The Modeling Instruction program at Arizona State University has developed a representational tool, called a system schema, to help students make a first level of abstraction of an actual physical situation [1]. A system schema consists of identifying and labeling all objects of interest from a given physical situation, as well as all the different types of interactions between the objects. Given all the relevant objects and their interactions, students can explicitly identify which are part of their system and which are not, and then go on to model the interactions affecting their choice of system as either (i) mechanisms for energy transfer, or (ii) forces being exerted. In this paper, I describe the system schema tool, give examples of its use in the context of forces, and present some evidence on its effectiveness in helping students understand Newton's Third Law.

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Abstract. After learning Newton's 2nd Law, students in a university modeling-based introductory physics class are asked to imagine a box sliding across a floor and slowing to a stop. Although they've had extensive experience with friction in the context of energy, this is their first exposure to friction within the context of force. They are asked to make different representations for this scenario, including a system schema, and force diagram. During their small group work, students quickly run into a difficulty: there are only two interactions with the box (contact, gravitational), so there should only be two forces, yet the box is slowing, which means it must have unbalanced forces in the direction of acceleration. In this paper, preliminary evidence from a student-led whole-class discussion is presented showing how the group reasons through sharp disagreement in their initial ideas to come to a useful consensus.

The upper level E&M course (i.e. based on Griffiths [1]) involves the extensive integration of vector calculus concepts and notation with abstract physics concepts like field and potential. We hope that students take what they have learned in their math classes and apply it to help represent and make sense of the physics. Previous work showed that physics majors at different levels (pre-E&M course, post-E&M course, 1st year graduate students) had great difficulty using non-Cartesian unit vector symbols appropriately in a particular context [2]. Since then we have developed a series of problems they work on in groups and discuss as a whole class [3] to help them confront and resolve some of their difficulties. This paper presents those problems, typical in-class group responses, and three years of post-test data. Results show that students have (i) a very strong initial negative reaction to the vagueness of ther symbol, and (ii) an improved functional understanding of the notation as demonstrated by a better ability to use the symbols appropriately.

This paper analyzes two examples of whiteboard meetings from a college calculus-based introductory physics course taught using University Modeling Instruction. In this pedagogy, students work in small groups to create a solution to the same problem on 2 × 3 whiteboards. They then sit in a large circle with their whiteboards held facing in and conduct a student-led whole-class discussion ("board" meeting) to reach a consensus. One example is given of a conversation where students overcame sharp disagreements to eventually reach whole-class consensus and another example is given where they did not. We examine how social positioning contributed to students either successfully examining and resolving different ideas or failing to do so. Initial results from two different "board" meetings tentatively support the idea that meetings where "experts" soften their position by "hedging" more frequently are better able to overcome sharp initial disagreements to reach consensus on their own. Our analysis suggests that the way students position themselves in discussions may open or close the collaborative space to productive sense-making.

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We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students to solve individually on their own, but which groups of students have been more successful at. Using think-aloud interviews with students in small groups, we ask them to solve together on a large whiteboard conceptual problems from this E&M context. The interviews were video and audio recorded, and qualitatively analyzed using an emergent coding method and the resources framework [4]. Through this analysis, we observed one common mechanism in all three group-interviews whereby students collaborated effectively: first one student activated a conceptual resource and expressed it, then another student took up that idea, and finally the whole group together used that idea to move forward with the problem. This mechanism exemplifies a newer framework: shared resources [12]. We further analyzed students' collaboration through the lens of shared resources and identified multiple instances. We propose that the shared resources construct could be a potential tool to help understand how students collaborate in solving conceptual physics problems. In this paper, we report our methodology and the results from one group interview to illustrate one shared resource we identified and the role it played in helping students collaboratively solve the conceptual problem in this context. Future work and implications for instruction are suggested.