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1. 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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2. Deepening the Validity Argument for the Problem-Solving Measures 3-5

   Bostic, J.; Matney, G.; Folger, T.; Brown, N.; Evans, E.; May, T.; Stone G. (January 2022, Hawaii International Conference on Education)

   Problem solving is a theme within mathematics instructional standards, which suggests that assessments must address mathematics content and practices. This study examines grades 3-5 students’ strategy use on a test designed to measure students problem-solving performance within the context of mathematics standards used during instruction. The tests are called the Problem-Solving Measures. Results indicate that students use multiple and varied strategies to solve PSM items, which in turn supports prior validation studies. 

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3. Validating the use of student-level instruments to examine preservice teachers’ mathematical problem solving.

   Folger, T.; Stewart, M.; Bostic, J.; May, T. (December 2022, School science and mathematics)

   Problem solving is a central focus of mathematics teaching and learning. If teachers are expected to support students' problem-solving development, then it reasons that teachers should also be able to solve problems aligned to grade level content standards. The purpose of this validation study is twofold: (1) to present evidence supporting the use of the Problem Solving Measures Grades 3–5 with preservice teachers (PSTs), and (2) to examine PSTs' abilities to solve problems aligned to grades 3–5 academic content standards. This study used Rasch measurement techniques to support psychometric analysis of the Problem Solving Measures when used with PSTs. Results indicate the Problem Solving Measures are appropriate for use with PSTs, and PSTs' performance on the Problem Solving Measures differed between first-year PSTs and end-of-program PSTs. Implications include program evaluation and the potential benefits of using K-12 student-level assessments as measures of PSTs' content knowledge. 

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4. Validating the use of s tudent‐level instruments to examine preservice teachers' mathematical problem solving

   https://doi.org/10.1111/ssm.12558  

   Folger, Timothy D.; Stewart, Maria; Bostic, Jonathan; May, Toni A. (December 2022, School Science and Mathematics)

   Abstract Problem solving is a central focus of mathematics teaching and learning. If teachers are expected to support students' problem‐solving development, then it reasons that teachers should also be able to solve problems aligned to grade level content standards. The purpose of this validation study is twofold: (1) to present evidence supporting the use of the Problem Solving Measures Grades 3–5 with preservice teachers (PSTs), and (2) to examine PSTs' abilities to solve problems aligned to grades 3–5 academic content standards. This study used Rasch measurement techniques to support psychometric analysis of the Problem Solving Measures when used with PSTs. Results indicate the Problem Solving Measures are appropriate for use with PSTs, and PSTs' performance on the Problem Solving Measures differed between first‐year PSTs and end‐of‐program PSTs. Implications include program evaluation and the potential benefits of using K‐12 student‐level assessments as measures of PSTs' content knowledge. 

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5. COMPUTER ADAPTIVE MATHEMATICAL PROBLEM-SOLVING MEASURE: A BRIEF VALIDATION REPORT

   Bostic, Jonathan; May, Toni; Matney, Gabriel; Koskey, Kristin; Stone, Gregory; Folger, Timothy (March 2024, Research Council on Mathematics Learning)

   Kombe, Dennis; Wheeler, Ann (Ed.)

   The purpose of this proceeding is to share a component to a validity argument for a new, computer adaptive mathematics Problem-Solving Measure that is designed for grades six through eight (PSM 6-8). The PSM is a single test, which uses computer adaptive features to measure students’ performance using instructional standards. It is intended to measure students’ problem-solving performance related to instructional standards. 

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