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1. Exploring and examining quantitative measures

   Bostic, J. (October 2016, Proceedings for the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   The purpose of this working group is to bring together scholars with an interest in examining the research on quantitative tools and measures for gathering meaningful data, and to spark conversations and collaboration across individuals and groups with an interest in synthesizing the literature on large-scale tools used to measure student- and teacher-related outcomes. While syntheses of measures for use in mathematics education can be found in the literature, few can be described as a comprehensive analysis. The working group session will focus on (1) defining terms identified as critical (e.g., large-scale, quantitative, and validity evidence) for bounding the focus of the group, (2) initial development of a document of available tools and their associated validity evidence, and (3) identification of potential follow-up activities to continue the work to identify tools and developed related synthesis documents (e.g., the formation of sub-groups around potential topics of interest). The efforts of the group will be summarized and extended through both social media tools (e.g., creating a Facebook group) and online collaboration tools (e.g., Google hangouts and documents) to further promote this work. 

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2. Validity evidence of the use of quantitative measures of students in elementary mathematics education.

   Ing, M; Kosko, K; Jong, C; Shih, J (March 2024, School science and mathematics)

   Miller, B; Martin, C (Ed.)

   Quantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in elementary mathematics education. The review includes measures that focus on elementary students as the unit of analyses and attends to validity as defined by current conceptions of measurement. Findings suggest that one in ten measures in mathematics education include rigorous evidence to support intended uses. Recommendations are made to support mathematics education researchers to continue to take steps to improve validity evidence in the design and use of quantitative measures. 

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3. Validity evidence of the use of quantitative measures of students in elementary mathematics education

   https://doi.org/10.1111/ssm.12660  

   Ing, Marsha; Kosko, Karl_W; Jong, Cindy; Shih, Jeffrey_C (April 2024, School Science and Mathematics)

   Abstract Quantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in elementary mathematics education. The review includes measures that focus on elementary students as the unit of analyses and attends to validity as defined by current conceptions of measurement. Findings suggest that one in ten measures in mathematics education include rigorous evidence to support intended uses. Recommendations are made to support mathematics education researchers to continue to take steps to improve validity evidence in the design and use of quantitative measures. 

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4. Measures of mathematics teachers’ behavior and affect: An examination of the assessment landscape

   Gallagher, M.; Bardelli, E.; Folger, T.; Neely, A.; Bostic, J.; Walkowiak, T.; Wilhelm, A.; Zelkowski, J. (April 2022, Annual meeting program American Educational Research Association)

   Although the paradigm wars between quantitative and qualitative research methods and the associated epistemologies may have settled down in recent years within the mathematics education research community, the high value placed on quantitative methods and randomized control trials remain as the gold standard at the policy-making level (USDOE, 2008). Although diverse methods are valued in the mathematics education community, if mathematics educators hope to influence policy to cultivate more equitable education systems, then we must engage in rigorous quantitative research. However, quantitative research is limited in what it can measure by the quantitative tools that exist. In mathematics education, it seems as though the development of quantitative tools and studying their associated validity and reliability evidence has lagged behind the important constructs that rich qualitative research has uncovered. The purpose of this study is to describe quantitative instruments related to mathematics teacher behavior and affect in order to better understand what currently exists in the field, what validity and reliability evidence has been published for such instruments, and what constructs each measure. 1. How many and what types of instruments of mathematics teacher behavior and affect exist? 2. What types of validity and reliability evidence are published for these instruments? 3. What constructs do these instruments measure? 4. To what extent have issues of equity been the focus of the instruments found? 

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5. QUANTITATIVE INSTRUMENT REPOSITORY FOR MATHEMATICS EDUCATION RESEARCH WITH VALIDITY EVIDENCE

   Krupa, E; Folger, T; Bentley, B; Bostic, J; Folger, T; Burkett, K (October 2023, PMENA)

   Lamberg, T; Moss, D (Ed.)

   The paper reports on the developments of a repository of quantitative assessments used in mathematics education contexts. This repository centralizes assessments and the associated validity evidence. The repository is public and freely available and has potential to inform future quantitative mathematics education scholarship. 

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