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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.
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Making expert cognitive processes visible: planning and preliminary analysis in theoretical physics research
Many of the activities and cognitive processes that physicists use while solving problems are "invisible" to students, which can hinder their acquisition of important expert-like skills. Whereas the detailed calculations performed by researchers are often published in journals and textbooks, other activities such as those undertaken while planning how to approach a problem are rarely discussed in published research. Hence, these activities are especially hidden from students. To better understand how physicists solve problems in their professional research, we leveraged the framework of cognitive task analysis to conduct semi-structured interviews with theoretical physicists (N=11). Here we elucidate the role of planning and preliminary analysis in theorists' work. Theorists described using a variety of activities in order to decide if their project was doable while also generating possible solution paths. These actions included doing cursory calculations, reflecting on previous knowledge, gaining intuition and understanding by studying prior work, and reproducing previous results. We found that theorists typically did not pursue projects unless they had a clear idea of what the outcome of their project would be, or at least knew that they would be able to make progress on the problem. Thus, this preliminary design and analysis phase was highly important for theorists despite being largely hidden from students. We conclude by suggesting potential ways to incorporate our findings into the classroom to give students more numerous opportunities to engage in these expert-like practices.
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- Award ID(s):
- 1846321
- PAR ID:
- 10409048
- Editor(s):
- Frank, Brian W.; Jones, Dyan L.; Ryan, Qing X.
- Date Published:
- Journal Name:
- Physics Education Research Conference 2022
- Page Range / eLocation ID:
- 469 to 474
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1119/perc.2022.pr.Verostek
