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1. 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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2. A Sociocultural Perspective on Beginning Teachers Enacting Reasoning and Proving Practices

   Weingarden, M.; Buchbinder, O. (January 2022, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Higgins, A. (Ed.)

   The critical role of teachers in supporting student engagement with reasoning and proving has long been recognized (Nardi & Knuth, 2017; NCTM, 2014). While some studies examined how prospective secondary teachers (PSTs) develop dispositions and teaching practices that promote student engagement with reasoning and proving (e.g., Buchbinder & McCrone, 2020; Conner, 2007), very little is known about long-term development of proof-related practices of beginning teachers and what factors affect this development (Stylianides et al., 2017). During the supervised teaching experiences, interns often encounter tensions between balancing their commitments to the university and cooperating teacher, while also developing their own teaching styles (Bieda et al., 2015; Smagorinsky et al., 2004; Wang et al., 2008). Our study examines how sociocultural contexts of the teacher preparation program and of the internship school, supported or inhibited proof-related teaching practices of beginning secondary mathematics teachers. In particular, this study aims to understand the observed gap between proof-related teaching practices of one such teacher, Olive, in two settings: as a PST in a capstone course Mathematical Reasoning and Proving for Secondary Teachers (Buchbinder & McCrone, 2020) and as an intern in a high-school classroom. We utilize activity theory (Leont’ev, 1979) and Engeström’s (1987) model of an activity system to examine how the various components of the system: teacher (subject), teaching (object), the tasks (tools), the curriculum and the expected teaching style (rules), the cooperating teacher (community) and their involvement during the teaching (division of labor) interact with each other and affect the opportunities provided to students to engage with reasoning and proving (outcome). The analysis of four lessons from each setting, lesson plans, reflections and interviews, showed that as a PST, Olive engaged students with reasoning and proving through productive proof-related teaching practices and rich tasks that involved conjecturing, justifying, proving and evaluating arguments. In a sharp contrast, as an intern, Olive had to follow her school’s rigid curriculum and expectations, and to adhere to her cooperating teacher’s teaching style. As a result, in her lessons as an intern students received limited opportunities for reasoning and proving. Olive expressed dissatisfaction with this type of teaching and her desire to enact more proof-oriented practices. Our results show that the sociocultural components of the activity system (rules, community and division of labor), which were backgrounded in Olive’s teaching experience as a PST but prominent in her internship experience, influenced the outcome of engaging students with reasoning and proving. We discuss the importance of these sociocultural aspects as we examine how Olive navigated the tensions between the proof-related teaching practices she adopted in the capstone course and her teaching style during the internship. We highlight the importance of teacher educators considering the sociocultural aspects of teaching in supporting beginning teachers developing proof-related teaching practices. 

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3. 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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4. 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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5. 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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