Extracting information from the Hertzsprung-Russell diagram: An eye-tracking study

The Hertzsprung-Russell diagram (HRD) is a fundamental representation in stellar physics. It contains information about key properties of stars and allows inferences about stellar evolution. The use of the HRD is an important disciplinary activity in astrophysics. For example, it is particularly important to have a graphical understanding of the HRD in order to understand elementary astrophysical relationships (e.g., about the luminosity, temperature, radius, and mass of stars). However, several research papers indicate that students often have difficulty interpreting the HRD, apparently due to its visual complexity, and a number of learning difficulties have been described. Yet, there is still no evidence concerning how learners actually select and extract information from the HRD when completing tasks. In this study, we examined the gaze patterns and think-aloud protocols of 35 physics students as they performed 14 open-response tasks. Benchmarking against traditional $x\text{−}y$ diagrams shows that the HRD imposes a significantly higher cognitive load on students, particularly due to the representation of luminosity, magnitude, and spectral class. Students reported a variety of learning difficulties related to information selection and extraction, sometimes mechanistically copying procedures from typical $x\text{−}y$ diagrams. Eye-movement analysis confirmed these learning difficulties on a procedural level and show whether the students fixated on task-relevant parts of the HRD. Based on the study results, preliminary recommendations can be made in order to create engaging learning materials relating to the HRD.

Figure 1

A typical Hertzsprung-Russell diagram that contains information about central stellar properties. The spectral class and effective temperature (in kelvins) are shown in the horizontal direction, and the absolute magnitude (in mag) and the luminosity (in solar luminosity) are shown in the vertical direction. The colored background represents the color of the star. This example contains the Sun and four luminosity classes that are part of the stages of stellar evolution (see text for details).

Figure 2

Isomorphic pair of items as originally used in the study (English translations can be found in the Supplemental Material [51]). The top item shows three points in an $x\text{−}y$ coordinate system (C,H,L), and students must compare the $y$ values to find the point with the largest $y$ value. The bottom item shows three stars (S,C,Y), and students must select the star with the largest absolute magnitude. Note the parallel item design, especially the congruent position of the points or stars in the diagrams.

Figure 3

Procedure of item presentation and answer submission as originally used in the study (English translations can be found in the Supplemental Material [51]). The item text appears on the left half of the screen. The corresponding item diagram is displayed under the user’s control. In between, the user looks at a fixation cross. When the participant has solved the item in his or her head, he or she presses the space bar and gets to the input page. Here, the background fades out, and the prompt to speak the answer appears.

Figure 4

Definition of areas of interest (AOIs) for all items as originally used in the study (English translations can be found in the Supplemental Material [51]). Two global AOIs cover the text (T) and the diagram (D). The D-AOI includes nine smaller, local AOIs, namely, the interior of the diagram (i) and each axis (AL, AR, AT, AB) and axis label (LL, LR, LT, LB) in the left, right, top, and bottom.

Figure 5

Histograms of the achieved test scores for the HRD items (left, maximum score 32) and the CFD items using an $x\text{−}y$ diagram (right, maximum score 10). Scores lower than 13 (HRD) and 6 (CFD) were not found for the items and are therefore not shown for clarity. The three students with the lowest and highest HRD scores are designated as extreme performance groups (RQ3).

Figure 6

Histogram of the item difficulties for all items used. The 14 HRD items (T1–T14) are ordered by item difficulty from easy (left) to difficult (right). For the items marked with the $†$ symbol, there exists an isomorphic item with an $x\text{−}y$ diagram. Error bars indicate the standard errors of the mean values.

Figure 7

Results for intrinsic cognitive load and germane cognitive load in a comparison of dealing with the HRD and an isomorphic $x\text{−}y$ diagram. Error bars indicate the standard errors of the mean values.

Figure 8

Listing of the three local AOIs that receive the most attention per item. For this purpose, the TVD was normalized to the size of the AOI. Cells colored in gray indicate the AOIs that are addressed by the item text. This consists of the AOIs of the axes (A) and labels (L) in all four directions (L)eft, (R)ight, (T)op, and (B)ottom, as well as the AOI for the interior of the diagram (i).

Figure 9

Heat maps of an isomorphic pair of items ($\mathrm{T}8†$) as originally used in the study (English translations can be found in the Supplemental Material [51]). These heat maps are for all participants. Information must be taken from the left $y$ axis (top) and from the right luminosity axis (bottom). In both cases, the relevant values of the points or stars must be extracted and compared. Note the more extensive consideration of the logarithmic luminosity axis (bottom) compared to the linear $y$ axis (bottom).

Figure 10

Heat maps of all high performers (top) and all low performers (bottom) in comparison. The heat maps refer to the stimuli as originally used in the study (English translations can be found in the Supplemental Material [51]) where students were learning about the HRD for the first time (without problem solving).

Figure 11

Heat maps of all high performers (top) and all low performers (bottom) in comparison. The heat maps show the visual attention when solving item T6 as originally used in the study (English translations can be found in the Supplemental Material [51]). Here, three stars are given, and the problem requires comparing their magnitude values to identify the brightest one (bottom right).