Abstract
Much of the wealth of industrialized societies is based on knowledge that is laid down and communicated in scientific/technical/engineering/mathematical documents: highly structured documents that contain diagrams, images, and – most daunting to many readers – mathematical formulae. It seems clear that digital, interactive documents have the potential to improve reading these kind of documents, and thus learning and applying this kind of knowledge.
To understand how such improvements could be designed, we explore how formula understanding interacts with the surrounding text in mathematical documents. We report on an eye-tracking experiment with 23 engineering students reading a “solved problem” based on a simple differential equation. We observe for instance that – triggered by formulae – readers backjump to previously identified semantic loci and that this behavior is independent of depth of understanding in mathematically trained readers. Based on our observations, we propose novel in-document interactions that could potentially enhance reading efficiency.
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Notes
- 1.
Document triage refers to readers’ practice of rapidly evaluating documents to determine whether they contain wanted information or not.
- 2.
Figures 12 and 15 together show the full document content, see https://kwarc.info/people/mkohlhase/data/DuStd-18/radiocarbon.html for the transcription.
- 3.
This has been unsuccessful, it seems that the English/Thai language barrier combined with a cultural reluctance to speak without preparation together with the unfamiliar situation induced prohibitive cognitive load which prevented students from speaking. When we realized this, we asked one student to “think aloud in Thai”, but this largely only resulted in a translation of the document, in particular not in the desired stream of cognition, so we dropped this idea.
- 4.
The eye moves discontinuously, making short stops (called fixations; we count any stop that is longer than 60 ms) and separating by rapid jumps (called saccades).
- 5.
There is of course the practical problem of how to determine whether F is focused. We could use in-place-and-time eye-tracking data instead of forcing the reader to e.g. hover the mouse over F to “focus” it, as this might be too distracting.
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Acknowledgements
The authors gratefully acknowledge the Erasmus+ Staff Mobility for Teaching program that provided the institutional setting of the design research, and the students of the course for their participation in the eye-tracking study.
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Kohlhase, A., Kohlhase, M., Ouypornkochagorn, T. (2018). Discourse Phenomena in Mathematical Documents. In: Rabe, F., Farmer, W., Passmore, G., Youssef, A. (eds) Intelligent Computer Mathematics. CICM 2018. Lecture Notes in Computer Science(), vol 11006. Springer, Cham. https://doi.org/10.1007/978-3-319-96812-4_14
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