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1. 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)

   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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2. GATHERING VALIDITY EVIDENCE TO SUPPORT MATHEMATICS EDUCATION SCHOLARSHIP

   Bostic, J. ; Krupa, E. ; Folger, T. ; Bentley, B. ; Stokes, D. ( October 2022 , Psychology of Mathematics Education North America)

   A. Lischka, E. Dyer (Ed.)

   Validity and validation is central to conducting high quality quantitative mathematics education scholarship. This presentation aims to support scholars engaged in quantitative research by providing information about the degrees to which validity evidence related to their instrument use or interpretation, were found in mathematics education scholarship. Findings have potential to steer future quantitatively focused scholarship and support equity aims. 

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3. 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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4. Developing a problem-solving measure for grade 4.

   Bostic, J. ( July 2019 , Proceedings of the 43rd Meeting of the International Group for the Psychology of Mathematics Education)

   Problem solving is central to mathematics learning (NCTM, 2014). Assessments are needed that appropriately measure students’ problem-solving performance. More importantly, assessments must be grounded in robust validity evidence that justifies their interpretations and outcomes (AERA et al., 2014). Thus, measures that are grounded in validity evidence are warranted for use by practitioners and scholars. The purpose of this presentation is to convey validity evidence for a new measure titled Problem-Solving Measure for grade four (PSM4). The research question is: What validity evidence supports PSM4 administration? The PSM4 is one assessment within the previously published PSM series designed for elementary and middle grades students. Problems are grounded in Schoenfeld’s (2011) framework and rely upon Verschaffel et al. (1999) perspective that word problems be open, complex, and realistic. The mathematics in the problems is tied to USA grade-level content and practice standards (CCSSI, 2010). 

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5. Race, Gender, and Teacher Equity Beliefs: Construct Validation of the Attributions of Mathematical Excellence Scale

   https://doi.org/10.1177/23328584221130999  

   Jacobson, Erik ; Cross Francis, Dionne ; Willey, Craig ; Wilkins-Yel, Kerrie ( January 2022 , AERA Open)

   Teachers’ beliefs can have powerful consequences on instructional decisions and student learning. However, little research focuses on how teachers’ beliefs about the role of race and gender in mathematics teaching and learning influence educational equity within classrooms. This gap is partly due to the lack of studies focused on variation within classrooms, which in turn is hampered by the lack of instruments designed to measure mathematics-specific equity beliefs. In this study of 313 preservice and practicing elementary teachers, we report evidence of construct validity for the Attributions of Mathematical Excellence Scale. Factor analyses provide support for a four-factor structure, including genetic, social, personal, and educational attributions. The findings suggest that the same system of attribution beliefs underlies both racial and gender prejudice among elementary mathematics teachers. The Attributions of Mathematical Excellence Scale has the potential to provide a useful outcome measure for equity-focused interventions in teacher education and professional development. 

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