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1. Hands-On Statics to Improve Conceptual Understanding and Representational Competence

   Davishahl, E.; Singleton, L.; Haskell, T.; Rupe, K. (June 2022, 2022 ASEE Annual Conference & Exposition)

   Mechanics instructors frequently employ hands-on learning with goals such as demonstrating physical phenomena, aiding visualization, addressing misconceptions, exposing students to “real-world” problems, and promoting an engaging classroom environment. This paper presents results from a study exploring the importance of the “hands-on” aspect of a hands-on modeling curriculum we have been developing that spans several topics in statics. The curriculum integrates deep conceptual exploration with analysis procedure tutorials and aims to scaffold students’ development of representational competence, the ability to use multiple representations of a concept as appropriate for learning, problem solving, and communication. We conducted this study over two subsequent terms in an online statics course taught in the context of remote learning amidst the COVID-19 pandemic. The intervention section used a take-home adaptation of the original classroom curriculum. This adaptation consisted of eight activity worksheets with a supplied kit of manipulatives and model-building supplies students could use to construct and explore concrete representations of figures and diagrams used in the worksheets. In contrast, the control section used activity worksheets nearly identical to those used in the hands-on curriculum, but without the associated modeling parts kit. We only made minor revisions to the worksheets to remove reference to the models. The control and intervention sections were otherwise identical in how they were taught by the same instructor. We compare learning outcomes between the two sections as measured via pre-post administration of a test of 3D vector concepts and representations called the Test of Representational Competence with Vectors (TRCV). We also compare end of course scores on the Concept Assessment Test in Statics (CATS) and final exam scores. In addition, we analyze student responses on two “multiple choice plus explain” concept questions paired with each of five activities covering the topics of 3D moments, 3D particle equilibrium, rigid body equilibrium (2D and 3D), and frame analysis (2D). The mean pre/post gain across all ten questions was higher for the intervention section, with the largest differences observed on questions relating to 3D rigid body equilibrium. Students in the intervention section also made larger gains on the TRCV and scored better on the final exam compared to the control section, but these results are not statistically significant perhaps due to the small study population. There were no appreciable differences in end-of-course CATS scores. We also present student feedback on the activity worksheets that was slightly more positive for the versions with the models. 

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2. Hands-On Statics to Improve Conceptual Understanding and Representational Competence

   Davishahl, E.; Singleton, L.; Haskell, T.; Rupe, K. (June 2022, Proceedings ASEE annual conference)

   Mechanics instructors frequently employ hands-on learning with goals such as demonstrating physical phenomena, aiding visualization, addressing misconceptions, exposing students to “real-world” problems, and promoting an engaging classroom environment. This paper presents results from a study exploring the importance of the “hands-on” aspect of a hands-on modeling curriculum we have been developing that spans several topics in statics. The curriculum integrates deep conceptual exploration with analysis procedure tutorials and aims to scaffold students’ development of representational competence, the ability to use multiple representations of a concept as appropriate for learning, problem solving, and communication. We conducted this study over two subsequent terms in an online statics course taught in the context of remote learning amidst the COVID-19 pandemic. The intervention section used a take-home adaptation of the original classroom curriculum. This adaptation consisted of eight activity worksheets with a supplied kit of manipulatives and model-building supplies students could use to construct and explore concrete representations of figures and diagrams used in the worksheets. In contrast, the control section used activity worksheets nearly identical to those used in the hands-on curriculum, but without the associated modeling parts kit. We only made minor revisions to the worksheets to remove reference to the models. The control and intervention sections were otherwise identical in how they were taught by the same instructor. We compare learning outcomes between the two sections as measured via pre-post administration of a test of 3D vector concepts and representations called the Test of Representational Competence with Vectors (TRCV). We also compare end of course scores on the Concept Assessment Test in Statics (CATS) and final exam scores. In addition, we analyze student responses on two “multiple choice plus explain” concept questions paired with each of five activities covering the topics of 3D moments, 3D particle equilibrium, rigid body equilibrium (2D and 3D), and frame analysis (2D). The mean pre/post gain across all ten questions was higher for the intervention section, with the largest differences observed on questions relating to 3D rigid body equilibrium. Students in the intervention section also made larger gains on the TRCV and scored better on the final exam compared to the control section, but these results are not statistically significant perhaps due to the small study population. There were no appreciable differences in end-of-course CATS scores. We also present student feedback on the activity worksheets that was slightly more positive for the versions with the models. 

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3. Scaffolding Spatial Abilities in Integral Calculus

   Davishahl, E.; Singleton, L.; Haskell, T.; Rupe, K.; Glen, L. (June 2022, 2022 ASEE Annual Conference & Exposition)

   This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with hands-on models and manipulatives. We are exploring how best to design these activities to support learners’ development of conceptual understanding and representational competence in integral calculus and engineering statics, two foundational courses for most engineering majors. A second goal is to leverage the model-based activities to scaffold spatial skills development in the context of traditional course content. As widely reported in the literature, well-developed spatial abilities correlate with student success and persistence in many STEM majors. We provided calculus students in selected intervention sections taught by four instructors at three different community colleges with take-home model kits that they could reference for a series of asynchronous learning activities. Students in these sections completed the Purdue Spatial Visualization Test: Rotations (PSVT:R) in the first and last weeks of their course. We also administered the assessment in multiple control sections (no manipulatives) taught by the same faculty. This paper analyzes results from fall 2020 through fall 2021 to see if there is any difference between control and intervention sections for the courses as a whole and for demographic subgroups including female-identifying students and historically-underserved students of color. All courses were asynchronous online modality in the context of the COVID-19 pandemic. We find that students in intervention sections of calculus made slightly larger gains on the PSVT:R, but this result is not statistically significant as a whole or for any of the demographic subgroups considered. We also analyzed final course grades for differences between control and intervention sections and found no differences. We found no significant effect of the presence of the model-based activities leading to increased PSVT:R gains or improved course grades. We would not extend this conclusion to face-to-face implementation, however, due primarily to the compromises made to adapt the curriculum from in-person group learning to asynchronous individual work and inconsistent engagement of the online students with the modeling activities. 

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4. Scaffolding Spatial Abilities in Integral Calculus

   Davishahl, E.; Singleton, L.; Haskell, T.; Rupe, K.; Glen, L. (June 2022, Proceedings ASEE annual conference)

   This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with hands-on models and manipulatives. We are exploring how best to design these activities to support learners’ development of conceptual understanding and representational competence in integral calculus and engineering statics, two foundational courses for most engineering majors. A second goal is to leverage the model-based activities to scaffold spatial skills development in the context of traditional course content. As widely reported in the literature, well-developed spatial abilities correlate with student success and persistence in many STEM majors. We provided calculus students in selected intervention sections taught by four instructors at three different community colleges with take-home model kits that they could reference for a series of asynchronous learning activities. Students in these sections completed the Purdue Spatial Visualization Test: Rotations (PSVT:R) in the first and last weeks of their course. We also administered the assessment in multiple control sections (no manipulatives) taught by the same faculty. This paper analyzes results from fall 2020 through fall 2021 to see if there is any difference between control and intervention sections for the courses as a whole and for demographic subgroups including female-identifying students and historically-underserved students of color. All courses were asynchronous online modality in the context of the COVID-19 pandemic. We find that students in intervention sections of calculus made slightly larger gains on the PSVT:R, but this result is not statistically significant as a whole or for any of the demographic subgroups considered. We also analyzed final course grades for differences between control and intervention sections and found no differences. We found no significant effect of the presence of the model-based activities leading to increased PSVT:R gains or improved course grades. We would not extend this conclusion to face-to-face implementation, however, due primarily to the compromises made to adapt the curriculum from in-person group learning to asynchronous individual work and inconsistent engagement of the online students with the modeling activities. 

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5. Best 2019 PIC III Paper: Do They Understand Your Language? Access Their Fluency with Vector Representation

   https://doi.org/10.18260/1-2--34205  

   Davishahl, Eric; Haskell, Todd; Davishahl, Jill; Singleton, Lee; Goodridge, Wade (June 2020, 2020 ASEE Virtual Annual Conference Content Access)

   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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