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Abstract Title: Contrasting Cases and Invention Activities in PER: Grounding students' understanding of conceptual and mathematical relations in physical contexts
Abstract: Recent research has demonstrated the learning benefits of having students generate their own representations and explanations of phenomena.  This session will showcase the use of contrasting cases to guide student-generated connections between mathematical structures and physics problem contexts.  Contrasting cases are sets of examples having a common underlying structure but varying surface features.  The structure can highlight mathematical rules, physical concepts, or problem-solving approaches.  Typically, learners examine the cases to generate a rule or index that represents the underlying structure. Contrasting cases provide a basis for testing predictions, and show the range of situations to which rules should apply.  In this symposium, the speakers will describe different approaches to using contrasting cases and invention activities to promote deep understanding.  The talks will span classroom and laboratory settings, discuss various principles for design and implementation, and illustrate how contrasting cases can help students learn mathematical principles in physics.
Abstract Type: Talk Symposium

Author/Organizer Information

Primary Contact: Nicole Hallinen
Temple University

Symposium Specific Information

Presentation 1 Title: Choosing the right examples: How contrasting cases can affect learning and future learning
Presentation 1 Authors: Nicole R. Hallinen, Temple University
Daniel L. Schwartz, Stanford University
Presentation 1 Abstract: Inventing with contrasting cases is effective for helping students notice functional relations.  However, instructors may need more guidance about selecting cases for instruction.  In two-factor relations, cases could show main effects of each variable or their interaction.  In a series of studies, community college students invented explanations for two-dimensional inelastic collisions.  Some received cases isolating main effects, which led to a qualitative understanding.  Others who saw cases where mass and speed trade off were more likely to find a multiplicative solution, receiving higher posttest scores.  On a transfer task, all participants received balance scale contrasting cases showing enough variation that qualitative rules would not be sufficient.  Participants who used the simplified momentum materials learned less from the transfer balance scale cases, even performing lower than control students who did not do the momentum activity. I will discuss the effects of contrasting cases on both learning and transfer to future learning.
Presentation 2 Title: Using contrasting cases to support strategic mathematization: Coordinate system rotation
Presentation 2 Authors: Thanh K. LĂȘ, Jonathan T. Shemwell, and MacKenzie R. Stetzer
University of Maine
Presentation 2 Abstract: Being strategic when mathematizing physical situations is an important part of thinking like a physicist. Otherwise, students may be guided by surface features, resulting in non-optimal mathematization decisions. We investigated how students can learn to optimize the rotation of a coordinate system in static equilibrium problems to yield the simplest mathematical expression, despite surface features suggesting non-optimal rotation.  In an experiment, introductory physics college students used contrasting cases to abstract a rule for strategic rotation that would be independent of surface features. There were two sets of cases. After a pretest, half of the students processed one set of cases, while the other half processed both sets.  On a post-test, all students improved in their ability to strategically optimize coordinate rotation, despite distracting surface features. Students who processed both sets of cases made larger improvements. Our results suggest that students learned to separate strategy-guiding information from distracting surface features.
Presentation 3 Title: A Distant Look at a Water Lily Pond: Inventing Physics Rules from Interactive Simulation or Contrasting Cases
Presentation 3 Authors: Shima Salehi, Stanford University
Martin Francis Keil, Stanford University
Eric Kuo, University of Pittsburgh
Carl Wieman, Stanford University
Presentation 3 Abstract: Studies show that having students attempt to invent a scientific rule before receiving direct instruction benefits their learning. However, "what kinds of invention activities aid learning?" is a question subject to further research. Here, we compare two different invention activities for learning about buoyancy. In one treatment condition, students explored a PhET simulation to invent a buoyancy rule. In another condition, students invented the rule from several contrasting cases of objects sinking or floating in a fluid. In general, students using contrasting cases invented more complete rules and performed significantly better in solving buoyancy problems. In the simulation condition, students risked not exploring all of the simulation's features, inventing a solution before they'd seen all facets of a phenomenon.  These results show that the benefits of invention activities depend on scaffolding that helps expose students to the underlying structure of a phenomenon.
Presentation 4 Title: Impact of Various Contrasting Case Scaffolds on Students' Problem Solving
Presentation 4 Authors: Marianna Lamnina, Teacher's College, Columbia University
Helena Connolly, Teacher's College, Columbia University
Vincent Aleven, Carnegie Mellon University
Catherine C. Chase, Teacher's College, Columbia University
Presentation 4 Abstract: This work explores ways to scaffold Invention activities to facilitate productive exploration of ratio structures in physical science equations, the goal of which is to prepare students to learn from later expository instruction.  We have developed the first computerized Invention Coach that provides adaptive guidance as middle school students work through Invention tasks.  This talk will discuss the rationale behind our novel pedagogical model, which draws upon empirical studies of human teachers guiding Invention and earlier prototype versions of our Coach, as well as prior research on the core learning processes that Invention promotes.  Preliminary findings from a classroom study of the Invention Coach shed light on the process of guided Invention and provide some evidence of the system's efficacy in enhancing conceptual learning and transfer.
Presentation 5 Title: Promoting Student Mathematization using Physics Invention Tasks
Presentation 5 Authors: Andrew Boudreaux, Western Washington University
Suzanne White Brahmia, University of Washington
Stephen E. Kanim, New Mexico State University
Presentation 5 Abstract: Physics experts develop ideas through mathematization, reasoning that connects the physical and symbolic worlds. Research has shown that students often struggle with the idiosyncratic ways that mathematics is used in physics. Other work has shown that invention tasks can help students use math productively in science and statistics.  This presentation describes our physics invention tasks, classroom activities designed to support construction of quantitative physics concepts and relationships and to prepare students to understand subsequent formal instruction. These tasks present contrasting cases, and ask students to invent a way to characterize the system according to some key property. We will share examples of physics invention tasks as well as assessment data from a preliminary study of the impact on student learning.
Presentation 6 Title: Impact of Various Contrasting Case Scaffolds on Students' Problem Solving
Presentation 6 Authors: Carina M. Rebello, David M. Beardmore, & Bryce A. Towle, Purdue University
Presentation 6 Abstract: Prior studies reveal that both contrasting cases and argumentation tasks can support deeper learning and problem solving skills. Yet, studies suggest that appropriate scaffolds are needed for these instructional strategies to be successful. We investigate three alternative forms of writing prompts (similarities and differences, invent a unified explanation, and argumentation) for multiple cases that address the momentum and energy principles. These scaffolds were integrated within physics problems utilized during calculus-based physics recitations, and we assessed their impact on students' learning. Results suggest that prompts for identifying similarities and differences within cases tended to promote identification of surface features in ways that were irrelevant to solving all case problems. However, argumentation prompts to evaluate competing theories tended to support deeper understanding of underlying principles and appropriate application of principles.