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Learning Spatial Transformations and Their Mathematical Representations for Architecture and STEM: An AR-Powered Approach
Abstract
In Computer-Aided Design (CAD), Building Information Modeling (BIM), etc., students suffer from non-proficient use of the modeling software due to a lack of mathematical knowledge. Deficient knowledge and skills may lead students to use the modeling software through trial-and-error without understanding the logic behind computational algorithms. Understanding spatial transformations is recognized as one of the key factors in learning modeling software. Literature confirms the difficulties of learning/teaching spatial transformations and related mathematics.
This research proposes a novel educational Augmented Reality (AR) application (BRICKxAR/T) to help students intuitively learn spatial/geometric transformations and the corresponding mathematics through play. The proposed application leverages AR features, such as augmentation of abstract information in the physical environment, physical/virtual object interplay, embodied learning, and natural perspective alignment to create a meaningful context for the mathematical concepts behind spatial transformations. Two prototypes of AR applications are developed at the primary and advanced levels to help students learn the geometric reasoning behind the transformation matrices. Prototype 1 is a puzzle game-like mobile app to help students learn the mathematical notations of rotation, translation, and scale while understanding the mathematical components of transformations, such as variables, parameters, and functions, through an interactive AR environment. Prototype 2 covers combined transformation matrices and the trigonometric equations behind calculations of transformation matrices focusing on embodied learning. The app (BRICKxAR/T) of the prototypes was developed for iOS devices and deployed as AR and non-AR versions for a comparative study. This research includes test cases (N=59) participating in AR (N=29) and non-AR (N=30) groups along with discussion and analysis. Test cases were conducted for Prototype 1 to evaluate the learning gain of using the app and compare the AR and non-AR environments. The AR group used the AR version of the app integrated with physical model interaction in the AR environment, and the non-AR group had similar playing and learning sessions with the non-AR version of the app and the physical model separately. Pre- and post-tests were utilized to measure students’ improvement in mental rotation and math skills using the Purdue Visualization of Rotation Test (PVRT) and a math test on transformation matrices, respectively. A NASA_TLX survey and a motivation questionnaire (MSLQ) were applied to evaluate the task load of the app and students’ motivation in playing with the app.
The statistical analysis revealed that students’ PVRT scores improved more significantly in the non-AR group compared to the AR group, which was not expected based on literature. Students’ math scores improved significantly in the post-tests of AR and non-AR groups which shows the positive impact of BRICKxAR/T in improving students’ math skills, specifically for spatial transformations. The NASA_TLX results showed that using BRICKxAR/T was a low demanding task. The MSLQ results showed that most students found BRICKxAR/T an interesting and useful app to learn the targeted subject.
Subject
Augmented RealityEducational Application
Human-Computer-Interaction
Visualization
Embodied Learning
Spatial Transfor-mations
Matrices
Trigonometry
Parametric Modeling
Citation
Shaghaghian, Zohreh (2022). Learning Spatial Transformations and Their Mathematical Representations for Architecture and STEM: An AR-Powered Approach. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /198601.