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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.more »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.« less
2. 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 commonlymore »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.« less
3. Do They Understand Your Language? Assess Their Fluency with Vector Representations

   Davishahl, E. ; Haskell, T. R. ; Davishahl, J. ; Singleton, L. ; Goodridge, W. H. ( June 2019 , ASEE Annual Conference proceedings)

   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 commonlymore »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.« less
4. WIP: Hands-On Statics in the Online “Classroom”

   Davishahl, Eric ; Self, Brian P. ; Fuentes, Mathew Parsons ( July 2021 , 2021 ASEE Virtual Annual Conference Content Access)

   Engineering instructors often use physical manipulatives such as foam beams, rolling cylinders, and large representations of axis systems to demonstrate mechanics concepts and help students visualize systems. Additional benefits are possible when manipulatives are in the hands of individual students or small teams of students who can explore concepts at their own pace and focus on their specific points of confusion. Online learning modalities require new strategies to promote spatial visualization and kinesthetic learning. Potential solutions include creating videos of the activities, using CAD models to demonstrate the principles, programming computer simulations, and providing hands-on manipulatives to students for at-home use. This Work-in-Progress paper discusses our experiences with this last strategy in statics courses two western community colleges and a western four-year university where we supplied students with their own hands-on kits. We have previously reported on the successful implementation of a hands-on statics kit consisting of 3D printed components and standard hardware. The kit was originally designed for use by teams of students during class to engage with topics such as vectors, moments, and rigid body equilibrium. With the onset of the COVID-19 pandemic and shift to online instruction, the first author developed a scaled down version of themore »kit for at-home use by individual students and modified the associated activity worksheets accordingly. For the community college courses, local students picked up their models at the campus bookstore. We also shipped some of the kits to students who were unable to come to campus, including some in other countries. Due to problems with printing and availability of materials, only 18 kits were available for the class of 34 students at the university implementation. Due to this circumstance, students were placed in teams and asked to work together virtually, one student showing the kit to the other student as they worked through the worksheet prompts. One community college instructor took this approach as well for a limited number of international students who did not receive their kits in a timely manner due to shipping problems. Two instructors assigned the hands-on kits as asynchronous learning activities in their respective online courses, with limited guidance on their use. The third used the kits primarily in synchronous online class meetings. We found that students’ reaction to the models varied by pilot site and presume that implementation differences contributed to this variation. In all cases, student feedback was less positive than it has been for face-to-face courses that used the models from which the take home kit was adapted. Our main conclusion is that implementation matters. Doing hands-on learning in an online course requires some fundamental rethinking about how the learning is structured and scaffolded.« less
5. Engaging STEM Learners with Hands-on Models to Build Representational Competence

   https://doi.org/10.18260/1-2--34541  

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

   Modern 3D printing technology makes it relatively easy and affordable to produce physical models that offer learners concrete representations of otherwise abstract concepts and representations. We hypothesize that integrating hands-on learning with these models into traditionally lecture-dominant courses may help learners develop representational competence, the ability to interpret, switch between, and appropriately use multiple representations of a concept as appropriate for learning, communication and analysis. This approach also offers potential to mitigate difficulties that learners with lower spatial abilities may encounter in STEM courses. Spatial thinking connects to representational competence in that internal mental representations (i.e. visualizations) facilitate work using multiple external representations. A growing body of research indicates well-developed spatial skills are important to student success in many STEM majors, and that students can improve these skills through targeted training. 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 3D-printed models, build the theoretical basis for how they support learning, and assess their effectiveness in the classroom. We are exploring how such models can support learners’ development of conceptual understanding and representational competence in calculus and engineering statics. We are also exploring howmore »to leverage the model-based activities to embed spatial skills training into these courses. The project is addressing these questions through parallel work piloting model-based learning activities in the classroom and by investigating specific attributes of the activities in lab studies and focus groups. To date we have developed and piloted a mature suite of activities covering a variety of topics for both calculus and statics. Class observations and complementary studies in the psychology lab are helping us develop a theoretical framework for using the models in instruction. Close observation of how students use the models to solve problems and as communication tools helps identify effective design elements. We are administering two spatial skills assessments as pre/post instruments: the Purdue Spatial Visualizations Test: Rotations (PSVT:R) in calculus; and the Mental Cutting Test (MCT) in statics. We are also developing strategies and refining approaches for assessing representational competence in both subject areas. Moving forward we will be using these assessments in intervention and control sections of both courses to assess the effectiveness of the models for all learners and subgroups of learners.« less