Graphical representations of data in STEM education

Ruf, Verena (2024): Graphical representations of data in STEM education: investigation of graphing and graph comprehension. Dissertation, LMU München: Fakultät für Psychologie und Pädagogik

Abstract

Learning materials usually consist of various types of representations. For example, graphical representations, such as illustrations or graphs, are often used in instructions in combination with text. Graphical representations of data are a subgroup of graphical representation that is common not only in education but also in news media. These types of representations depict data and can be informative to learners when presenting them solely or in addition to text. Dealing with such information is a key skill of the 21st century and has been frequently researched. Skills dealing with graphs can be summarised under the term graphing competence, describing the creation (graphing) and the comprehension of graphs. However, graphing competence is not an easy skill for students to learn and students’ difficulties are frequently reported. This thesis presents research that aims to contribute to previous findings regarding graphing competence, thereby enhancing the use of graphs as an educational tool. Both aspects of graphing competence – graphing and graph comprehension – are addressed in this thesis. The first research direction concerns graphing; how graphing is investigated, what benefits it has, and the types of difficulties students have during graphing. The second research direction addresses the second aspect of graphing competence: graph comprehension. Graph comprehension skills change with varying levels of expertise. Expertise differences can be analysed using eye movements as indicators of cognitive processing. Therefore, this thesis analyses eye movements during learning and problem-solving with graphs, specifically paying attention to the differences between the visual processing of experts and non-experts. Furthermore, differences in graph comprehension between various study disciplines are examined. Based on current empirical research, physics students can be considered experts compared to students of other disciplines, because they seem to solve graph comprehension tasks better, independently of the task context. Building on previous research, the visual behaviour of physics and non-physics students is studied. Extending previous research, machine-learning methods are used to predict correct and incorrect solvers based on their eye movements. The three research directions are addressed in the three studies presented in this thesis. The first study describes a systematic literature review of the empirical research on graphing in K-12 science, technology, engineering, and maths (STEM) education. The second study reviews the literature comparing experts’ and non-experts’ visual processing during learning and problem-solving with graphs. The third study investigates the differences in learning gain and visual behaviour between physics and non-physics students solving graph comprehension tasks. The first study narratively summarises how graphing is implemented in studies researching graphing in K-12 education. Furthermore, information on the added value of graphing and students’ difficulties during graphing are considered. Fourty-four studies investigated this topic published from 1979 until March 2022, when the search was conducted. Many studies instructed the graphing of line graphs over more than one lesson. The synthesis of the study results indicates that different types of graphing instruction have a positive effect not only on graphing skills but also on graph comprehension. However, the review findings indicate that students have difficulties both with the graphing conventions as well as with the theoretical implications of the data depicted in the graph. As theoretical difficulties are also common in graph comprehension, this indicates that both types of difficulties influence graphing skills. Furthermore, the two aspects of graphing competence – graphing and graph comprehension – might affect each other. The second study presents a literature review of studies comparing the visual processing of experts and non-experts during learning and problem-solving with graphs. Thirty-two studies published between 2003 and 2022 were analysed regarding the eye-tracking metrics used to investigate visual behaviour and the reported differences between experts and non-experts. Most studies used more than one eye-tracking metric. The findings indicate that experts pay more attention to relevant areas of the graph than non-experts. This is in line with the information-reduction hypothesis, suggesting that experts can ignore irrelevant information on a perceptual level. Definitions of expertise vary, implying that an overarching definition of expertise is missing. However, over the course of this review, four possibly relevant factors for expertise in graph comprehension were identified: (1) graphical literacy, (2) domain knowledge, (3) prior mathematical knowledge, and (4) task knowledge. The third study empirically investigates differences in learning gain and visual behaviour of physics and medical or veterinary students. Twelve physics and twelve non-physics students, respectively, voluntarily solved 24 graph comprehension tasks in the contexts of math, physics, and medicine at the beginning and the end of their first semester. There were no statistically significant differences in learning gain between groups. This might indicate similar transfer skills between these study disciplines as both participant groups took STEM courses. Correct and incorrect solvers could be predicted via machine learning based on their eye movements. Therefore, machine learning optimised for small datasets can be a valuable tool for assessing expertise by analysing eye movements. The research presented in this thesis supports the relevance of instructing graphing competence. Both aspects of graphing competence, graphing and graph comprehension, should be considered during teaching. In particular, graphing instruction could be beneficial for students because it does not only seem to facilitate graphing skills but also graph comprehension. Furthermore, graphing instruction seems relatively easy to implement as the findings indicated that it was advantageous in various forms. However, students had difficulties during graphing. Student difficulties based on graphing conventions or based on theoretical aspects, such as with interpretation, were reported in many studies, indicating that both types of student difficulties should be considered during instruction. Furthermore, future research should consider the visual behaviour of K-12 students and experts during graphing because eye movements can indicate expertise in processing graphs. During learning and problem-solving with graphs, a comparison of the visual processing of experts and non-experts supports the information-reduction hypothesis. This indicates that experts can ignore irrelevant information on a perceptual level and process information more efficiently than non-experts. Showing students experts’ strategies might, therefore, be beneficial for them by guiding their focus to relevant information. Future research should consider levels of expertise based on measurable factors due to the diverse possibilities in which graph comprehension might be facilitated. For example, STEM instruction could promote the transfer of problem-solving skills, such as graph comprehension, to other domains. In summary, the results of this thesis highlight influencing factors for graphing competence, both graphing and graph comprehension, not only in K-12 but also in higher education.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Themengebiete: 300 Sozialwissenschaften ; 300 Sozialwissenschaften > 370 Erziehung, Schul- und Bildungswesen
• Fakultäten: Fakultät für Psychologie und Pädagogik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 26. März 2024
• 1. Bericht­erstatter:in: Kuhn, Jochen