Investigating unprompted and prompted diagrams generated by physics majors during problem solving

Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Physics problem solvers may generate diagrams to orient to a scenario, to organize information, to directly obtain an answer, or as a tool of communication. In this study, we asked 19 undergraduate and graduate physics majors to answer 18 multiple-choice (MC) physics questions and then complete six diagramming tasks of situations similar to six of the MC problems: the MC problems contained no prompting regarding diagrams, while the diagramming tasks explicitly asked participants to carefully generate diagrams. This prompting placed participants in one of two epistemic frames, problem solving or communicating, which allowed us to explore which elements and features the students include (or not) in diagrams generated when students are working within these two frames. By comparing students’ spontaneously generated diagrams to their prompted diagrams, we found differences in size, accuracy, and amount of detail in unprompted problem-solving diagrams and prompted communicating diagrams. We also looked at correlations between the presence and features of unprompted diagrams with participants’ answer choice. Looking at the different cohorts (e.g., lower-division undergraduate and graduate students), we found that the differences in diagramming between cohorts were generally smaller than the differences within a cohort. We also explore implications for teaching and research.

Figure 1

An illustration of the coding performed on all student diagrams. Actual coding was done in a spreadsheet and not as a markup of each diagram. We also time stamped each detail (excluding units) for the unprompted diagrams.

Figure 2

Examples of unprompted (left) and prompted (right) student diagrams for the maps problem-task pair, with each pair of images being from one student. Detail of unprompted diagrams (left) varied widely.

Figure 3

Examples of unprompted (left) and prompted (right) student diagrams for the blocks problem-task pair, with each pair of images being from one student.

Figure 4

Examples of unprompted (left) and prompted (right) student diagrams for the decay problem-task pair, with each pair of images being from one student.

Figure 5

Examples of unprompted (left) and prompted (right) student diagrams for the mirrors problem-task pair, with each pair of images being from one student. As can be seen in these examples, many students drew the mirrors multiple times for both the MC problem and the diagramming task.

Figure 6

Examples of unprompted (left) and prompted (right) student diagrams for the maps problem-task pair, with each pair of images being from one student.

Figure 7

Examples of unprompted (left) and prompted (right) student diagrams for the maps problem-task pair, with each pair of images being from one student.

Figure 8

The percentage of students who drew an unprompted diagram for each MC problem. The darker shading indicates instances in which a diagram was drawn but not the first thing the student put onto the paper.

Figure 9

Histogram of student diagram details (marks, labels, and axes) by 10 sec intervals for 219 unprompted diagrams. For example, between 10 and 20 sec after starting a problem, students put a total of 201 markings (e.g., arrows, objects, etc.), 86 nonaxis labels, and 19 axis details (axes or axis labels) on diagrams. These graphs include 97% ($n=1705$) of diagram details, with the remaining 3% ($n=46$) occurring between 200 and 598 sec. Vertical bars indicate median times. Note: The vertical axis for the axes plot is different because of the low number of axes details. The times for 20 marks were not recorded, generally because the students’ hand obscured their work.

Figure 10

Histogram of timing of student diagram details (marks, labels, and axes) as a fraction of total time spent on each problem. For example, a total of 218 markings, 109 nonaxis labels, and 23 axis details were drawn by students in the first 10% of time spent problem solving. Vertical bars indicate median times. Note: The vertical axis for the axes plot is different because of the low number of axes details.

Figure 11

The percent of diagrams drawn (for each problem prompt) that included axes. Axes were most common for the problems that directly (center of mass, E-potential) or indirectly (delta) provided coordinate information in the problem prompt.