty and discrimination, evidence to support both concurrent and predictive validity with the standardized early mathematics test, and the tasks appeared to be measuring the construct of early numeracy proficiency.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Lee, Y. S., & Lembke, E. (2016). Developing and evaluating a kindergarten to third grade CBM mathematics assessment. ZDM: The International Journal on Mathematics Education, 48(7), 1019–1030. https://eric.ed.gov/?id=EJ1116870

From the ERIC abstract: “The present study examined the technical adequacy of curriculum-based measurement (CBM) measure of early numeracy for kindergarten through third grade students. Our CBM measures were developed to reflect broad and theoretically derived categories of mathematical thinking: quick retrieval, written computation, and number sense. The mastery of these three categories comprises the larger construct of numeracy proficiency for the early elementary grades. Approximately 300 students in each grade (Kindergarten to Grade 3) were administered a standardized measure, WJ-III, and the following timed measures: kindergarten—counting, missing number, number identification, quantity discrimination; Grade 1—counting, missing number, next number, number facts, number identification, quantity discrimination; Grades 2 and 3—computation, concepts, missing number, number facts, quantity discrimination. ‘Alpha’ and test-retest reliabilities were assessed, and construct validity and criterion validity were examined for the CBM measures developed in the study. Overall, the results indicated that the measures were reliable and showed evidence to support both construct and concurrent validity. Methods to improve the measures are discussed.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Lembke, E., & Foegen, A. (2009). Identifying early numeracy indicators for kindergarten and first-grade students. Learning Disabilities Research & Practice, 24(1), 12–20. https://eric.ed.gov/?id=EJ827129

From the ERIC abstract: “Recent studies have documented positive effects for early intervention in improving the mathematics performance of low-achieving children. Consequently, educators need technically sound mathematics screening measures to identify children at risk and then intervene to improve achievement. In this article, we describe preliminary technical adequacy evidence for four early numeracy measures (number identification, quantity discrimination, quantity array, and missing number). We assessed over 300 kindergarten and first-grade students in two states to evaluate the reliability and criterion validity of the four measures. Fall and spring administrations of the measures for one subgroup provided preliminary evidence of students’ growth on the measures over time. The results supported three of the four measures as potential tools for screening in the early grades.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Martinez, R. S., Missall, K. N., Graney, S. B., Aricak, O. T., & Clarke, B. (2009). Technical adequacy of early numeracy curriculum-based measurement in kindergarten. Assessment for Effective Intervention, 34(2), 116–125. https://eric.ed.gov/?id=EJ831590

From the ERIC abstract: “The current study examines the technical adequacy of four Early Numeracy Curriculum-Based Measurement (EN-CBM) screening tasks: ‘Oral Counting’ (OC), ‘Number Identification’ (NI), ‘Quantity Discrimination’ (QD), and ‘Missing Number’ (MN). Results from 59 kindergarten students assessed in the fall and spring reveal moderate to high test-retest and delayed alternate-form reliability. In addition, data from the four measures demonstrate adequate concurrent and predictive validity by comparing them to an established measure of early numeracy. The measures demonstrated growth over time from the beginning to the end of kindergarten. Finally, combinations of the measures were evaluated post hoc, and the combination of NI, QD, and MN produced the highest reliability, validity, and rate of growth coefficients. Overall, results support the technical adequacy of EN-CBM for use with kindergarten-aged children.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Purpura, D. J., & Lonigan, C. J. (2013). Informal numeracy skills: The structure and relations among numbering, relations, and arithmetic operations in preschool. American Educational Research Journal, 50(1), 178–209. https://eric.ed.gov/?id=EJ995829

From the ERIC abstract: “Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining the structure of these three numeracy skill domains and examining the relations among these domains. Three hundred ninety-three children participated in the study (51.7% girls, 55.7% White, 33.8% African American, and 10.5% other). Results indicated that the relations among the informal numeracy skills were best explained by a three-factor model that included Numbering, Relations, and Arithmetic Operations factors, and this factor structure was the same in both younger and older preschool children.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Purpura, D. J., & Lonigan, C. J. (2015). Early numeracy assessment: The development of the preschool early numeracy scales. Early Education and Development, 26(2), 286–313. https://eric.ed.gov/?id=EJ1050571

From the ERIC abstract: “Research Findings: The focus of this study was to construct and validate 12 brief early numeracy assessment tasks that measure the skills and concepts identified as key to early mathematics development by the National Council of Teachers of Mathematics (2006) and the National Mathematics Advisory Panel (2008)-as well as critical developmental precursors to later mathematics skills noted in the Common Core State Standards (2010). Participants were 393 preschool children ages 3 to 5 years old. Measure development and validation occurred through 3 analytic phases designed to ensure that the measures were brief, reliable, and valid. These measures were 1-to-1 counting, cardinality, counting subsets, subitizing, number comparison, set comparison, number order, numeral identification, set-to-numerals, story problems, number combinations, and verbal counting. Practice or Policy: Teachers have extensive demands on their time, yet they are tasked with ensuring that all students’ academic needs are met. To identify individual instructional needs and measure progress, they need to be able to efficiently assess children’s numeracy skills. The measures developed in this study not only are reliable and exhibit evidence of validity but also are easy to use and can be utilized for measuring the effects of targeted instruction on individual numeracy skills.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Schoen, R. C., Anderson, D., & Bauduin, C. (2017). Elementary mathematics student assessment: Measuring the performance of grade K, 1, and 2 students in counting, word problems, and computation in Spring 2016 (Research Report No. 2017-22). Learning Systems Institute, Florida State University. https://eric.ed.gov/?id=ED599647

From the ERIC abstract: “This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades K, 1, and 2 student abilities. The test was administered to 4,535 participating grade K, 1, and 2 students in 66 schools located in 9 public school districts in Florida during spring 2016. Focused on number, operations, and equality, the student assessment was designed to serve as a baseline measure of student achievement in a randomized controlled trial evaluating the impact of a teacher professional development program called Cognitively Guided Instruction (CGI) on student learning.”

Shanley, L., Clarke, B., Doabler, C., Kurtz-Nelson, E., & Fien, H. (2018). Measuring early mathematics knowledge via number skills and task types. Mathematical Thinking and Learning, 20(4), 324–336. https://eric.ed.gov/?id=EJ1191849

From the ERIC abstract: “Early number skills are a critical aspect of early mathematics development. However, the constructs that comprise early number skills differ across assessments, and previous studies have proposed various models of early mathematics skills comprised of formal and informal tasks. This study explored the factor structure of a researcher-developed measure of mathematics administered to a large, geographically diverse sample of kindergarten students at risk for mathematics difficulty (n = 580) in a randomized control trial. Consistent with previous research, factors representing early number skills and task types emerged. Importantly though, the best fitting model was one in which both skill types (e.g., number identification, magnitude comparison) and task types (i.e., informal and formal) were modeled. The inclusion of task type as a factor in early mathematics assessment has many potentially important ramifications. Recommendations for attending to task types when assessing early number skills, and implications for instruction and measurement are discussed.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.

Sitabkhan, Y., Platas, L. M., & Ketterlin-Geller, L. R. (2018). Capturing children’s mathematical knowledge: An assessment framework. Global Education Review, 5(3), 106–124. https://eric.ed.gov/?id=EJ1193975

From the ERIC 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.”

VanDerHeyden, A. M., Broussard, C., Snyder, P., George, J., Lafleur, S. M., & Williams, C. (2011). Measurement of kindergartners’ understanding of early mathematical concepts. School Psychology Review, 40(2), 296–306. https://eric.ed.gov/?id=EJ936458

From the ERIC abstract: “Early measures of mathematics skill and development have focused on early numeracy skills like counting, number identification, and sequencing of numbers. This study attempted to expand early mathematics assessment. Six new measures of early mathematics skill competence were developed and evaluated. Four existing measures also were examined. Measures were developed to directly assess kindergarten children’s understanding of concepts including number sense (ordinality, subitivity, cardinality), shape recognition, and patterning. Technical adequacy estimates were examined including test-retest reliability, concurrent and longitudinal correlation with criterion measures, and sensitivity. The Pattern Completion, Set Comparison with Unequal-Sized Items, and Subitivity measures performed best. Existing early numeracy measures performed comparably to or better than the new measures.”

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Weiland, C., Wolfe, C. B., Hurwitz, M. D., Clements, D. H., Sarama, J. H., & Yoshikawa, H. (2012). Early mathematics assessment: Validation of the short form of a prekindergarten and kindergarten mathematics measure. Educational Psychology, 32(3), 311–333. https://eric.ed.gov/?id=EJ963018

From the ERIC abstract: “In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young children. In this article, using data from two large samples of diverse populations of prekindergarten and kindergarten children, we provide evidence regarding the psychometric validity of a new theory-based early mathematics assessment. The new measure is the short form of a longer, validated measure. Our results suggest the short form assessment is valid for assessing prekindergarten and kindergarten children’s numeracy and geometry skills and is sensitive to differences in early mathematics development among young children.”

Note: REL Midwest was unable to locate a link to the full-text version of this resource. Although REL Midwest tries to provide publicly available resources whenever possible, it was determined that this resource may be of interest to you. It may be found through university or public library systems.