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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 bodymore »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.« less
2. 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
3. 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.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
4. Toward Benchmarking Student Progress in Mechanics: Assessing Learning Cycles through Mastery Learning and Concept Questions

   Papadopoulos, C. ; Santiago-Román, A. I. ; Hillman, E. F. ; Figueroa, G. L. ; Vega Morales, I. ( July 2021 , ASEE Virtual Annual Conference)

   In mechanics, the standard 3-credit, 45-hour course is sufficient to deliver standard lectures with prepared examples and questions. Moreover, it is not only feasible, but preferable, to employ any of a variety of active learning and teaching techniques. Nevertheless, even when active learning is strategically used, students and instructors alike experience pressure to accomplish their respective learning and teaching goals under the constraints of the academic calendar, raising questions as to whether the allocated time is sufficient to enable authentic learning. One way to assess learning progress is to examine the learning cycles through which students attempt, re-think, and re-attempt their work. This article provides data to benchmark the time required to learn key Statics concepts based on results of instruction of approximately 50 students in a Statics class at a public research university during the Fall 2020 semester. Two parallel techniques are employed to foster and understand student learning cycles. • Through a Mastery Based Learning model, 15 weekly pass/fail “Mastery Tests” are given. Students who do not pass may re-test with a different but similar test on the same topic each week until the semester’s conclusion. The tests are highly structured in that they are well posed andmore »highly focused. For example, some tests focus only on drawing Free Body Diagrams, with no equations or calculations. Other tests focus on writing equilibrium equations from a given Free Body Diagram. Passing the first six tests is required to earn the grade of D; passing the next three for C; the next three for B; and the final three for A. Evaluations include coding of student responses to infer student reasoning. Learning cycles occur as students repeat the same topics, and their progress is assessed by passing rates and by comparing evolving responses to the same test topics. • Concept Questions that elicit qualitative responses and written explanations are deployed at least weekly. The learning cycle here consists of students answering a question, seeing the overall class results (but without the correct answer), having a chance to explore the question with other students and the instructor, and finally an opportunity to re-answer the same question, perhaps a few minutes or up to a couple days later. Sometimes, that same question is given a third time to encourage further effort or progress. To date, results from both cycles appear to agree on one important conclusion: the rate of demonstrated learning is quite low. For example, each Mastery Test has a passing rate of 20%-30%, including for students with several repeats. With the Concept Questions, typically no more than half of the students who answered incorrectly change to the correct answer by the time of the final poll. The final article will provide quantitative and qualitative results from each type of cycle, including tracking coded responses on Mastery Tests, written responses on Concept Questions, and cross-comparisons thereof. Additional results will be presented from student surveys. Since the Mastery Tests and Concept Questions follow typical Statics topics, this work has potential to lead to a standardized set of benchmarks and standards for measuring student learning – and its rate – in Statics.« less
5. Results of an Intro to Mechanics Course Designed to Support Student Success in Physics I and Foundational Engineering Courses

   Menezes, Gustavo B. ; Nerenberg, Paul S. ; Li, Ni ; Allen, Emily L. ( June 2020 , ASEE Annual Conference Proceedings)

   This complete evidence-based practice paper discusses the strategies and results of an introduction to mechanics course, designed to prepare students for introductory-level physics and other fundamental courses in engineering, such as statics, strength of materials, and dynamics. The course was developed to address historically high failure (DFW) rates in the physics courses and is part of a set of interventions implemented to support student success in a college of engineering and computer science. The course focuses on providing in-depth understanding of Newton’s Laws of motion, free-body diagrams, and linear and projectile motion. Because it focuses on a limited number of competencies, it is possible to spend more time on inquiry-based activities and in-class discussions. The course framework was designed considering the Ebbinghaus’ Forgetting Curve, to provide students with learning opportunities in 6-day cycles: (i) day 1: a pre-class learning activity (reading or video) and a quiz; (ii) day 2: in-class Kahoot low-stakes quiz with discussion, a short lecture with embedded time for problem-solving and discussion, and in-class activities (labs, group projects); (iii) day 4: homework due two days after the class; (iv) day 6: homework self-reflection (autopsy based on provided solutions) two days after homework is due. The assessment ofmore »course performance is based on the well-characterized force concept inventory (FCI) exam that is administered before the intro to mechanics course and both before and after the Physics I course; and on student performance (grades) in Physics and Statics courses. Results from the FCI pre-test show that students who took the introduction to mechanics course (treatment group) started the physics course with a much better understanding of force concepts than other students in the course. The FCI post-test shows better normalized gain for the treatment group, compared to other students, which is also aligned with student performance in the course. Additionally, student performance is significantly better in statics, with 25% DWF rate compared to 50% for the other students. In summary, the framework of the course, which focuses on providing students with in-depth understanding of force concepts, has led to better learning and performance in Physics I, but importantly it has also helped students achieve better performance in the Statics course, the first fundamental course in civil and mechanical engineering programs.« less