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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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Augmented Arithmetic Operations Proposed for IEEE-754 2018
Algorithms for extending arithmetic precision through compensated summation or arithmetics like double-double rely on operations commonly called twoSum and twoProduct. The current draft of the IEEE 754 standard specifies these operations under the names augmentedAddition and augmentedMultiplication. These operations were included after three decades of experience because of a motivating new use: bitwise reproducible arithmetic. Standardizing the operations provides a hardware acceleration target that can provide at least a 33 % speed improvements in reproducible dot product, placing reproducible dot product almost within a factor of two of common dot product. This paper provides history and motivation for standardizing these operations. We also define the operations, explain the rationale for all the specific choices, and provide parameterized test cases for new boundary behaviors.
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- Award ID(s):
- 1339745
- PAR ID:
- 10089378
- Date Published:
- Journal Name:
- IEEE 25th Symposium on Computer Arithmetic (ARITH)
- Page Range / eLocation ID:
- 45 to 52
- Format(s):
- Medium: X
- 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/10.1109/ARITH.2018.8464813
