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1. 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)

   null (Ed.)

   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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2. WIP: Using Machine Learning to Automate Coding of Student Explanations to Challenging Mechanics Concept Questions

   Harpreet Auby; Namrata Shivagunde; Anna Rumshisky; Milo Koretsky (June 2022, ASEE Annual Conference proceedings)

   This work-in-progress paper describes a collaborative effort between engineering education and machine learning researchers to automate analysis of written responses to conceptually challenging questions in mechanics. These qualitative questions are often used in large STEM classes to support active learning pedagogies; they require minimum calculations and focus on the application of underlying physical phenomena to various situations. Active learning pedagogies using this type of questions has been demonstrated to increase student achievement (Freeman et al., 2014; Hake, 1998) and engagement (Deslauriers, et al., 2011) of all students (Haak et al., 2011). To emphasize reasoning and sense-making, we use the Concept Warehouse (Koretsky et al., 2014), an audience response system where students provide written justifications to concept questions. Written justifications better prepare students for discussions with peers and in the whole class and can also improve students’ answer choices (Koretsky et al., 2016a, 2016b). In addition to their use as a tool to foster learning, written explanations can also provide valuable information to concurrently assess that learning (Koretsky and Magana, 2019). However, in practice, there has been limited deployment of written justifications with concept questions, in part, because they provide a daunting amount of information for instructors to process and for researchers to analyze. In this study, we describe the initial evaluation of large pre-trained generative sequence-to-sequence language models (Raffel et al., 2019; Brown et al., 2020) to automate the laborious coding process of student written responses. Adaptation of machine learning algorithms in this context is challenging since each question targets specific concepts which elicit their own unique reasoning processes. This exploratory project seeks to utilize responses collected through the Concept Warehouse to identify viable strategies for adapting machine learning to support instructors and researchers in identifying salient aspects of student thinking and understanding with these conceptually challenging questions. 

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3. Getting Your Hands Dirty in Integral Calculus

   https://doi.org/10.18260/1-2--34707  

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

   The landscapes of many elementary, middle, and high school math classrooms have undergone major transformations over the last half-century, moving from drill-and-skill work to more conceptual reasoning and hands-on manipulative work. However, if you look at a college level calculus class you are likely to find the main difference is the professor now has a whiteboard marker in hand rather than a piece of chalk. It is possible that some student work may be done on the computer, but much of it contains the same type of repetitive skill building problems. This should seem strange given the advancements in technology that allow more freedom than ever to build connections between different representations of a concept. Several class activities have been developed using a combination of approaches, depending on the topic. Topics covered in the activities include Riemann Sums, Accumulation, Center of Mass, Volumes of Revolution (Discs, Washers, and Shells), and Volumes of Similar Cross-section. All activities use student note outlines that are either done in a whole group interactive-lecture approach, or in a group work inquiry-based approach. Some of the activities use interactive graphs designed on desmos.com and others use physical models that have been designed in OpenSCAD and 3D-printed for students to use in class. Tactile objects were developed because they should provide an advantage to students by enabling them to physically interact with the concepts being taught, deepening their involvement with the material, and providing more stimuli for the brain to encode the learning experience. Web-based activities were developed because the topics involved needed substantial changes in graphical representations (i.e. limits with Riemann Sums). Assessment techniques for each topic include online homework, exams, and online concept questions with an explanation response area. These concept questions are intended to measure students’ ability to use multiple representations in order to answer the question, and are not generally computational in nature. Students are also given surveys to rate the overall activities as well as finer grained survey questions to try and elicit student thoughts on certain aspects of the models, websites, and activity sheets. We will report on student responses to the activity surveys, looking for common themes in students’ thoughts toward specific attributes of the activities. We will also compare relevant exam question responses and online concept question results, including common themes present or absent in student reasoning. 

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4. 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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5. A Bayesian Hierarchical Model for Extracting Individuals' Theory-based Causal Knowledge

   https://doi.org/10.1115/1.4055596  

   Hans, Atharva; Chaudhari, Ashish M.; Bilionis, Ilias; Panchal, Jitesh H. (September 2022, Journal of Computing and Information Science in Engineering)

   Abstract Extracting an individual's scientific knowledge is essential for improving educational assessment and understanding cognitive tasks in engineering activities such as reasoning and decision making. However, knowledge extraction is an almost impossible endeavor if the domain of knowledge and the available observational data are unrestricted. The objective of this paper is to quantify individuals' theory-based causal knowledge from their responses to given questions. Our approach uses directed acyclic graphs (DAGs) to represent causal knowledge for a given theory and a graph-based logistic model that maps individuals' question-specific subgraphs to question responses. We follow a hierarchical Bayesian approach to estimate individuals' DAGs from observations.The method is illustrated using 205 engineering students' responses to questions on fatigue analysis in mechanical parts. In our results, we demonstrate how the developed methodology provides estimates of population-level DAG and DAGs for individual students. This dual representation is essential for remediation since it allows us to identify parts of a theory that a population or individual struggles with and parts they have already mastered. An addendum of the method is that it enables predictions about individuals' responses to new questions based on the inferred individual-specific DAGs. The latter has implications for the descriptive modeling of human problem-solving, a critical ingredient in sociotechnical systems modeling. 

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