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1. 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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2. Teachers’ Disciplinary Boundedness in the Implementation of Integrated Computational Modeling in Physics

   https://doi.org/10.1007/s10956-021-09938-9  

   Vieyra, Rebecca; Himmelsbach, Joshua (April 2022, Journal of Science Education and Technology)

   Abstract This study explored teachers’ conceptualizations of integrated computational modeling in secondary physics by exposing twelve experienced physics teachers to programming and then analyzing interview responses. Responses revealed that teachers fell along a spectrum of disciplinary boundary–stretching mentalities. This paper presents a preliminary conceptual framework for exploring both horizontal (interdisciplinary) and vertical (intradisciplinary) boundary stretching, as well as for identifying bounded mentalities as teachers consider integration. Horizontal boundary stretchers envisioned opportunities to use computational modeling to shift their curriculum or pedagogical approaches in physics to help students enhance skills underlying multiple fields, while vertical boundary stretchers considered how computing might allow students to explore physics concepts more deeply. Teachers with more boundary-stretching indicators at the outset of an integrated curriculum development workshop were more likely to persist in the implementation of computational modeling–integrated materials in their physics classrooms than those who expressed more bounded thinking. These findings emphasize the importance of considering teachers’ perceptions about how their own science discipline is connected to similar fields and provide implications about how to identify potential adopters of innovative teaching approaches. 

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3. Teachers’ Beliefs in Enacting an Interdisciplinary Engineering Project in Inclusive and General Classroom Contexts

   Lilly, Sarah; McAlister, Anne M.; Chiu, Jennifer (January 2022, Annual meeting of the American Society for Engineering Education.)

   In this study, we examine the reported beliefs of two elementary science teachers who co-taught a four-week engineering project in which students used a computational model to design engineering solutions to reduce water runoff at their school (Lilly et al., 2020). Specifically, we explore the beliefs that elementary science teachers report while enacting an engineering project in two different classroom contexts and how they report that their beliefs may have affected instructional decisions. Classroom contexts included one general class with a larger proportion of students in advanced mathematics and one inclusive class with a larger proportion of students with individualized educational programs. During project implementation, we collected daily surveys and weekly interviews to consider teachers’ beliefs of the class sections, classroom activities, and curriculum. Two researchers performed a thematic analysis of the surveys and interviews to code reflections on teachers’ perceived differences between students in the class sections and their experiences teaching engineering in the class sections. Results suggest that teachers’ beliefs about students in these two different classroom contexts may have influenced opportunities that students had to understand and engage in disciplinary practices. The teachers reported making changes to activities based on their perceptions of student understanding and engagement and to save time which led to different experiences for students in each class section, specifically a more teacher-centered implementation for the inclusive class. Teachers also suggested specific professional development and educative supports to help teachers to support all students to engage in engineering tasks. Thus, it is important to understand teachers’ beliefs to build support for teachers in their implementation of engineering projects that meet the needs of their students and ensure that students have access and support to engage in engineering practices. 

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4. Introducing the PrimeD Framework: Teacher Practice and Professional Development through Shulman’s View of Professionalism

   https://doi.org/10.3390/educsci14091032  

   Saderholm, Jon; Ronau, Robert N; Rakes, Christopher R; Bush, Sarah B; Mohr-Schroeder, Margaret J (September 2024, Education Sciences)

   This paper clarifies and expands the definition of teacher professional practice, grounded in the commonplaces of professionalism outlined by Lee Shulman. We present the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework as a lens for transforming professional development into a practice that engages teachers as professionals. This discussion explores teachers’ roles in both their classrooms and the profession. The inclusion of PrimeD evaluation and research in the development and practice of mathematics teachers addresses Shulman’s professionalism commonplaces. PrimeD was tested as a lens for professionalism in mathematics teacher education programs at four universities. In the study, teachers collaborated as professionals on developing and testing novel ways to approach mathematics lessons. In general, teachers’ efforts to conduct structured experimentation in their lessons were disconnected from traditional views of the role of a teacher. As a result, teachers who did develop and test lesson trials in this PD program did not frequently continue experimentation. Typically, teachers wanted to collaborate on testing classroom activities but did not have resources to do so (e.g., time, collaborative planning). Systemic changes are needed to promote sustainable change, allowing teachers to collaborate and share the results of classroom research. 

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5. Interrogation of Social Justice Contexts in Mathematical Modeling: The Use of Simulations of Practice in the Mathematical Preparation of Teachers

   https://doi.org/10.37626/GA9783959872188.0.006  

   Anhalt, C.; Cortez, R.; Kohler, B.; Tidwell, W. (August 2022, Proceedings of the International Conference of The Mathematics Education for the Future Project.)

   Morska, J.; Rogerson, A. (Ed.)

   Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The Mathematics of Doing, Understanding, Learning, and Educating for Secondary Students [MODULE(S2)]* project developed a curriculum in modeling for teacher education that includes simulations of practice, in which prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of Indigenous people. This problem explores a critical social issue and calls for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results. 

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