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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. 

Response Process Validity (RPV) reflects the degree to which items are interpreted as intended by item developers. In this study, teacher responses to constructed response (CR) items to assess pedagogical content knowledge (PCK) of middle school mathematics teachers were evaluated to determine what types of teacher responses signaled weak RPV. We analyzed 38 CR pilot items on proportional reasoning across up to 13 middle school mathematics teachers per item. By coding teacher responses and using think-alouds, we found teachers' responses deemed indicative of low item RPV often had one of the following characteristics: vague answers, unanticipated assumptions, a focus on unintended topics, and paraphrasing. To develop a diverse pool of items with strong RPV, we suggest it is helpful to be aware of these symptoms, use them to consider how to improve items, and then revise and retest items accordingly. 

Research processes are often messy and include tensions that are unnamed in the final products. In our attempt to update and generalize a framework used to examine teachers’ support for collective argumentation in mathematics education classrooms to examining teachers’ work in interdisciplinary STEM contexts, we have experienced significant linguistic tensions because of the context-dependent nature of language. We aim to acknowledge the difficulty of generalizing research beyond the mathematics education community, describe our attempts to resolve the problem we face, and discuss potential conclusions pertaining to the feasibility of generalizing frameworks beyond mathematics education. 

Graduate student peer-mentoring programs benefit participants by providing unique academic, social, psychological, and career development opportunities (Lorenzatti et al., 2019). However, the positive effects of research-oriented peer-mentoring programs are much better understood than teaching-oriented ones. In our poster, we consider mentees and mentors’ perceptions of effective mentoring in a teaching-oriented peer mentorship program. 

Many higher education institutions in the United States provide mathematics tutoring services for undergraduate students. These informal learning experiences generally result in increased final course grades (Byerly & Rickard, 2018; Rickard & Mills, 2018; Xu et al., 2014) and improved student attitudes toward mathematics (Bressoud et al., 2015). In recent years, research has explored the beliefs and practices of undergraduate and, sometimes graduate, peer tutors, both prior to (Bjorkman, 2018; Johns, 2019; Pilgrim et al., 2020) and during the COVID19 pandemic (Gyampoh et al., 2020; Mullen et al., 2021; Van Maaren et al., 2021). Additionally, Burks and James (2019) proposed a framework for Mathematical Knowledge for Tutoring Undergraduate Mathematics adapted from Ball et al. (2008) Mathematical Knowledge for Teaching, highlighting the distinction between tutor and teacher. The current study builds on this body of work on tutors’ beliefs by focusing on mathematical sciences graduate teaching assistants (GTAs) who tutored in an online setting during the 2020-2021 academic year due to the COVID-19 pandemic. Specifically, this study addresses the following research question: What were the mathematical teaching beliefs and practices of graduate student tutors participating in online tutoring sessions through the mathematics learning center (MLC) during the COVID-19 pandemic? 

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. 

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. 

The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers’ use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broad ways teachers used public records—manipulating and referencing—to support establishing and maintaining students’ thinking as objects in sense-making discussions.