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.

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.

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