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Growing interest in “flipped” classrooms has made video lessons an increasingly prominent component of post-secondary mathematics curricula. However, relatively little is known about how students watch and learn from instructional videos. We describe and use an eye-tracking methodology to investigate attentive fidelity—the degree to which students attend to the visual imagery that is the subject of the video narration at each moment in time. Our preliminary study suggests that students’ attentive fidelity varies widely, but there was no evidence that this fidelity is connected to students’ ability to solve calculus problems. 

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. 

In this study we investigate how students watch and learn from a set of calculus instructional videos focused on reasoning about quantities needed to graph the function modeling the instantaneous speed of a car. Using pre- and post-video problems, a survey about the students’ sense-making and data about the students’ interactions with the video, we found that many students did not appear to make significant gains in their learning and that students appeared to not recognize their own moments of confusion or lack of understanding. These results highlight potential issues related to learning from instructional videos.