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  1. Spatial ability is a well-known predictor of success in science, technology, engineering, and mathematics (STEM) fields. The purpose of this study was to investigate and understand the spatial strategies that were used by blind and low-vision (BLV) individuals as they solved problems on the tactile mental cutting test (TMCT), an instrument that was designed to measure the spatial ability of BLV audiences. The TMCT is an accessible adaptation of the older, 1938 version of the mental cutting test (MCT) that has been used extensively in spatial ability research. Additionally, this paper seeks to compare these strategies with existing strategies that have been investigated with sighted populations. The BLV community is underrepresented in engineering and in spatial ability research. By understanding how BLV students understand and solve spatial problems and concepts, educators can develop and enhance educational content that is relevant to this population. By incorporating perspectives from the BLV community and making STEM curricula accessible to this population, more BLV individuals may be encouraged to pursue STEM or engineering career pathways. 
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    Free, publicly-accessible full text available July 6, 2024
  2. This article presents tactile drafting techniques developed in collaboration with blind educators and students that have the potential to increase BLV students’ access to drafting and engineering graphic curriculum in K-12 and higher education. This work builds on previous work funded by the National Science Foundation (Goodridge et al., 2019; Ashby et al., 2018; Lopez et al., 2020; Goodridge et al., 2021a; Goodridge et al., 2021b) and it is the authors’ hope that some of the practices included herein will allow BLV youth to further develop technological and engineering literacy in related technology and engineering graphics courses. 
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  3. Spatial skills are fundamental to learning and developing expertise in engineering. This paper describes a new virtual and physical manipulatives (VPM) technology that this research team recently developed to enhance undergraduate engineering students’ spatial skills. This technology consists of ten manipulatives spanning a variety of levels of geometrical complexity. Each manipulative is authentic due to their real-world engineering applications that were chosen to stimulate student interest in engineering. A computer program was developed to connect virtual and physical manipulatives, allowing students to receive spatial training anytime, anywhere through the Internet. Quasi-experimental research, involving an intervention group (n = 37) and a control group (n = 34), was conducted. Each group completed a pre- and post-test using the same assessment instrument that measured students’ spatial skills. Normality tests were conducted. The results show that the data involved in the present study did not have a normal distribution. Thus, non-parametric statistical analysis was performed, including descriptive analysis, correlation analysis, and Mann-Whitney U tests. The results show that the mean value of normalized learning gains is 41.2% for the intervention group, which is 33% higher than that for the control group (8.2%). A statistically significant difference exists between the intervention and control groups in terms of normalized learning gains (P < 0.01). The new VPM technology developed from the present study has a medium effect size (0.34) on improving students’ spatial skills. 
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  4. The current study examined the neural correlates of spatial rotation in eight engineering undergraduates. Mastering engineering graphics requires students to mentally visualize in 3D and mentally rotate parts when developing 2D drawings. Students’ spatial rotation skills play a significant role in learning and mastering engineering graphics. Traditionally, the assessment of students’ spatial skills involves no measurements of neural activity during student performance of spatial rotation tasks. We used electroencephalography (EEG) to record neural activity while students performed the Revised Purdue Spatial Visualization Test: Visualization of Rotations (Revised PSVT:R). The two main objectives were to 1) determine whether high versus low performers on the Revised PSVT:R show differences in EEG oscillations and 2) identify EEG oscillatory frequency bands sensitive to item difficulty on the Revised PSVT:R.  Overall performance on the Revised PSVT:R determined whether participants were considered high or low performers: students scoring 90% or higher were considered high performers (5 students), whereas students scoring under 90% were considered low performers (3 students). Time-frequency analysis of the EEG data quantified power in several oscillatory frequency bands (alpha, beta, theta, gamma, delta) for comparison between low and high performers, as well as between difficulty levels of the spatial rotation problems.   Although we did not find any significant effects of performance type (high, low) on EEG power, we observed a trend in reduced absolute delta and gamma power for hard problems relative to easier problems. Decreases in delta power have been reported elsewhere for difficult relative to easy arithmetic calculations, and attributed to greater external attention (e.g., attention to the stimuli/numbers), and consequently, reduced internal attention (e.g., mentally performing the calculation). In the current task, a total of three spatial objects are presented. An example rotation stimulus is presented, showing a spatial object before and after rotation. A target stimulus, or spatial object before rotation is then displayed. Students must choose one of five stimuli (multiple choice options) that indicates the correct representation of the object after rotation. Reduced delta power in the current task implies that students showed greater attention to the example and target stimuli for the hard problem, relative to the moderate and easy problems. Therefore, preliminary findings suggest that students are less efficient at encoding the target stimuli (external attention) prior to mental rotation (internal attention) when task difficulty increases.  Our findings indicate that delta power may be used to identify spatial rotation items that are especially challenging for students. We may then determine the efficacy of spatial rotation interventions among engineering education students, using delta power as an index for increases in internal attention (e.g., increased delta power). Further, in future work, we will also use eye-tracking to assess whether our intervention decreases eye fixation (e.g., time spent viewing) toward the target stimulus on the Revised PSVT:R. By simultaneously using EEG and eye-tracking, we may identify changes in internal attention and encoding of the target stimuli that are predictive of improvements in spatial rotation skills among engineering education students.  
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  5. In teaching mechanics, we use multiple representations of vectors to develop concepts and analysis techniques. These representations include pictorials, diagrams, symbols, numbers and narrative language. Through years of study as students, researchers, and teachers, we develop a fluency rooted in a deep conceptual understanding of what each representation communicates. Many novice learners, however, struggle to gain such understanding and rely on superficial mimicry of the problem solving procedures we demonstrate in examples. The term representational competence refers to the ability to interpret, switch between, and use multiple representations of a concept as appropriate for learning, communication and analysis. In engineering statics, an understanding of what each vector representation communicates and how to use different representations in problem solving is important to the development of both conceptual and procedural knowledge. Science education literature identifies representational competence as a marker of true conceptual understanding. This paper presents development work for a new assessment instrument designed to measure representational competence with vectors in an engineering mechanics context. We developed the assessment over two successive terms in statics courses at a community college, a medium-sized regional university, and a large state university. We started with twelve multiple-choice questions that survey the vector representations commonly employed in statics. Each question requires the student to interpret and/or use two or more different representations of vectors and requires no calculation beyond single digit integer arithmetic. Distractor answer choices include common student mistakes and misconceptions drawn from the literature and from our teaching experience. We piloted these twelve questions as a timed section of the first exam in fall 2018 statics courses at both Whatcom Community College (WCC) and Western Washington University. Analysis of students’ unprompted use of vector representations on the open-ended problem-solving section of the same exam provides evidence of the assessment’s validity as a measurement instrument for representational competence. We found a positive correlation between students’ accurate and effective use of representations and their score on the multiple choice test. We gathered additional validity evidence by reviewing student responses on an exam wrapper reflection. We used item difficulty and item discrimination scores (point-biserial correlation) to eliminate two questions and revised the remaining questions to improve clarity and discriminatory power. We administered the revised version in two contexts: (1) again as part of the first exam in the winter 2019 Statics course at WCC, and (2) as an extra credit opportunity for statics students at Utah State University. This paper includes sample questions from the assessment to illustrate the approach. The full assessment is available to interested instructors and researchers through an online tool. 
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