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1. Feel the force! An inquiry-based approach to teaching free-body diagrams for rigid body analysis

   Davishahl, Eric ; Haskell, Todd ; Singleton, Lee W. ( January 2020 , ASEE annual conference exposition)

   Perusal of any common statics textbook will reveal a reference table of standard supports in the section introducing rigid body equilibrium analysis. Most statics students eventually memorize a heuristic approach to drawing a free-body diagram based on applying the information in this table. First, identify the entry in the table that matches the schematic representation of a connection. Then draw the corresponding force and/or couple moment vectors on the isolated body according to their positive sign conventions. Multiple studies have noted how even high performing students tend to rely on this heuristic rather than conceptual reasoning. Many students struggle when faced with a new engineering connection that does not match an entry in the supports table. In this paper, we describe an inquiry-based approach to introducing support models and free body diagrams of rigid bodies. In a series of collaborative learning activities, students practice reasoning through the force interactions at example connections such as a bolted flange or a hinge by considering how the support resists translation and rotation in each direction. Each team works with the aid of a physical model to analyze how changes in the applied loads affect the reaction components. A second model of the isolated body provides opportunity to develop a tactile feel for the reaction forces. We emphasize predicting the direction of each reaction component, rather than following a standard sign convention, to provide opportunities for students to practice conceptual application of equilibrium conditions. Students’ also draw detailed diagrams of the force interactions at the mating surfaces in the connection, including distributed loadings when appropriate. We use equivalent systems concepts to relate these detailed force diagrams to conventional reaction components. Targeted assessments explore whether the approach described above might improve learning outcomes and influence how students think about free-body diagrams. Students use an online tool to attempt two multiple-choice concept questions after each activity. The questions represent near and far transfer applications of the concepts emphasized and prompt students for written explanation. Our analysis of the students’ explanations indicates that most students engage in the conceptual reasoning we encourage, though reasoning errors are common. Analysis of final exam work and comparison to an earlier term in which we used a more conventional approach indicate a majority of students incorporate conceptual reasoning practice into their approach to free-body diagrams. This does not come at the expense of problem-solving accuracy. Student feedback on the activities is overwhelmingly positive. 

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2. Board 418: Understanding Context: Propagation and Effectiveness of the Concept Warehouse in Mechanical Engineering at Five Diverse Institutions and Beyond – Results from Year 4

   Self, B. P. ; Koretsky, M. ; Nolen, S. B. ; Dal Bello, D. J. ; Widmann, J. M. ; Prince, M. J. ; Papadopoulos, C. ( June 2023 , 2023 ASEE Annual Conference & Exposition)

   Several consensus reports cite a critical need to dramatically increase the number and diversity of STEM graduates over the next decade. They conclude that a change to evidence-based instructional practices, such as concept-based active learning, is needed. Concept-based active learning involves the use of activity-based pedagogies whose primary objectives are to make students value deep conceptual understanding (instead of only factual knowledge) and then to facilitate their development of that understanding. Concept-based active learning has been shown to increase academic engagement and student achievement, to significantly improve student retention in academic programs, and to reduce the performance gap of underrepresented students. Fostering students' mastery of fundamental concepts is central to real world problem solving, including several elements of engineering practice. Unfortunately, simply proving that these instructional practices are more effective than traditional methods for promoting student learning, for increasing retention in academic programs, and for improving ability in professional practice is not enough to ensure widespread pedagogical change. In fact, the biggest challenge to improving STEM education is not the need to develop more effective instructional practices, but to find ways to get faculty to adopt the evidence-based pedagogies that already exist. In this project we seek to propagate the Concept Warehouse, a technological innovation designed to foster concept-based active learning, into Mechanical Engineering (ME) and to study student learning with this tool in five diverse institutional settings. The Concept Warehouse (CW) is a web-based instructional tool that we developed for Chemical Engineering (ChE) faculty. It houses over 3,500 ConcepTests, which are short questions that can rapidly be deployed to engage students in concept-oriented thinking and/or to assess students’ conceptual knowledge, along with more extensive concept-based active learning tools. The CW has grown rapidly during this project and now has over 1,600 faculty accounts and over 37,000 student users. New ConcepTests were created during the current reporting period; the current numbers of questions for Statics, Dynamics, and Mechanics of Materials are 342, 410, and 41, respectively. A detailed review process is in progress, and will continue through the no-cost extension year, to refine question clarity and to identify types of new questions to fill gaps in content coverage. There have been 497 new faculty accounts created after June 30, 2018, and 3,035 unique students have answered these mechanics questions in the CW. We continue to analyze instructor interviews, focusing on 11 cases, all of whom participated in the CW Community of Practice (CoP). For six participants, we were able to compare use of the CW both before and after participating in professional development activities (workshops and/or a community or practice). Interview results have been coded and are currently being analyzed. To examine student learning, we recruited faculty to participate in deploying four common questions in both statics and dynamics. In statics, each instructor agreed to deploy the same four questions (one each for Rigid Body Equilibrium, Trusses, Frames, and Friction) among their overall deployments of the CW. In addition to answering the question, students were also asked to provide a written explanation to explain their reasoning, to rate the confidence of their answers, and to rate the degree to which the questions were clear and promoted deep thinking. The analysis to date has resulted in a Work-In-Progress paper presented at ASEE 2022, reporting a cross-case comparison of two instructors and a Work-In-Progress paper to be presented at ASEE 2023 analyzing students’ metacognitive reflections of concept questions. 

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3. WIP Toward a Free-Body Diagram Mobile Application

   Sloboda, A. R. ; Wodin-Schwartz, S. ; Lechasseur, K. ; deWinter, J. ( June 2023 , ASEE annual conference exposition proceedings)

   No skill is more important for a student of mechanics than the ability to draw a complete and accurate free-body diagram (FBD). A good FBD facilitates proper accounting of forces when writing the balances that lead to governing equations in statics, solid mechanics, and dynamics. Because this skill is essential, educational approaches that improve the ability of students to draw correct FBDs are critical for maximizing the potential of the next generation of engineers. Traditionally, learning to draw FBDs involves classroom instruction followed by homework practice consisting of problems drawn from a textbook. Homework as practice does not serve all students well, because it does not scaffold the process of drawing FBDs in terms of distinct tasks (e.g., isolating the body, considering support reactions) nor does it offer immediate feedback, which students often need to avoid falling into the same error repeatedly. To address these shortcomings, we embarked on the design, implementation, and testing of a mobile application (app) that offers an alternative venue for FBD practice. The app provides students with asynchronous opportunities for training, varied tasks that target specific FBD issues, and several levels of immediate feedback. We hypothesize that the gamified environment and puzzle-based gameplay will improve student skill and self-efficacy in drawing FBDs, particularly for women, who may feel less confident in their spatial skills. Data collected to describe student experiences may also provide additional insight into how to improve FBD instruction generally. In this paper, we detail the process for designing and implementing the app and provide initial data regarding student impressions and use. The app was piloted in Fall 2022 in a large Introduction to Statics course as a non-graded study activity; all students except one (n=97) participated in an evaluation of its design features and user experiences. Approximately half (54%) of students indicated they had played half or more of the available games. When commenting about how the FBD app did, or did not, help their learning, 49% of respondents appreciated that the app allowed additional opportunities for practice. Students used these opportunities to further develop several skills, such as visualizing the system and setting up accurate diagrams, which strengthened their confidence and reviewed key concepts. While describing the value of practicing through the app, 21% of students called out how the app provided feedback. They specifically mentioned the positive experiences of receiving feedback that is immediate, that explains boundary connections, and that deepens learning after mistakes are made. These and other findings from the pilot study are discussed with corresponding next steps for development. 

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4. WIP Toward a Free-Body Diagram Mobile Application

   Sloboda, A. R. ; & Wodin-Schwartz, S. ; & Lechasseur, K. ; deWinter, J. ( June 2023 , ASEE annual conference exposition proceedings)

   No skill is more important for a student of mechanics than the ability to draw a complete and accurate free-body diagram (FBD). A good FBD facilitates proper accounting of forces when writing the balances that lead to governing equations in statics, solid mechanics, and dynamics. Because this skill is essential, educational approaches that improve the ability of students to draw correct FBDs are critical for maximizing the potential of the next generation of engineers. Traditionally, learning to draw FBDs involves classroom instruction followed by homework practice consisting of problems drawn from a textbook. Homework as practice does not serve all students well, because it does not scaffold the process of drawing FBDs in terms of distinct tasks (e.g., isolating the body, considering support reactions) nor does it offer immediate feedback, which students often need to avoid falling into the same error repeatedly. To address these shortcomings, we embarked on the design, implementation, and testing of a mobile application (app) that offers an alternative venue for FBD practice. The app provides students with asynchronous opportunities for training, varied tasks that target specific FBD issues, and several levels of immediate feedback. We hypothesize that the gamified environment and puzzle-based gameplay will improve student skill and self-efficacy in drawing FBDs, particularly for women, who may feel less confident in their spatial skills. Data collected to describe student experiences may also provide additional insight into how to improve FBD instruction generally. In this paper, we detail the process for designing and implementing the app and provide initial data regarding student impressions and use. The app was piloted in Fall 2022 in a large Introduction to Statics course as a non-graded study activity; all students except one (n=97) participated in an evaluation of its design features and user experiences. Approximately half (54%) of students indicated they had played half or more of the available games. When commenting about how the FBD app did, or did not, help their learning, 49% of respondents appreciated that the app allowed additional opportunities for practice. Students used these opportunities to further develop several skills, such as visualizing the system and setting up accurate diagrams, which strengthened their confidence and reviewed key concepts. While describing the value of practicing through the app, 21% of students called out how the app provided feedback. They specifically mentioned the positive experiences of receiving feedback that is immediate, that explains boundary connections, and that deepens learning after mistakes are made. These and other findings from the pilot study are discussed with corresponding next steps for development.   

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5. 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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