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The idea of intellectual need, which proposes that learning is the result of students wrestling with a problem that is unsolvable by their current knowledge, has been used in instructional design for many years. However, prior research has not described a way to empirically determine whether, and to what extent, students’ experience intellectual need. In this paper, we present a methodology to identify students’ intellectual need and also report the results of a study that investigated students’ reactions to intellectual need-provoking tasks in first-semester calculus classes. 

We report the results of an investigation into the factors that affect students’ learning from calculus instructional videos. We designed 32 sets of videos and assessed students’ learning with pre- and post-video questions. We examined how students’ engagement and self-identified ways of interacting with the videos connected to their learning. Our results indicate that there is a complicated relationship between the student, curriculum, instructional practices, and the video content, and that the effectiveness of instructional videos may be contextualized by both instructional practices and the extent to which the understandings supported in the videos are compatible with the meanings promoted during instruction. 

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. 

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. 

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. 

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. 

Growing interest in “flipped” classrooms has made video lessons an increasingly prominent component of post-secondary mathematics curricula. This format, where students watch videos outside of class, can be leveraged to create a more active learning environment during class. Thus, for very challenging but essential classes in STEM, like calculus, the use of video lessons can have a positive impact on student success. However, relatively little is known about how students watch and learn from calculus instructional videos. This research generates knowledge about how students engage with, make sense of, and learn from calculus instructional videos.