We investigate if the visual representation of vectors can affect which methods students use to add them. We gave students one of four questions with different graphical representations, asking students to add the same two vectors. For students in an
algebra-based class the arrangement of the vectors had a statistically significant effect on the vector addition method chosen while the addition or removal of a grid did not.
Students in interviews on a wave physics topic give answers through embodied actions which connect their understanding of the physics to other common experiences. When answering a question about wavepulses propagating along a long taut spring, studen
ts gestures help them recruit information about balls thrown the air. I analyze gestural, perceptual, and verbal information gathered using videotaped interviews and classroom interactions. I use conceptual blending to describe how different elements combine to create new, emergent meaning for the students and compare this to a knowledge-in-pieces approach.
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games as partic
ular pathways of solutions along resource graphs containing linked procedural and conceptual resources. Using transcript data, we define several procedural resources, show how they can be organized into two facets of a previously described epistemic game, and produce a resource graph that allows visualization of this portion of the epistemic games. By representing two correct mathematical procedures in terms of shared resources, we help clarify the types of thinking in which students engage when learning to apply mathematical reasoning to physics and illustrate how a failure to connect two ideas often hinders students successful problem solving.
We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a soph
omore level mechanics class at some point wrote Newtons Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one students detailed explanation to suggest that students issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.
Traditional methods of reporting changes in student responses have focused on class-wide averages. Such models hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Steven
Kanim on escalator diagrams which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and post-instruction results on questions. Our extension consists of consistency plots in which we represent three forms of data: method of solution and correctness of solution both before and after instruction. Our data are from an intermediate mechanics class, and come from (nearly) identical midterm and final examination questions.
We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on pre-/post-testing a
nd the correctness of responses (either on the overall test or on clusters of questions defined solely by content). We use a resources framework, taking special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. Furthermore, we show that false positives can be found, especially on questions dealing with Newtons Third Law.
