Using think-aloud interviews to characterize model-based reasoning in electronics for a laboratory course assessment

Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly acquired observations, or change their apparatus to better represent their models when they encounter discrepancies between actual and expected behavior of a system. While modeling is a nationally recognized learning outcome for undergraduate physics lab courses, no assessments of students’ model-based reasoning exist for upper-division labs. As part of a larger effort to create two assessments of students’ modeling abilities, we used the Modeling Framework to develop and code think-aloud problem-solving activities centered on investigating an inverting amplifier circuit. This study is the second phase of a multiphase assessment instrument development process. Here, we focus on characterizing the range of modeling pathways students employ while interpreting the output signal of a circuit functioning far outside its recommended operation range. We end by discussing four outcomes of this work: (i) Students engaged in all modeling subtasks, and they spent the most time making measurements, making comparisons, and enacting revisions; (ii) each subtask occurred in close temporal proximity to all other subtasks; (iii) sometimes, students propose causes that do not follow from observed discrepancies; (iv) similarly, students often rely on their experiential knowledge and enact revisions that do not follow from articulated proposed causes.

Figure 1

Modeling Framework for Experimental Physics: Originally conceptualized by Zwickl et al. [12], this schematic of the Modeling Framework from Dounas-Frazer [9] shows how five interconnected tasks—construct models, make measurements, make comparisons, propose causes, and enact revisions—describe the ways scientists bring data and predictions from models into agreement. In the Modeling Framework, we distinguish between physical models or apparatus (e.g., models of the op-amp) and measurement models or apparatus (e.g., models of digital multimeters).

Figure 2

A circuit diagram of the inverting amplifier circuit used in the TAPS interviews. The students were given a handout with this circuit diagram at the beginning of the activity. The values of the feedback and input resistors were written. Purposefully missing are the values of the power rails (initially set at $\pm 10\mathrm{V}$), and the capacitors from each power rail to ground (100 pF)

Figure 3

A simulated plot of the input (solid line) and output (dashed line) voltage signals on an oscilloscope with given power rails (dotted line). (a) With the initial conditions, the output signal will appear clipped due to the power rail limit. The slight slant of the output signal is due to slew-rate limits. (b) After hypothetically increasing the power rails and decreasing $V_{\mathrm{in}}$, the clipping and the slight distortion due to the slew rate limit is fixed.

Figure 4

Aggregated data from participants on duration and sequence of modeling subtasks. This schematic shows the commonality of the five modeling subtasks: construct models, make measurements, make comparisons, propose causes, and enact revisions. The area of the circles represents the number of 30-sec intervals coded with that particular subtask; the thickness of the gray connectors between all five subtasks represents the number of times a subtask was coded directly after the other, or within the same 30-sec interval. This representation is similar to the transition graphs presented in Ref. [32].