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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. 

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? 

This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy, and elevating justice. We illustrate how these goals work together to advance equity and cultivate civic empathy through classroom vignettes of community-based modeling lessons. Through this theoretical synthesis, implications for community-based mathematical modeling instruction will be discussed. 

Mathematical modeling can be a lever for equity in the elementary math classroom, as it empowers teachers to build on the knowledge and cultural resources that children bring to the classroom and empowers students to draw on their experiences and identities to inform their mathematical work. To better support this transformative synergy between mathematical modeling and equity-oriented practices, we need a tool to deepen our understanding of variations and potential trajectories of teacher practice. In this report, we briefly describe our process for developing an equity-oriented mathematical modeling classroom observation protocol. We then discuss two sample dimensions from our tool to illustrate our integrated attention to equity-focused and mathematical modeling-specific teaching practices.