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Mechanics instructors frequently employ hands-on demonstrations and activities in hopes of improving student learning outcomes. This paper presents results from a study exploring the effectiveness of a hands-on statics curriculum that spans several topics and is designed for implementation over multiple weeks. The modeling kit and associated series of activities integrates conceptual exploration with analysis procedure tutorials and aims to scaffold students’ development of representational competence, their ability to use multiple representations of a concept as appropriate for learning, problem solving, and communication. We conducted this study over two subsequent fall terms in multiple sections of a statics course at a mid-size public university. The intervention sections in fall 2023 were taught by two instructors who were both using the modeling kit for the first time. Both instructors administered a test of 3D vector concepts and representations called the Test of Representational Competence with Vectors (TRCV) in weeks 1 and at mid-term, the Mental Cutting Test (MCT) for spatial abilities in weeks 1 and at end-of-term (nine weeks later), and the Concept Assessment Test in Statics (CATS) at end of term. The control sections were taught by the same two instructors in fall 2022. These sections administered the same assessments on the same schedule but did not use the hands-on curriculum. We compare learning outcomes between the control and intervention sections as measured by the scores on the assessments described above as well as final course grades. We also share reflections from the two faculty participants regarding their experiences teaching with the models. 

This NSF-IUSE exploration and design project began in Fall 2018 and features cross-disciplinary collaboration between engineering, math, psychology, and math education faculty to develop learning activities with 3D-printed models for integral calculus and engineering statics. We are exploring how such models can scaffold spatial abilities and support learners’ development of conceptual understanding and representational competence. 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. After a year of classroom implementation and data collection at the institution where the curriculum was developed, the project team recruited math and engineering faculty from three other colleges to pilot the models starting Fall 2020. The goal of this expansion was to increase sample sizes and diversity for statistical analysis of classroom data and to learn about the experiences of faculty as they integrated the curriculum materials into their own courses. The original vision was for faculty to use the models in face-to-face instruction, but the transition to online modality in response to the COVID-19 pandemic forced a rapid pivot during this expansion that we reported on previously. Faculty participants who chose to continue with the project worked to incorporate the models in parallel with their respective efforts to adapt to online teaching. This poster focuses on the experiences of the participating math faculty. Ultimately these faculty taught online calculus courses both with and without the models from Fall 2020 through Spring 2022. We conducted pre and post participation interviews and report on their experiences. All participants reported their intention to continue to use the models beyond conclusion of the project and planned to try them in face-to-face instruction. The paper will discuss more details about the interview findings and conclude by making some recommendations for others who may be interested in exploring the use of hands-on models in Calculus instruction. 

This paper describes the results from an ongoing project where hands-on models and associated activities are integrated throughout an undergraduate statics course with the goal of deepening students’ conceptual understanding, scaffolding spatial skills, and therefore developing representational competence with foundational concepts such as vectors, forces, moments, and free-body diagrams. Representational competence refers to the fluency with which a subject expert can move between different representations of a concept (e.g. mathematical, symbolic, graphical, 2D vs. 3D, pictorial) as appropriate for communication, reasoning, and problem solving. This study sought to identify the characteristics of modeling activities that make them effective for all learners. Student volunteers engaged in individual interviews in which they solved problems that included 2D diagrams, 3D models, and worked calculations. Participating students had prior experience with the models and related activity sheets earlier in the course. Data was collected at the end of the quarter and the activities emphasized conceptual understanding. Thematic analysis was used to develop codes and identify themes in students’ use of the models as it relates to developing representational competence. Students used the models in a variety of ways. They wrote directly on the models, touched and gestured with the model, adjusted components, and observed the model from multiple orientations. They added new elements and deconstructed the models to feel the force or imagine how measurements would be impacted if one parameter was changed while all others held constant. In interviews students made connections to previous courses as well as previous activities and experiences with the models. In addition to using the 3D models, participants also used more than one representation (e.g. symbolic or 2D diagram) to solve problems and communicate thinking. While the use of models and manipulatives is commonplace in mechanics instruction, this work seeks to provide more nuanced information about how students use these learning aids to develop and reinforce their own understanding of key concepts. The authors hope these findings will be useful for others interested in designing and refining hands-on mechanics activities toward specific learning goals.