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1. Thinking With Algebra, Two Professors Perspective

   McGathey, N. ( January 2023 , Proceedings of the seventh annual Indiana STEM Conference. West Lafayette, IN)

   s research brief will share insights from using the curriculum, Thinking With Algebra (TWA), a National Science Foundation Project (DUE 2021414). The focus will be on the value of using this curriculum when working specifically with students who have taken Algebra I and Algebra II in high school, but were not prepared for college algebra or precalculus. This curriculum is specifically designed for STEM-track students who place below the level of college algebra when they enter college. The authors have found that TWA helps instructors honor the mathematical knowledge and ideas that students bring into the classroom. The curriculum units give instructors the freedom to choose the topics that suit their objectives. TWA also offers a variety of approaches to help students connect with mathematics in a new way. This brief will expand on these them students that the authors observed when teaching with this curriculum. 

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2. Students’ Perspective of Thinking With Algebra

   Feikes, D. ( January 2023 , Proceedings of the seventh annual Indiana STEM Conference. West Lafayette, IN)

   Thinking With Algebra (TWA) is a curriculum development project for college students needing introductory/intermediate algebra. Unique guiding principles of the project are a focus on algebraic structure, mixed review, equity, and a classroom approach emphasizing small-group work and whole- class discussion (Feikes et al., 2022). Results are derived from a survey given to one class of fifteen students taking an intermediate algebra summer course. The paper shares both Likert and open-ended responses. Data demonstrates that the students believed that the TWA curriculum was beneficial. 

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3. Students’ perspectives of Thinking With Algebra

   2. Feikes, D. ( January 2023 , Proceedings of the eighth annual Indiana STEM Education Conference. West Lafayette, IN.)

   W. S. Walker, III (Ed.)

   Thinking With Algebra (TWA) is a curriculum development project for college students needing introductory/intermediate algebra. Unique guiding principles of the project are a focus on algebraic structure, mixed review, equity, and a classroom approach emphasizing small-group work and whole- class discussion (Feikes et al., 2022). Results are derived from a survey given to one class of fifteen students taking an intermediate algebra summer course. The paper shares both Likert and open-ended responses. Data demonstrates that the students believed that the TWA curriculum was beneficial. 

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4. College Geometry from an Advanced Historical Standpoint for Mathematics Education

   Ekici, C. ( July 2023 , History and Epistemology in Mathematics Education- Proceedings of the 9th European Summer University)

   E. Barbin, R. Capone (Ed.)

   Following Felix Klein, an advanced historical standpoint is here presented for teaching college geometry for teachers. Three main ways of developing an advanced historical standpoint are discussed with classroom experiments. One is building connections among geometries by developing an inquiry into definitions of geometric objects such as rhombus, their extensibility with their family relationships across Euclidean and non-Euclidean geometries. Second is on the multiplicity and extensibility of transformations as represented by two historical approaches advocated by Klein and Usiskin. The third way to develop an advanced standpoint is by developing a critical look into a geometry practice tracing its change with the reforms in school geometry. The practice of constructions to connect geometry and algebra is impacted by two historical efforts. One is a supportive effort by Hilbert on the practice of constructions by Hilbert’s Algebra of Segments dating back to 1902 to connect geometry and algebra. The other historical reform effort is by School Mathematics Study Groups (SMSG) during 1960s, which led to weakening the axiomatic foundations of the practice of constructability and exactness. The case of SMSG’s angle construction axiom is criticized in their revision of axiomatic foundations of school geometry. Three approaches to develop an advanced standpoint informing research and practice of geometry teacher education towards a more historically connected stance. 

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5. Innovations in university teaching based on mathematics education research.

   Florensa, I. ; Hoffman, M. ; Romo Vázquez, A. ; Zandieh, M. ; Martínez-Planell, R. ( January 2022 , Proceedings of the Conference of the International Network for Didactic Research in University Mathematics)

   Trigueros, M. ; Barquero, B. ; Hochmuth, R. ; Peters, J. (Ed.)

   We report on a variety of innovative projects that are at different stages of development and implementation. We start by presenting a project still in development to help address Klein’s second discontinuity problem, that is, the perception of pre-college teachers that the advanced mathematics courses they took at the university are of little use in the practice of their profession. Then we briefly discuss the study and research paths (SRP). This is the proposal from the Anthropological Theory of the Didactic (ATD) to foment a move from the prevailing paradigm of visiting works to that of questioning the world. This is followed by the discussion of an online course for in- service teachers, designed to help them experience, adapt, and class-test a modeling intervention, as well as reflect on institutional issues that might constrain the future application of modeling in their teaching. We end with a discussion of a project based on the idea of guided reinvention, to design and study the implementation of inquiry-oriented linear algebra. 

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