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1. Design and Evaluation of an Augmented Reality App for Learning Spatial Transformations and their Mathematical Representations

   https://doi.org/10.1109/VRW55335.2022.00155  

   Shaghaghian, Zohreh; Burte, Heather; Song, Dezhen; Yan, Wei (March 2022, 2022 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW))

   There is a close relation between spatial thinking and mathematical problem-solving. This paper presents a newly developed educational Augmented Reality (AR) mobile application, BRICKxAR/T, to help students intuitively learn spatial transformations and the related mathematics through play. A pilot study with 7 undergraduate students evaluates students learning gain through a mental rotation and a math test on transformation matrices. The results show most students performed better with a higher score after learning with the app. Students found the app interesting to play and useful for learning geometric transformations and matrices. 

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2. 3DnST: A Framework Towards Understanding Children's Interaction with Tinkercad and Enhancing Spatial Thinking Skills.

   https://doi.org/10.1145/3459990.3460717  

   Bhaduri, S. (June 2021, IDC 2021)

   With the proliferation of 3D printing technologies in schools and makerspaces, there is a need for teaching 3D modeling to students. Learning 3D modeling enhances spatial thinking skills, an essential skill for success in STEM. Creating 3D models requires students to have a deep understanding of 3D space, including rotating and scaling. In this study, we propose a framework developed through video-coding from analyzing screen recordings of middle-school students’ usage of a 3D modeling tool - Tinkercad. The proposed framework focuses on identifying challenges students encounter during 3D modeling. These challenges include spatial thinking skills, working with the Tinkercad interface, and mental model formation. We authenticated the framework by collecting and analyzing data from a 3D printing unit in three middle schools. Our results and subsequent analysis can guide educators and researchers on how to use this framework to support students in having productive learning experiences with Computer-Aided Design tools. 

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3. Web-based Interactive Polyhedral Graphics Statics Platform

   CHAI, Hua; AKBARZADEH, Masoud (October 2021, International Association of Shell and Spatial Structures)

   This paper introduces a web-based interactive educational platform for 3D/polyhedral graphic statics (PGS) [1]. The Block Research Group (BRG) at ETH Zürich developed a dynamic learning and teaching platform for structural design. This tool is based on traditional graphic statics. It uses interactive 2D drawings to help designers and engineers with all skill levels to understand and utilize the methods [2]. However, polyhedral graphic statics is not easy to learn because of its characteristics in three-dimensional. All the existing computational design tools are heavily dependent on the modeling software such as Rhino or the Python-based computational framework like Compass [3]. In this research, we start with the procedural approach, developing libraries using JavaScript, Three.js, and WebGL to facilitate the construction by making it independent from any software. This framework is developed based on the mathematical and computational algorithms deriving the global equilibrium of the structure, optimizing the balanced relationship between the external magnitudes and the internal forces, visualizing the dynamic reciprocal polyhedral diagrams with corresponding topological data. This instant open-source application and the visualization interface provide a more operative platform for students, educators, practicers, and designers in an interactive manner, allowing them to learn not only the topological relationship but also to deepen their knowledge and understanding of structures in the steps for the construction of the form and force diagrams and analyze it. In the simplified single-node example, the multi-step geometric procedures intuitively illustrate 3D structural reciprocity concepts. With the intuitive control panel, the user can move the constraint point’s location through the inserted gumball function, the force direction of the form diagram will be dynamically changed from compression-only to tension and compression combined. Users can also explore and design innovative, efficient spatial structures with changeable boundary conditions and constraints through real-time manipulating both force distribution and geometric form, such as adding the number of supports or subdividing the global equilibrium in the force diagram. Eventually, there is an option to export the satisfying geometry as a suitable format to share with other fabrication tools. As the online educational environment with different types of geometric examples, it is valuable to use graphical approaches to teach the structural form in an exploratory manner. 

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4. Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study

   https://doi.org/10.1007/s40753-020-00131-8  

   Merck, Madeline F.; Gallagher, Melissa A.; Habib, Emad; Tarboton, David (July 2021, International Journal of Research in Undergraduate Mathematics Education)

   null (Ed.)

   Abstract Engineering students need to spend time engaging in mathematical modeling tasks to reinforce their learning of mathematics through its application to authentic problems and real world design situations. Technological tools and resources can support this kind of learning engagement. We produced an online module that develops students’ mathematical modeling skills while developing knowledge of the fundamentals of rainfall-runoff processes and engineering design. This study examined how 251 students at two United States universities perceived mathematical modeling as implemented through the online module over a 5-year period. We found, subject to the limitation that these are perceptions from not all students, that: (a) the module allowed students to be a part of the modeling process; (b) using technology, such as modeling software and online databases, in the module helped students to understand what they were doing in mathematical modeling; (c) using the technology in the module helped students to develop their skill set; and (d) difficulties with the technology and/or the modeling decisions they had to make in the module activities were in some cases barriers that interfered with students’ ability to learn. We advocate for instructors to create modules that: (a) are situated within a real-world context, requiring students to model mathematically to solve an authentic problem; (b) take advantage of digital tools used by engineers to support students’ development of the mathematical and engineering skills needed in the workforce; and (c) use student feedback to guide module revisions. 

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5. Factors Mediating Learning and Application of Computational Modeling by Life Scientists

   https://doi.org/10.1109/FIE.2018.8659328  

   Madamanchi, Aasakiran; Cardella, Monica E.; Glazier, James A.; Umulis, David M. (October 2018, 2018 IEEE Frontiers in Education Conference (FIE))

   This Work-in-Progress paper in the Research Category uses a retrospective mixed-methods study to better understand the factors that mediate learning of computational modeling by life scientists. Key stakeholders, including leading scientists, universities and funding agencies, have promoted computational modeling to enable life sciences research and improve the translation of genetic and molecular biology high- throughput data into clinical results. Software platforms to facilitate computational modeling by biologists who lack advanced mathematical or programming skills have had some success, but none has achieved widespread use among life scientists. Because computational modeling is a core engineering skill of value to other STEM fields, it is critical for engineering and computer science educators to consider how we help students from across STEM disciplines learn computational modeling. Currently we lack sufficient research on how best to help life scientists learn computational modeling. To address this gap, in 2017, we observed a short-format summer course designed for life scientists to learn computational modeling. The course used a simulation environment designed to lower programming barriers. We used semi-structured interviews to understand students' experiences while taking the course and in applying computational modeling after the course. We conducted interviews with graduate students and post- doctoral researchers who had completed the course. We also interviewed students who took the course between 2010 and 2013. Among these past attendees, we selected equal numbers of interview subjects who had and had not successfully published journal articles that incorporated computational modeling. This Work-in-Progress paper applies social cognitive theory to analyze the motivations of life scientists who seek training in computational modeling and their attitudes towards computational modeling. Additionally, we identify important social and environmental variables that influence successful application of computational modeling after course completion. The findings from this study may therefore help us educate biomedical and biological engineering students more effectively. Although this study focuses on life scientists, its findings can inform engineering and computer science education more broadly. Insights from this study may be especially useful in aiding incoming engineering and computer science students who do not have advanced mathematical or programming skills and in preparing undergraduate engineering students for collaborative work with life scientists. 

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