A histogram, as one of the common graphical representations, is a fundamental tool for visually understanding both data and its distribution. Given its ability to visually convey data distribution, interpreting histograms is essential for statistical literacy (Boels et al., 2019). Boels et al. (2019) stated that students and teachers misinterpret histograms due to conceptual difficulties. These misinterpretations can be categorized into two main types: (1) data-related misinterpretations, which involve systematic errors such as miscalculating the mean by confusing frequency with measured values (i.e., frequency-value confusion) or by solely calculating the sum of frequencies (i.e., sum for mean), and (2) distribution-related misinterpretations such as overemphasizing individual bars rather than considering the histogram as a whole while comparing histograms (i.e., pairwise stack comparison).

Although previous research has identified common systematic errors in histogram interpretation, little is known about how to design effective interventions that help pre-service teachers address these issues. This study addresses these systematic errors by re-using eye-tracking data, which uncovers hidden visual search patterns and provides insights into where students focus their attention while interpreting histograms. By analyzing these patterns, pre-service teachers can diagnose systematic errors in histogram interpretation and better understand students' thought processes related to their search patterns.

Using the Four-Component Instructional Design Model (4C/ID), vignettes have been developed to help pre-service teachers engage with the eye-tracking data and refine their diagnostic skills. The 4C/ID consists of (1) learning tasks, (2) supportive information, (3) procedural information, and (4) additional practice (Van Merriënboer & Kirschner, 2018). In this study, the learning task involves diagnosing students’ errors in histogram interpretation. Each vignette contains students’ gaze data on a histogram task (Boels, 2023). Pre-service mathematics teachers engage with eye-tracking data by analyzing gaze patterns and students’ answers, followed by reviewing student explanations from cued recall data. This process allows them to apply their knowledge, practice diagnostic skills in real time, and receive immediate feedback through the supportive and procedural information provided within the vignette. Furthermore, each vignette concludes with an additional task as a formative assessment. For histogram interpretation, three primary types of systematic errors are addressed in the tasks: pairwise stack comparison, sum for mean, and frequency value confusion.

Eye-tracking histogram vignettes, developed using the 4C/ID model, aim to help pre-service teachers diagnose and address these systematic errors. Eye-tracking data, combined with cued recall interviews, provides insights into how students visually engage with histograms, helping identify patterns that lead to specific errors (Boels, 2023). This study explores how pre-service teachers engage with designed vignettes to refine their diagnostic skills by analyzing and interpreting eye-tracking data from students’ gaze patterns. This study is part of a larger research project called Eye-teach-stats, which focuses on developing innovative methods, the eye-tracking vignettes, to help mathematics teachers diagnose and address misinterpretations of statistical graphs and improve their statistical knowledge for teaching. Within this broader context, the present study explores how pre-service teachers engage with histogram interpretation. The research question guiding this study is: How do pre-service mathematics teachers engage with students’ eye-tracking data when diagnosing students’ systematic errors in histogram interpretation?

By analyzing eye-tracking data, pre-service mathematics teachers can see how students visually process histograms. This not only helps diagnose systematic errors and underlying conceptual difficulties but also enhances their statistical knowledge for teaching by allowing them to apply it in varied scenarios, leading to improved instructional practices.

Data will be collected from pre-service mathematics teachers in spring 2025, recording their interactions with the eye-tracking histogram vignettes through audio and video. The think-aloud method will capture their reasoning processes as they engage with the vignettes. Semi-structured interviews will follow to examine potential biases and their underlying assumptions in their work on the eye-tracking vignettes. Thematic analysis (Braun & Clarke, 2008) will be used to qualitatively analyze the interview data, focusing on identifying patterns in their diagnostic skills, engagement with eye-tracking data, and use of supportive and procedural information. The analysis aims to trace how their reasoning evolves throughout the vignettes.

By analyzing students' eye-tracking data, we expect pre-service teachers to improve their ability to identify and understand systematic errors, specifically pairwise stack comparison, the sum for mean and frequency value confusion, and their underlying conceptual difficulties in the histogram interpretation of students. In addition, the supportive and procedural information provided within the vignettes is expected to improve pre-service teachers' diagnostic accuracy as they engage with complex data. Over time, as they work through multiple vignettes, pre-service teachers are expected to refine their diagnostic skills to develop more precise strategies for addressing student errors in histogram interpretation.

Boels, L. (2023). Histograms: An educational eye [Doctoral dissertation, Utrecht University]. https://dspace.library.uu.nl/handle/1874/430641 Boels, L., Bakker, A., Van Dooren, W., & Drijvers, P. (2019). Conceptual difficulties when interpreting histograms: A review. Educational Research Review, 28, 100291. https://doi.org/10.1016/j.edurev.2019.100291 Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa Van Merriënboer, J. J., & Kirschner, P. A. (2018). 4C/ID in the context of instructional design and the learning sciences. In F. Fischer, C. E. Hmelo-Silver, S. R. Goldman, & P. Reimann (Eds.), International handbook of the learning sciences (pp. 169–179). Routledge. See also: https://www.4cid.org/