Discourse phenomena in mathematical documents

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.