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1. Feel the Force! An Inquiry-based Approach to Teaching Free-body Diagrams for Rigid-body Analysis

   https://doi.org/10.18260/1-2--34669  

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

   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. 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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3. 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 how 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. 

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4. Low-Barrier Strategies to Increase Student-Centered Learning Low-Barrier Strategies to Increase Student-Centered Learning

   Friend, Nicole Erin Woodcock ( July 2021 , ASEE annual conference exposition proceedings)

   Evidence has shown that facilitating student-centered learning (SCL) in STEM classrooms enhances student learning and satisfaction [1]–[3]. However, despite increased support from educational and government bodies to incorporate SCL practices [1], minimal changes have been made in undergraduate STEM curriculum [4]. Faculty often teach as they were taught, relying heavily on traditional lecture-based teaching to disseminate knowledge [4]. Though some faculty express the desire to improve their teaching strategies, they feel limited by a lack of time, training, and incentives [4], [5]. To maximize student learning while minimizing instructor effort to change content, courses can be designed to incorporate simpler, less time-consuming SCL strategies that still have a positive impact on student experience. In this paper, we present one example of utilizing a variety of simple SCL strategies throughout the design and implementation of a 4-week long module. This module focused on introductory tissue engineering concepts and was designed to help students learn foundational knowledge within the field as well as develop critical technical skills. Further, the module sought to develop important professional skills such as problem-solving, teamwork, and communication. During module design and implementation, evidence-based SCL teaching strategies were applied to ensure students developed important knowledge and skills within the short timeframe. Lectures featured discussion-based active learning exercises to encourage student engagement and peer collaboration [6]–[8]. The module was designed using a situated perspective, acknowledging that knowing is inseparable from doing [9], and therefore each week, the material taught in the two lecture sessions was directly applied to that week’s lab to reinforce students’ conceptual knowledge through hands-on activities and experimental outcomes. Additionally, the majority of assignments served as formative assessments to motivate student performance while providing instructors with feedback to identify misconceptions and make real-time module improvements [10]–[12]. Students anonymously responded to pre- and post-module surveys, which focused on topics such as student motivation for enrolling in the module, module expectations, and prior experience. Students were also surveyed for student satisfaction, learning gains, and graduate student teaching team (GSTT) performance. Data suggests a high level of student satisfaction, as most students’ expectations were met, and often exceeded. Students reported developing a deeper understanding of the field of tissue engineering and learning many of the targeted basic lab skills. In addition to hands-on skills, students gained confidence to participate in research and an appreciation for interacting with and learning from peers. Finally, responses with respect to GSTT performance indicated a perceived emphasis on a learner-centered and knowledge/community-centered approaches over assessment-centeredness [13]. Overall, student feedback indicated that SCL teaching strategies can enhance student learning outcomes and experience, even over the short timeframe of this module. Student recommendations for module improvement focused primarily on modifying the lecture content and laboratory component of the module, and not on changing the teaching strategies employed. The success of this module exemplifies how instructors can implement similar strategies to increase student engagement and encourage in-depth discussions without drastically increasing instructor effort to re-format course content. Introduction. 

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5. 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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