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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. 

Using a test for a purpose it was not intended for can promote misleading results and interpretations, potentially leading to negative consequences from testing (AERA et al., 2014). For example, a mathematics test designed for use with grade 7 students is likely inappropriate for use with grade 3 students. There may be cases when a test can be used with a population related to the intended one; however, validity evidence and claims must be examined. We explored the use of student measures with preservice teachers (PSTs) in a teacher-education context. The present study intends to spark a discussion about using some student measures with teachers. The Problem-solving Measures (PSMs) were developed for use with grades 3-8 students. They measure students’ problem-solving performance within the context of the Common Core State Standards for Mathematics (CCSSI, 2010; see Bostic & Sondergeld, 2015; Bostic et al., 2017; Bostic et al., 2021). After their construction, the developers wondered: If students were expected to engage successfully on the PSMs, then might future grades 3-8 teachers also demonstrate proficiency? 

The COVID-19 pandemic disrupted many school accountability systems that rely on student-level achievement data. Many states encountered uncertainty about how to meet federal accountability requirements without typical school data. Prior research provides evidence that student achievement is correlated to students’ social background, which raises concerns about the predictive bias of accountability systems. This mixed-methods study (a) examines the predictive ability of non-achievement-based variables (i.e., students’ social background) on school districts’ report card letter grade in Ohio, and (b) explores educators’ perceptions of report card grades. Results suggest that social background and community demographic variables have a significant impact on measures of school accountability. 

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. 

The COVID-19 pandemic disrupted many school accountability systems that rely on student-level achievement data. Many states encountered uncertainty about how to meet federal accountability requirements without typical school data. Prior research provides evidence that student achievement is correlated to students’ social background, which raises concerns about the predictive bias of accountability systems. This mixed-methods study (a) examines the predictive ability of non-achievement-based variables (i.e., students’ social background) on school districts’ report card letter grade in Ohio, and (b) explores educators’ perceptions of report card grades. Results suggest that social background and community demographic variables have a significant impact on measures of school accountability. 

This Research Commentary addresses the need for an instrument abstract—termed an Interpretation and Use Statement (IUS)—to be included when mathematics educators present instruments for use by others in journal articles and other communication venues (e.g., websites and administration manuals). We begin with presenting the need for IUSs, including the importance of a focus on interpretation and use. We then propose a set of elements—identified by a group of mathematics education researchers, instrument developers, and psychometricians—to be included in the IUS. We describe the development process, the recommended elements for inclusion, and two example IUSs. Last, we present why IUSs have the potential to benefit end users and the field of mathematics education. 

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? 

The COVID-19 pandemic disrupted many school accountability systems that rely on student- level achievement data. Many states have encountered uncertainty about how to meet federal accountability requirements without typical school data. Prior research provides an abundance of evidence that student achievement is correlated to students' social background, which raises concerns about the predictive bias of accountability systems. The focus of this quantitative study is to explore the predictive ability of non-achievement based variables (i.e., students' social background) on measures of school accountability in one Midwest state. Results suggest that social background and community demographic variables have a significant impact on measures of school accountability, and might be interpreted cautiously. Implications for policy and future research are discussed. 

A way to evaluate an assessment’s worth is in its contributions to student learning (Cronbach, 1988). “Classrooms are complex social environments. Economic, language, cultural, and mental health issues are just some of the key variables that need to be considered in relation to students [learning]” (Leighton, 2020, p. 27). Teachers provide a unique influence on their students’ learning through their beliefs, content knowledge, and pedagogical content knowledge (Brookhart, 2003). A classroom’s social context is an area where teacher-created assessments differ from externally-developed standardized assessments. One goal of standardized testing is to eliminate psychometric noise like social contexts by attempting to account for factors not related to the construct being measured (AERA et al., 2014). On the other hand, teacher-created assessments are contextually relevant as they are developed with certain students in mind (Brookhart, 2003). Teacher-created assessments are more likely to align with a unique social context of a classroom. The purpose of this study is to explore middle grades math teachers assessment practices and impact on student learning. 

Quantitative assessment development is a challenging process. The ways in which an assessment might be used, as well as how its score can be interpreted should be clear to intended users. This manuscript provides a discussion about important and useful elements that should be provided by assessment developers. In turn, this information can foster greater usability and portability of quantitative assessments, which can support scholarship focusing on a specific issue.