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1. Using Network Analysis Techniques to Probe Student Understanding of Expressions Across Notations in Quantum Mechanics

   Riihiluoma, William; Topdemir, Zeynep; Thompson, John R. (January 2022, Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Higgins, A (Ed.)

   One important outcome of physics instruction is for students to be capable of relating physical concepts and phenomena to multiple mathematical representations. In quantum mechanics (QM), students are asked to work between multiple symbolic notations, some not previously encountered. To investigate student understanding of the relationships between expressions used in these various notations, many of which describe analogous physical concepts, a survey was distributed to students enrolled in upper-division QM courses at multiple institutions. Network analysis techniques were shown to be useful for gaining information about how students relate these expressions. Preliminary analysis suggests that students view Dirac bras and kets as more similar to generic vectors than to their physically analogous wave function counterparts, and that Dirac bras and kets serve as a bridge between vector and wave function expressions. 

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2. Detailing Racialized and Gendered Mechanisms of Undergraduate Precalculus and Calculus Classroom Instruction

   https://doi.org/10.1080/07370008.2020.1849218  

   Leyva, Luis A.; Quea, Ruby; Weber, Keith; Battey, Dan; López, Daniel (January 2021, Cognition and Instruction)

   null (Ed.)

   Undergraduate mathematics education can be experienced in discouraging and marginalizing ways among Black students, Latin
   students, and white women. Precalculus and calculus courses, in particular, operate as gatekeepers that contribute to racialized and gendered attrition in persistence with mathematics coursework and pursuits in STEM (science, technology, engineering, and mathematics). However, student perceptions of instruction in these introductory mathematics courses have yet to be systematically examined as a contributor to such attrition. This paper presents findings from a study of 20 historically marginalized students’ perceptions of precalculus and calculus instruction to document features that they found discouraging and marginalizing. Our analysis revealed how students across different race-gender identities reported stereotyping as well as issues of representation in introductory mathematics classrooms and STEM fields as shaping their perceptions of instruction. These perceptions pointed to the operation of three racialized and gendered mechanisms in instruction: (i) creating differential opportunities for participation and support, (ii) limiting support from same-race, same-gender peers to manage negativity in instruction, and (iii) activating exclusionary ideas about who belongs in STEM fields. We draw on our findings to raise implications for research and practice in undergraduate mathematics education. 

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3. Bringing exploratory learning online: Problem-solving before instruction improves remote undergraduate physics learning

   https://doi.org/10.3389/feduc.2023.1215975  

   DeCaro, Marci S; Isaacs, Raina A; Bego, Campbell R; Chastain, Raymond J (August 2023, Frontiers in Education)

   STEM undergraduate instructors teaching remote courses often use traditional lecture-based instruction, despite evidence that active learning methods improve student engagement and learning outcomes. One simple way to use active learning online is to incorporate exploratory learning. In exploratory learning, students explore a novel activity (e.g., problem solving) before a lecture on the underlying concepts and procedures. This method has been shown to improve learning outcomes during in-person courses, without requiring the entire course to be restructured. The current study examined whether the benefits of exploratory learning extend to a remote undergraduate physics lesson, taught synchronously online. Undergraduate physics students (N = 78) completed a physics problem-solving activity either before instruction (explore-first condition) or after (instruct-first condition). Students then completed a learning assessment of the problem-solving procedures and underlying concepts. Despite lower accuracy on the learning activity, students in the explore-first condition demonstrated better understanding on the assessment, compared to students in the instruct-first condition. This finding suggests that exploratory learning can serve as productive failure in online courses, challenging students but improving learning, compared to the more widely-used lecture-then-practice method. 

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4. Abstraction in students’ mathematics strategies: Productive starting points for introducing CT concepts.

   Rich, K. M.; Yadav, A.; Zhu, M. (January 2019, The Journal of computers in mathematics and science teaching)

   Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in mathematics education. In this study, we examined elementary students’ solutions to a commonplace mathematics task to determine whether and how students moved among levels of abstraction as they solved the task. Furthermore, we analyzed student errors, categorizing them according to whether they related to moves among levels of abstraction or to purely mathematical steps. Our analysis showed: (1) students implicitly shift among levels of abstraction when solving “real- world” mathematics problems; (2) students make errors when making those implicit shifts in abstraction level; (3) the errors students make in abstraction outnumber the errors they make in purely mathematical skills. We discuss the implications for these findings, arguing they establish that there are opportunities for explicit instruction in abstraction in elementary mathematics, and that students’ overall mathematics achievement and problem-solving skills have the potential to benefit from applying these computer-science ideas to mathematics instruction. 

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5. THE QUANTUM FOR ALL PROJECT: TEACHER PROFESSIONAL DEVELOPMENT MODEL

   https://doi.org/10.21125/edulearn.2023.0919  

   Matsler, Karen; Lopez, Ramon (July 2023, https://library.iated.org/)

   Quantum information science (QIS) is of growing importance to economic and national security, commerce, and technology. The development of a "quantum smart" workforce needs to begin before college since most students will not major in physics. Thus, it is vital to expose K-12 students to quantum concepts that are relevant to everyday experiences with credit card security, phones, computers, and basic technology and to prepare teachers to teach this content. The logical venue for exposure to basic ideas in quantum science might be a high school physics course, or even a physical science course if a full physics course is not offered. Professional development (PD) for educators typically includes 1-2 weeks of intensive instruction, usually in the summer. Teachers are then expected to remember what they learned and implement it several months after the PD. The model is based on prior research indicating that an educator needs a minimum of 80 hours of PD to become comfortable enough to implement the new instruction in their classroom. However, little research has been done as to how much they actually implement. For the past three years, we have been engaged in a project funded by the US National Science Foundation to build mechanisms (materials and PD strategies) for educating a quantum-ready workforce. Our PD model is based on pedagogical techniques used in classrooms, specifically the components of learn then practice in order to avoid cognitive overload. Instruction is more effective when the learners (teachers or students) are given opportunities to actively engage in the learning process through interaction/collaboration with peers, exploring challenges, and practicing what they have learned. This paper will share the logistics of our new PD new model, challenges, finding from our current research, and implications for future PD in K-16. 

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