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1. Categorizing student interactions with manipulatives in statics

   Rupe, K. M.; Davishahl, E. (May 2022, 2022 ASEE Zone IV Conference)

   This work in progress paper describes ongoing work to understand the ways in which students make use of manipulatives to develop their representational competence and deepen their conceptual understanding of course content. Representational competence refers to the fluency with which a subject expert can move between different representations of a concept (e.g. mathematical, symbolic, graphical, 2D vs. 3D, pictorial) as appropriate for communication, reasoning, and problem solving. Several hands-on activities for engineering statics have been designed and implemented in face-to-face courses since fall 2016. In the transition to online learning in response to the COVID 19 pandemic, modeling kits were sent home to students so they could work on the activities at their own pace and complete the associated worksheets. An assignment following the vector activities required students to create videotaped or written reflections with annotated pictures using the models to explain their thinking around key concepts. Students made connections between abstract symbolic representations and their physical models to explain concepts such as a general 3D unit vector, the difference between spherical coordinate angles and coordinate direction angles, and the meaning of decomposing a vector into components perpendicular and parallel to a line. Thematic analysis of the video and written data was used to develop codes and identify themes in students’ use of the models as it relates to developing representational competence. The student submissions also informed the design of think-aloud exercises in one-on-one semi-structured interviews between researchers and students that are currently in progress. This paper presents initial work analyzing and discussing themes that emerged from the initial video and written analysis and plans for the subsequent think-aloud interviews, all focused on the specific attributes of the models that students use to make sense of course concepts. The ultimate goal of this work is to develop some general guidelines for the design of manipulatives to support student learning in a variety of STEM topics. 

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2. Categorizing student interactions with manipulatives in statics

   Rupe K.; Davishahl, E. (May 2022, 2022 ASEE Zone IV Conference)

   This work in progress paper describes ongoing work to understand the ways in which students make use of manipulatives to develop their representational competence and deepen their conceptual understanding of course content. Representational competence refers to the fluency with which a subject expert can move between different representations of a concept (e.g. mathematical, symbolic, graphical, 2D vs. 3D, pictorial) as appropriate for communication, reasoning, and problem solving. Several hands-on activities for engineering statics have been designed and implemented in face-to-face courses since fall 2016. In the transition to online learning in response to the COVID 19 pandemic, modeling kits were sent home to students so they could work on the activities at their own pace and complete the associated worksheets. An assignment following the vector activities required students to create videotaped or written reflections with annotated pictures using the models to explain their thinking around key concepts. Students made connections between abstract symbolic representations and their physical models to explain concepts such as a general 3D unit vector, the difference between spherical coordinate angles and coordinate direction angles, and the meaning of decomposing a vector into components perpendicular and parallel to a line. Thematic analysis of the video and written data was used to develop codes and identify themes in students’ use of the models as it relates to developing representational competence. The student submissions also informed the design of think-aloud exercises in one-on-one semi-structured interviews between researchers and students that are currently in progress. This paper presents initial work analyzing and discussing themes that emerged from the initial video and written analysis and plans for the subsequent think-aloud interviews, all focused on the specific attributes of the models that students use to make sense of course concepts. The ultimate goal of this work is to develop some general guidelines for the design of manipulatives to support student learning in a variety of STEM topics. 

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3. A Research Introduction for Early College Students: Based on the OSU–HBCU Pilot Project

   https://doi.org/10.1080/10511970.2024.2396497  

   Fernando, Anne; Gurski, Katharine; Ma, Timmy (September 2024, PRIMUS)

   We joined an initiative to engage faculty and undergraduate students in research by scheduling regular early college-level mathematics research presentations with pre- and post-lecture exercises. While our program featured six talks that were predominantly in the mathematical biosciences, the concept of creating themed topics for presentations can be extended to other areas of mathematical research, and the length of the program can also be scaled. This article discusses three of the presentations, including QR codes to access their recordings. The purpose of this article is to present the materials of the talks from this initiative and how faculty members can use the materials for potential explorations with students. The hope is the audience may use these, as presented, for study with students, with minimal start-up investment and to use this as a model for future undergraduate research efforts. 

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4. Creating student autonomy and building functional reasoning through an entrepreneurial design challenge.

   Krupa, EE; Belcher, M; Borden, ML; Loftis, A; Anderson, RK (November 2024, Proceedings of the forty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Kosko, K W; Caniglia, J; Courtney, S A; Zolfaghari, M; Morris, G A (Ed.)

   At the core of engaging students in mathematics is having them use their mathematical knowledge to solve personally relevant and authentic problems. We have created entrepreneurial-based design challenges (Confrey, et al., 2019) that engage students in rich mathematics. In this paper, we report on 30 students participating in one such challenge. Students were tasked with designing a business that helps users change unwanted behaviors or develop new healthy habits through tracking and visualizing their progress. We present results to show how the challenge provided opportunities for student autonomy in their solutions and in the mathematics they utilized. 

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5. Using evidence of student thinking as resources in a digital collaborative platform

   Park, Sunyoung; Edson, Alden J (August 2024, Mathematics education research and practice)

   Learning mathematics in a student-centered, problem-based classroom requires students to develop mathematical understanding and reasoning collaboratively with others. Despite its critical role in students’ collaborative learning in groups and classrooms, evidence of student thinking has rarely been perceived and utilized as a resource for planning and teaching. This is in part because teachers have limited access to student work in paper-and-pencil classrooms. As an alternative approach to making student thinking visible and accessible, a digital collaborative platform embedded with a problem-based middle school mathematics curriculum is developed through an ongoing design-based research project (Edson & Phillips, 2021). Drawing from a subset of data collected for the larger research project, we investigated how students generated mathematical inscriptions during small group work, and how teachers used evidence of students’ solution strategies inscribed on student digital workspaces. Findings show that digital flexibility and mobility allowed students to easily explore different strategies and focus on developing mathematical big ideas, and teachers to foreground student thinking when facilitating whole-class discussions and planning for the next lesson. This study provides insights into understanding mathematics teachers’ interactions with digital curriculum resources in the pursuit of students’ meaningful engagement in making sense of mathematical ideas. 

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