Characterizing representational learning: A combined simulation and tutorial on perturbation theory

Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence”) is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.

Figure 1

The study design and time line of data collection.

Figure 2

A screenshot of the “Energy corrections in a perturbed infinite well” simulation.

Figure 3

Pretest questions on perturbations to infinite square wells of width $a$. In 2016, the pretest questions were given to students as multiple choice without the option to explain their reasoning, while in 2017 they were asked on paper with a prompt to explain their reasoning for each question.

Figure 4

The mid- and post-test questions using two perturbed infinite wells of width $a$. Students were given the graphs shown and asked the questions below the graphs, with a prompt to explain their reasoning for each question.

Figure 5

Examples of student responses to one of the pretest questions (responses a and $b$ to the top question) and one of the midtest questions (response $c$ to the bottom question). These examples illustrate the representational competence level framework used to characterize students’ reasoning. From top to bottom, the responses were coded as levels 1, 3, and 5, respectively.

Figure 6

The percentage of responses with fully consistent (all), partially consistent (partial), and inconsistent (no) use of representations across the pre-, mid-, and post-test responses. Code na was used for students’ responses with only a single representation or with no reasoning.

Figure 7

The distributions across the representational competence levels for the pre-, mid-, and post-test responses for the 2016 and 2017 data. Levels 1 and 2 correspond to perceptual, level 3 to syntactic and levels 4 and 5 to semantic use of representations. Code na was used for responses with no reasoning.