Investigating the role of model-based reasoning while troubleshooting an electric circuit

We explore the overlap of two nationally recognized learning outcomes for physics lab courses, namely, the ability to model experimental systems and the ability to troubleshoot a malfunctioning apparatus. Modeling and troubleshooting are both nonlinear, recursive processes that involve using models to inform revisions to an apparatus. To probe the overlap of modeling and troubleshooting, we collected audiovisual data from think-aloud activities in which eight pairs of students from two institutions attempted to diagnose and repair a malfunctioning electrical circuit. We characterize the cognitive tasks and model-based reasoning that students employed during this activity. In doing so, we demonstrate that troubleshooting engages students in the core scientific practice of modeling.

Figure 1

Cognitive troubleshooting tasks. These tasks describe the iterative process of repairing a malfunctioning apparatus. Performing each task requires up to six types of knowledge: domain, system, procedural, strategic, metacognitive, and experiential. This figure is based on the Cognitive Task Analysis proposed by Schaafstal et al. [14].

Figure 2

Modeling Framework for experimental physics. This framework describes the iterative process of constructing models of the measurement and physical systems, comparing measurements to predictions, proposing explanations for discrepancies, and revising models and/or apparatus. Darker shades of gray correspond to phases common in the troubleshooting process. Bold phrases indicate aspects of the framework that informed our a priori analysis scheme. This figure is adapted from the visualization presented by Zwickl et al. [5].

Figure 3

(Left) Schematic diagram of inverting cascade amplifier, with design elements highlighted. A comparison of nominal voltages and resistances in both functioning and malfunctioning versions of the circuit is provided in Table 2. (Right) Theoretical output signals of the inverting cascade amplifier with an input signal of amplitude 100 mV and frequency 100 Hz. In all plots, the vertical scales on the left and right respectively correspond to the output signals of stages 1 or 2 (solid black curves) and the input signal to stage 1 (dashed gray curves). Plots (a) and (b) show the outputs of stages 1 and 2, respectively, in a functioning circuit. Plot (c) shows the output of stage 2 due to the faulty op-amp, and plot (d) shows the output of stage 2 when both op-amps are functional but the input signal is sufficiently large that clipping occurs.

Figure 4

Photograph of the setup for the TAPPS interview.

Figure 5

Schematic diagram of inverting cascade amplifier, provided to study participants during the TAPPS activity. The diagram was accompanied by the following text: “Figure 1 is a schematic of the inverting cascade amplifier we built. The [output] of this circuit is [given by Eq. (1)]. The main advantage of a cascade amplifier over a regular amplifier is that we can achieve high gain while maintaining a relatively large bandwidth. Disadvantages of this circuit compared to the regular amplifier include more components and increased power consumption.”

Figure 6

Cognitive troubleshooting task coding results. Codes were applied to discrete 2-min time intervals. Colored bands indicate the times during which each pair engaged in the following tasks: formulate problem description (FRM, light gray); generate causes (GEN, medium-light gray); test (TST, medium-dark gray); and repair and evaluate (REP, darkest gray). White triangles and stars in the dark gray REP bands indicate times at which students replaced the $100\mathrm{\Omega }$ resistor and faulty op-amp, respectively. White circles in the medium-light GEN bands indicate times at which students employed the split-half strategy. There are no codes in the first 2 min of the activity because the interviewer was giving verbal instructions during these times. Subplots (a)–(h) correspond to pairs A through H.