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1. 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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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. Development and initial validation of a mathematics-specific spatial vocabulary scale

   https://doi.org/10.3389/feduc.2023.1189674  

   Ünal, Zehra E. ; Ridgley, Lisa M. ; Li, Yaoran ; Graves, Cassandra ; Khatib, Lora ; Robertson, Taryn ; Myers, Perla ; Geary, David C. ( June 2023 , Frontiers in Education)

   This study describes the development and initial validation of a mathematics-specific spatial vocabulary measure for upper elementary school students. Reviews of spatial vocabulary items, mathematics textbooks, and Mathematics Common Core State Standards identified 720 mathematical terms, 148 of which had spatial content (e.g., edge). In total, 29 of these items were appropriate for elementary students, and a pilot study (59 fourth graders) indicated that nine of them were too difficult (< 50% correct) or too easy (> 95% correct). The remaining 20 items were retained as a spatial vocabulary measure and administered to 181 (75 girls, mean age = 119.73 months, SD =4.01) fourth graders, along with measures of geometry, arithmetic, spatial abilities, verbal memory span, and mathematics attitudes and anxiety. A Rasch model indicated that all 20 items assessed an underlying spatial vocabulary latent construct. The convergent and discriminant validity of the vocabulary measure was supported by stronger correlations with theoretically related (i.e., geometry) than with more distantly related (i.e., arithmetic) mathematics content and stronger relations with spatial abilities than with verbal memory span or mathematics attitudes and anxiety. Simultaneous regression analyses and structural equation models, including all measures, confirmed this pattern, whereby spatial vocabulary was predicted by geometry knowledge and spatial abilities but not by verbal memory span, mathematics attitudes and anxiety. Thus, the measure developed in this study helps in assessing upper elementary students' mathematics-specific spatial vocabulary.

    

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