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Utilizing an innovative and theoretically-grounded approach, we extend the work of cognitive scientists and mathematics educators who have previously documented the impact of comparison on students’ learning in algebra with the goal of transforming the learning that occurs in eighth- grade geometry classrooms. The purpose of this paper is to examine the types of comparisons participants made during think aloud interviews when engaging with curricular materials that have them examine multiple solution strategies. This research seeks to extend the work of using comparisons in algebra to determine if using comparisons in geometry will help improve students’ mathematical understanding. 

Problem solving is a very important skill for students to learn (e.g., Bonilla-Rius, 2020; NGA, 2010), and part of developing problem solving skills is learning to persevere. One strategy for learning how to persevere is by providing students with materials that allow them the opportunity to engage with challenging problems (e.g., Kapur, 2010; Middleton et al., 2015). This study of the Volume unit of the AC2inG materials analyzes students’ strategies for problem solving and persevering. Findings from these think-aloud interviews indicate that different students will utilize one or more methods for solving challenging problems, such as asking clarifying questions, talking themselves through the problem, and attempting various mathematical approaches. 

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. 

Engagement in the mathematics classroom through interactions with the instructor, peers, and content are necessary for an effective learning experience. As such, it is important to understand the types of interactions that teachers utilize to engage students, especially as they have had to shift from a complete face-to-face setting to various remote modalities. Utilizing four interaction types (learner-content, learner-instructor, learner-learner, and learner-interface) this paper analyzes 35 videos of classroom instruction with the purpose of describing the interactions that take place throughout the course of the mathematics lesson. While there was not a significant difference in the type of interaction and the modality of instruction, there was a significant difference in the type of interaction enacted and the modality of instruction. 

This paper provides a brief introduction to the set of four manuscripts in the special issue. To provide a foundation for the issue, key terms are defined, a brief historical overview of validity is provided, and a description of several different validation approaches used in the issue are explained. Finally, the contribution of the manuscripts to further articulating argument-based validation approaches is discussed, along with questions for the field to consider. 

The purpose of this working group is to continue to bring together scholars with an interest in examining the use of and access to large-scale quantitative tools used to measure student- and teacher-related outcomes in mathematics education. The working group session will focus on (1) updating the workgroup on the progress made since the first working group at PME-NA in Tucson, Arizona, specifically focusing on the outcomes of the Validity Evidence for Measurement in Mathematics Education conference that took place in April, 2017, in San Antonio, (2) continued development of a document of available tools and their associated validity evidence, and (3) identification of potential follow-up activities to continue this work. The efforts of the group will be summarized and extended through both social media tools and online collaboration tools to further promote this work. 

As early as Descartes (1637/1970), logic and reason have been positioned as tools for individuals to advance their own understanding. By contrast, argumentation is an interactive, social exercise used for persuasion, collective cognition, and to advance shared knowledge (Mercier & Sperber, 2011, 2017). When one advances an argument, subjects it to the tests and challenges of others, and responds to questions and counterarguments, one’s thinking improves (Mercier & Sperber, 2017). Through argumentation, groups produce correct solutions more often than individuals (Moshman & Geil, 1998) and individual accuracy improves as well (Castelain, Girotto, Jamet, & Mercier, 2016). Since it was formally introduced by Kane (1990, 1992), the argument-based approach to validation has been promoted in the field of educational and psychological measurement as the preferred method for validating interpretations and uses of test scores (AERA, APA, & NCME, 2014; Kane, 2013; Schilling & Hill, 2007). Scholars continue to debate the best approaches for developing and supporting validity arguments, however (for examples, see Brennan, 2013; Kane, 2007).