Probing student understanding with alternative questioning strategies

Jeffrey M. Hawkins, Brian W. Frank, John R. Thompson, Michael C. Wittmann, and Thomas M. Weymss

AIP Conf. Proc. 1413, 207 (2012)

Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers they may not have chosen naturally, we can investigate students' abilities to explain something that is already established or to disprove an incorrect response. The results of these research tasks also provide us with information about how students' responses vary across the different tasks. We discuss three underused question types, their possible benefits, and some preliminary results from an electric circuits pretest utilizing these novel question types. We find that the answer students most commonly choose as correct is the same choice most commonly eliminated as incorrect. Also, given the correct answer, students can provide valuable reasoning to explain it, but they do not spontaneously identify it as the correct answer.

## 2012-10-01

### Hawkins, Frank, Thompson, Wittmann, and Wemyss on alternative question strategies

### Wittmann and Black on integration and separation of variables

When basic changes to a solution suggest meaningful differences in mathematics

Michael C. Wittmann and Katrina E. Black

AIP Conf. Proc. 1413, 93 (2012)

When solving two integrals arising from the separation of variables in a first order linear differential equation, students have multiple correct choices for how to proceed. They might set limits on both integrals or use integration constants on both or only one equation. In each case, the physical meaning of the mathematics is equivalent. But, how students choose to represent the mathematics can tell us much about what they are thinking. We observe students debating how to integrate the quantity dt. One student seeks a general function that works for everyone, and does not wish to specify the value of the integration constant. Another student seeks a function consistent with the specific physics problem. They compromise by using a constant, undefined in value for one student, zero in value for the other.

Labels: Black, mathematics, Mechanics, Wittmann

### Harrer, Scherr, Wittmann, Close and Frank on proximal formative assessment about energy

Elements of proximal formative assessment in learners' discourse about energy

Benedikt W. Harrer, Rachel E. Scherr, Michael C. Wittmann, Hunter G. Close, and Brian W. Frank

AIP Conf. Proc. 1413, 203 (2012)

Proximal formative assessment, the just-in-time elicitation of students' ideas that informs ongoing instruction, is usually associated with the instructor in a formal classroom setting. However, the elicitation, assessment, and subsequent instruction that characterize proximal formative assessment are also seen in discourse among peers. We present a case in which secondary teachers in a professional development course at SPU are discussing energy flow in refrigerators. In this episode, a peer is invited to share her thinking (elicitation). Her idea that refrigerators move heat from a relatively cold compartment to a hotter environment is inappropriately judged as incorrect (assessment). The "instruction" (peer explanation) that follows is based on the second law of thermodynamics, and acts as corrective rather than collaborative.

Labels: assessment, energy, Frank, Harrer, Wittmann

### Wittmann and Chase on embodied cognition in wave propagation

Evidence of embodied cognition about wave propagation

Michael C. Wittmann and Evan Chase

AIP Conf. Proc. 1413, 383 (2012)

That students think of wavepulses as if throwing balls down a long taut spring is well established. Typical questions involve students imagining the spring already pulled taut; a different scenario would imagine them pulling the spring tight first. This situation creates a different baseline of physical experience from which to reason. For example, it provides a physical experience in which tension is a relevant measure in the system. We investigated the effects of students pulling the spring (or not) in interviews after instruction. We also wrote two surveys, each giving a different physical description of a typical problem. From interviews, we find evidence that a different embodiment of the problem affects students' responses. In surveys, with students asked to imagine different situations, we found no such evidence.

Labels: Chase, embodiment, waves, Wittmann

## 2012-07-26

### Christensen and Thompson on graphical slope and derivative representations

W.M. Christensen and J.R. Thompson

Investigating graphical representations of slope and derivative without a physics context

*Phys. Rev. ST Physics Ed. Research* **8**, 023101 (2012).

http://link.aps.org/doi/10.1103/PhysRevSTPER.8.023101

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. As an extension from this work on students’ mathematical competency at the upper level in physics, we report on a preliminary investigation of mathematical understanding of fundamental concepts of slope and derivative among students in a third- semester multivariable calculus course. Among the first published findings of physics education research are investigations on students’ understanding of kinematics, with particular attention to graphical representations of position-, velocity-, and acceleration-versus-time graphs. Underlying these physical quantities are relationships that depend on derivatives and slopes. We report on our findings as we attempt to isolate students’ understanding of these mathematical concepts.

Labels: calculus, Christensen, derivative, mathematics, slope, Thompson