Previous research has illuminated and defined meanings and understandings that students demonstrate when reasoning about graphical images. This study used verbal and physical cues to classify students’ reasoning as either static or emergent thinking. Eye-tracking software provided further insight into precisely what students were attending to when reasoning about these graphical images. Eye-tracking results, such as eye movements, switches between depictions of relevant quantities, and total time spent on attending to attributes of the graph depicting quantities, were used to uncover patterns that emerged within groups of students that exhibited similar in-the-moment meanings and understandings. Results indicate that eye-tracking data supports previously defined verbal and physical indicators of students’ ways of reasoning, and can document a change in attention for participants whose ways of reasoning over the course of a task change.
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What are in looking at? Shape thinking and eye-tracking.
Previous research has illuminated and defined meanings and understandings that students demonstrate when reasoning about graphical images. This study used verbal and physical cues to classify students’ reasoning as either static or emergent thinking. Eye-tracking software provided further insight into precisely what students were attending to when reasoning about these graphical images. Eye-tracking results, such as eye movements, switches between depictions of relevant quantities, and total time spent on attending to attributes of the graph depicting quantities, were used to uncover patterns that emerged within groups of students that exhibited similar in-the-moment meanings and understandings. Results indicate that eye-tracking data supports previously defined verbal and physical indicators of students’ ways of reasoning, and can document a change in attention for participants whose ways of reasoning over the course of a task change.
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- Award ID(s):
- 1711837
- PAR ID:
- 10095472
- Date Published:
- Journal Name:
- Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education
- Page Range / eLocation ID:
- 646-653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Previous research has illuminated and defined meanings and understandings that students demonstrate when reasoning about graphical images. This study used verbal and physical cues to classify students’ reasoning as either static or emergent thinking. Eye-tracking software provided further insight into precisely what students were attending to when reasoning about these graphical images. Eye-tracking results, such as eye movements, switches between depictions of relevant quantities, and total time spent on attending to attributes of the graph depicting quantities, were used to uncover patterns that emerged within groups of students that exhibited similar in-the-moment meanings and understandings. Results indicate that eye-tracking data supports previously defined verbal and physical indicators of students’ ways of reasoning, and can document a change in attention for participants whose ways of reasoning over the course of a task change.more » « less
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null (Ed.)Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that prompted them to reason covariationally about the quantities involved in the phenomenon of the gravitational force. The results of a whole-class design experiment with sixth-grade students showed that covariational reasoning supported students’ understanding of the phenomenon of gravity. Also, the examination of the phenomenon of gravity provided a constructive space for students to construct meanings about co-varying quantities. Specifically, students reasoned about the change in the magnitudes and values of mass, distance, and gravity as those changed simultaneously as well as the multiplicative change of these quantities as they changed in relation to each other. They also reasoned multivariationally illustrating that they coordinated mass and distance working together to define the gravitational force. Their interactions with the design, which included the tool, tasks, representations, and questioning, showed to be a structuring factor in the formation and reorganization of meanings that students exhibited. Thus, this study illustrates the type of design activity that provided a constructive space for students’ forms of covariational reasoning in the context of gravity. This design can be used to develop other STEM modules that integrate scientific phenomena with covariational reasoning through technology.more » « less
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Abstract Background This study investigates undergraduate STEM students’ interpretation of quantities and quantitative relationships on graphical representations in biology (population growth) and chemistry (titration) contexts. Interviews (
n = 15) were conducted to explore the interplay between students’ covariational reasoning skills and their use of disciplinary knowledge to form mental images during graphical interpretation.Results Our findings suggest that disciplinary knowledge plays an important role in students’ ability to interpret scientific graphs. Interviews revealed that using disciplinary knowledge to form mental images of represented quantities may enhance students’ covariational reasoning abilities, while lacking it may hinder more sophisticated covariational reasoning. Detailed descriptions of four students representing contrasting cases are analyzed, showing how mental imagery supports richer graphic sense-making.
Conclusions In the cases examined here, students who have a deep understanding of the disciplinary concepts behind the graphs are better able to make accurate interpretations and predictions. These findings have implications for science education, as they suggest instructors should focus on helping students to develop a deep understanding of disciplinary knowledge in order to improve their ability to interpret scientific graphs.
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Abstract Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in‐lab eye tracking and a sample of 85 undergraduates from a STEM‐focused university, we investigated how higher‐order operator position (HOO; i.e., multiplication/division operators and the presence of superfluous brackets impacted students' time to first fixation to the HOO, response time, and percent of correct responses). Students solved order‐of‐operations problems presented in six ways (3 HOO positions × presence of brackets). We found that HOO position and presence of superfluous brackets had separate and combined impacts on calculating arithmetic expressions. Superfluous brackets most influenced undergraduates' performance when higher‐order operators were located in the center of mathematical expressions. Implications for learning and future directions are discussed about observing eye movements and gaining insights into students' processes when solving arithmetic expressions.
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