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1. More of the story: Ruminations on “How Mathematics Education in Ohio Impacted the Nation

   Foley, Gregory D (January 2025, Ohio journal of school mathematics)

   Edwards, Michael Todd (Ed.)

   This is one of three responses to two articles by James E. Schultz on how mathematics education in Ohio—and especially at Ohio State University—has influenced mathematics teaching and learning across the United States and beyond. Every mathematics teacher in Ohio should know this story. Schultz’s two contributions are oral histories in written form and possess a biographical and even autobiographical flavor. My response will follow suite. After a brief introduction, I reflect on—and add to—Schultz’s “Laying the Groundwork” article (2024a) and his “Incorporating Technology” piece (2024b). I then consider how the issues and legacy presented in these articles connect to mathematics teaching and learning today and how Ohio continues to influence mathematics education beyond its borders. I close with an epilogue on how I first met several key characters in this mathematical narrative. 

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2. Methodological Advancements for Analyzing Teachers’ Learning in a Community of Practice

   Leonard, Helene; Bonaccorso, Victoria; DiNapoli, Joseph; Murray, Eileen (January 2021, AERA 2021 Annual Meeting)

   null (Ed.)

   Professional development that privileges teachers’ voice, equity, and the investigation of high-quality instruction is essential to the mathematics education community. However, more research is needed to understand the process, content, and depth of teachers’ learning in this setting. This paper shares our analytic method designed to capture such learning. We integrate three complementary perspectives: Communities of Practice (theoretical framework), Teaching for Robust Understanding (conceptual framework), and Frame Analysis (analytical framework). We show how this method captures changes in teachers’ participation and reification, indicating the process, content, and depth of their learning across their professional development experience. Such work iterates on Frame Analysis and advances the methodology to highlight additional tools to better understand teacher learning about components of powerful classrooms. 

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3. Where’s My Whiteboard? The Challenge of Moving Active-learning Mathematics Classes Online

   Nelson, Jill K.; Rosenberg, Jessica; Fernandez, Kathryn; Shank, Julie (July 2021, 2021 ASEE Virtual Annual Conference)

   null (Ed.)

   This research paper studies the challenges that mathematics faculty and graduate teaching assistants (GTAs) faced when moving active and collaborative calculus courses from in-person to virtual instruction. As part of a larger pedagogical change project (described below), the math department at a public Research-1 university began transitioning pre-calculus and calculus courses to an active and collaborative learning (ACL) format in Fall 2019. The change began with the introduction of collaborative worksheets in recitations which were led by GTAs and supported by undergraduate learning assistants (LAs). Students recitation periods collaboratively solving the worksheet problems on whiteboards. When COVID-19 forced the rapid transition to online teaching, these ACL efforts faced an array of challenges. Faculty and GTA reflections on the changes to teaching and learning provide insight into how instructional staff can be supported in implementing ACL across various modes of instruction. The calculus teaching change efforts discussed in this paper are part of an NSF-supported project that aims to make ACL the default method of instruction in highly enrolled gateway STEM courses across the institution. The theoretical framework for the project builds on existing work on grassroots change in higher education (Kezar and Lester, 2011) to study the effect of communities of practice on changing teaching culture. The project uses course-based communities of practice (Wenger, 1999) that include instructors, GTAs, and LAs working together to design and enact teaching change in the targeted courses alongside ongoing professional development for GTAs and LAs. Six faculty and five GTAs involved in the teaching change effort in mathematics were interviewed after the Spring 2020 semester ended. Interview questions focused on faculty and GTA experiences implementing active learning after the rapid transition to online teaching. A grounded coding scheme was used to identify common themes in the challenges faced by instructors and GTAs as they moved online and in the impacts of technology, LA support, and the department community of practice on the move to online teaching. Technology, including both access and capabilities, emerged as a common barrier to student engagement. A particular barrier was students’ reluctance to share video or participate orally in sessions that were being recorded, making group work more difficult than it had been in a physical classroom. In addition, most students lacked access to a tablet for freehand writing, presenting a significant hurdle for sharing mathematical notation when physical whiteboards were no longer an option. These challenges point to the importance of incorporating flexibility in active learning implementation and in the professional development that supports teaching changes toward active learning, since what is conceived for a collaborative physical classroom may be implemented in a much different environment. The full paper will present a detailed analysis of the data to better understand how faculty and GTA experiences in the transition to online delivery can inform planning and professional development as the larger institutional change effort moves forward both in mathematics and in other STEM fields. 

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4. Building bridges: a review and synthesis of research on teaching knowledge for undergraduate instruction in science, engineering, and mathematics

   https://doi.org/10.1186/s40594-022-00380-w  

   Andrews, Tessa C.; Speer, Natasha M.; Shultz, Ginger V. (December 2022, International Journal of STEM Education)

   Abstract Here, we systematically review research on teaching knowledge in the context of undergraduate STEM education, with particular attention to what this research reveals about knowledge that is important for evidence-based teaching. Evidence-based teaching can improve student outcomes in undergraduate STEM education. However, the enactment of promising evidence-based teaching strategies depends greatly on the instructor and potentially on the teaching knowledge they are able to deploy. The review includes an overview of prevalent teaching knowledge theory, including pedagogical content knowledge, mathematical knowledge for teaching, and pedagogical knowledge. We compare and contrast teaching knowledge theory and terminology across STEM disciplines in order to build bridges for researchers across disciplines. Our search for peer-reviewed investigations of teaching knowledge in undergraduate science, engineering and mathematics yielded 45 papers. We examined the theoretical frameworks used in each study and analyzed study approaches, comparing across disciplines. Importantly, we also synthesized findings from research conducted in the context of evidence-based teaching. Overall, teaching knowledge research is sparse and siloed by discipline, and we call for collaborative work and better bridge-building across STEM disciplines. Though disciplinary divergences are common in discipline-based education research, the effect is magnified in this research area because the theoretical frameworks are themselves siloed by discipline. Investigations of declarative knowledge were common, and we call for increased attention to knowledge used in the practice of teaching. Finally, there are not many studies examining teaching knowledge in the context of evidence-based teaching, but the existing work suggests that components of pedagogical content knowledge, pedagogical knowledge, and content knowledge influence the implementation of evidence-based teaching. We describe implications for future teaching knowledge research. We also call on those who develop and test evidence-based strategies and curriculum to consider, from the beginning, the teaching knowledge needed for effective implementation. 

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5. On designing better structures for feedback in practice-based professional development: Using “failure” to innovate

   https://doi.org/10.1007/s10857-023-09588-1  

   Brown, Amanda M.; Herbst, Patricio G. (June 2023, Journal of Mathematics Teacher Education)

   This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth. 

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