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1. Exercises Integrating High School Mathematics with Robot Motion Planning

   https://doi.org/10.1109/FIE43999.2019.9028394  

   Greenberg, Ronald I.; Thiruvathukal, George K. (October 2019, 2019 IEEE Frontiers in Education Conference)

   This Innovative Practice Work in Progress presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align with Common Core State Standards for Mathematics. 

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2. Technology as a Support for Proof and Argumentation: A Systematic Literature Review

   https://doi.org/10.1564/tme_v27.2.04  

   Campbell, T.G.; Zelkowski, J. (July 2020, The international journal for technology in mathematics education)

   null (Ed.)

   Proof and argumentation are essential components of learning mathematics, and technology can mediate students’ abilities to learn. This systematic literature review synthesizes empirical literature which examines technology as a support for proof and argumentation across all content domains. The themes of this review are revealed through analyzing articles related to Geometry and mathematical content domains different from Geometry. Within the Geometry literature, five subthemes are discussed: (1) empirical and theoretical interplay in dynamic geometry environments (DGEs), (2) justifying constructions using DGEs, (3) comparing technological and non-technological environments, (4) student processing in a DGE, and (5) intelligent tutor systems. Within the articles related to content different from Geometry, two subthemes are discussed: technological supports for number systems/algebra and technological supports for calculus/real analysis. The technological supports for proof revealed in this review could aid future research and practice in developing new strategies to mediate students’ understandings of proof. 

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3. Geoclidean: Few-Shot Generalization in Euclidean Geometry

   Joy Hsu; Jiajun Wu; Noah D. Goodman (January 2023, NeurIPS 2022 Datasets and Benchmarks)

   Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to perceive and reason with them. Will computer vision models trained on natural images show the same sensitivity to Euclidean geometry? Here we explore these questions by studying few-shot generalization in the universe of Euclidean geometry constructions. We introduce Geoclidean, a domain-specific language for Euclidean geometry, and use it to generate two datasets of geometric concept learning tasks for benchmarking generalization judgements of humans and machines. We find that humans are indeed sensitive to Euclidean geometry and generalize strongly from a few visual examples of a geometric concept. In contrast, low-level and high-level visual features from standard computer vision models pretrained on natural images do not support correct generalization. Thus Geoclidean represents a novel few-shot generalization benchmark for geometric concept learning, where the performance of humans and of AI models diverge. The Geoclidean framework and dataset are publicly available for download. 

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4. Coherence and Transfer of Complex Learning with Fourier Analysis Learning Trajectories for Engineering Mathematics Education

   https://doi.org/10.1109/FIE44824.2020.9274075  

   Ekici, Celil; Mehrubeoglu, Mehrube; Palaniappan, Devanayagam; Alagoz, Cigdem (October 2020, IEEE Frontiers in Education (FIE))

   Fourier analysis learning trajectories are investigated in this full paper as a joint interdisciplinary construct for a scholarly collaboration among engineering and mathematics faculty. This is a dynamic and recursive construct for aligning, developing, and sharing research based innovative practices for engineering mathematics education. Towards building more coherence and transfer of learning between engineering and mathematics courses, these trajectories offer experimental practice templates for the interdisciplinary community of practice for engineering mathematics education. Conjectured learning trajectories for Fourier analysis thinking are here articulated and experimented in three courses - Trigonometry, Linear Algebra, and Signal Processing. Informed by the interdisciplinary perspectives from the team, these trajectories help to design instruction to support the complex learning of the mathematical, and engineering foundations for the advanced mathematical concepts and practices such as Fourier Analysis for engineers. The re- sults highlight the impact of collaborative, interdisciplinary, and innovative practices within and across courses to purposefully build and refine instruction to foster coherence and transfer with learning trajectories across mathematics and engineering courses for engineering majors. This offers a transformative process towards an interdisciplinary engineering mathematics education. The valid assessment and measurement of complex learning outcomes along learning trajectories are discussed for engineering mathematics education, paving the pathway for our future research direction. 

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5. On Track or Off Track? Identifying a Typology of Math Course-Taking Sequences in U.S. High Schools

   https://doi.org/10.1177/23780231231169259  

   Han, Seong Won; Kang, Chungseo; Weis, Lois; Dominguez, Rachel (January 2023, Socius: Sociological Research for a Dynamic World)

   The authors examine students’ linear progression histories in mathematics throughout high school years, using the High School Longitudinal Study of 2009. Although scholars have attended to this before, the authors provide a new organizing framework for thousands of heterogenous mathematics course-taking sequences. Using cluster analysis, the authors identify eight distinctive course-taking sequence typologies. Approximately 45 percent of students take a linear sequence of mathematics, whereas others stop taking mathematics altogether, repeat coursework, or regress to lower level courses. Only about 14 percent of students take the expected four-year linear sequence of Algebra 1–Geometry–Algebra II–Advanced Mathematics. Membership into different typologies is related to student characteristics and school settings (e.g., race, socioeconomic status, and high school graduation requirements). The results provide a tool for schools’ self-assessment of mathematics course-taking histories among students, creating intervention opportunities and a foundation for future research on advancing our understanding of stratification in math course-taking patterns, postsecondary access, and science, technology, engineering, and mathematics majors. 

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