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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 and 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. 

The shift to remote teaching with the COVID-19 pandemic has made delivery of concept- based active learning more challenging, especially in large-enrollment engineering classes. I report here a modification in the Concept Warehouse to support delivery of concept questions. The new feature allows instructors to make students’ reasoning visible to other students by showing selected written explanations to conceptually challenging multiple-choice questions. Data were collected for two large-enrollment engineering classes where examples are shown to illustrate how displaying written explanations can provide a resource for students to develop multi-variate reasoning skills 

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.