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The objective of this paper is to provide a holistic summary of ongoing research related to the development, implementation, assessment, and continuous refinement of an augmented reality (AR) app known as Vectors in Space. This Unity-based app was created by the authors and provides a self-guided learning experience for students to learn about fundamental vector concepts routinely encountered in undergraduate physics and engineering mechanics courses. Vectors are a fundamental tool in mechanics courses as they allow for the precise and comprehensive description of physical phenomena such as forces, moments, and motion. In early engineering coursework, students often perceive vectors as an abstract mathematical concept that requires spatial visualization skills in three dimensions (3D). The app aims to allow students to build these tacit skills while simultaneously allowing them to learn fundamental vector concepts that will be necessary in subsequent coursework. Three self-paced, guided learning activities systematically address concepts that include: (a) Cartesian components of vectors, (b) unit vectors and directional angles, (c) addition, (d) subtraction, (e) cross product using the right-hand rule, (f) angle between vectors using the dot product, and (g) vector projections using the dot product. The authors first discuss the app's scaffolding approach with special attention given to the incorporation of Mayer's principles of multimedia learning as well as the use of animations. The authors' approach to develop the associated statics learning activities, practical aspects of implementation, and lessons learned are shared. The effectiveness of the activities is assessed by applying analysis of covariance (ANCOVA) to pre- and post-activity assessment scores for control and treatment groups. Though the sample sizes are relatively small (less than 50 students), the results demonstrate that AR had a positive impact on student learning of the dot product and its applications. Larger sample sizes and refinements to the test instruments will be necessary in the future to draw robust conclusions regarding the other vector topics and operations. Qualitative feedback from student focus groups conducted with undergraduate engineering students identified the app's strengths as well as potential areas of improvement.
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Characterizing representational gestures in collaborative sense-making of vectors in introductory physics
An understanding of vectors and vector operations is crucial for success in physics, as this serves as the foundation for various essential concepts, including motion and forces. Previous research indicates that only a fraction of introductory physics students have a usable knowledge of vectors and vector operations, and that more attention should be given to how students make sense of vectors. We examined classroom video data from an introductory physics course wherein students worked collaboratively through learning activities to introduce vectors and vector operations. During these activities, students’ employment of gesture as a representational mode facilitated group sense-making. We propose a preliminary taxonomy of gestures for representing vector magnitudes, directions, and initial and terminal points. By identifying and characterizing the gestures used by students, we can gain insights into their learning processes and conceptual understanding of vectors, which can inform instructional design and teaching practices.
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- Award ID(s):
- 2201821
- PAR ID:
- 10508972
- Publisher / Repository:
- American Association of Physics Teachers
- Date Published:
- Journal Name:
- Proceedings of the Physics Education Research Conference 2023
- Page Range / eLocation ID:
- 290 to 295
- Format(s):
- Medium: X
- Location:
- Sacramento, CA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1119/perc.2023.pr.Scheuneman
