Math for Those with Severe Low Vision: From the Particulars to the Gestalt (And Back Again)

Abstract

Mathematics is indispensable to engineering and computer education. Indeed, the reading, performance and sharing of mathematics is analogous to the reading, writing and speaking of natural languages: Both are prerequisites for other fields of study, and both provide solutions to the very practical problems of communicating ideas across space, culture and time. Without mathematics, members of these fields would struggle to formalize, systemize and communicate ideas central to their missions. And yet the inaccessibility of conventional mathematical notation inhibits Individuals with Blindness or Severe Low Vision (IBSLV) from fully participating in this discipline. Such notations were designed by the sighted, for the sighted: They allow for the offloading of working memory to the page (as information is always accessible through sight) and take advantage of our immense capacity to remember both what information is present and where it can be found. If IBSLV are to be “first class citizens” of engineering and computer education, researchers must design tools that allow them to fully participate in the reading, performance and sharing of mathematics as well. In this paper, we make inroads into these problems by analyzing, contextualizing and framing the results of three computer-human interaction studies of MathSTAAR, a system which conveys mathematics to IBSLV. In the first, we found that a system which implements Vanderheiden's touch-and-speak model (in which participants can touch portions of a mathematical expression and have it spoken to them) allowed participants to correctly read more than 90% of expressions at a middle-school level, the level at which the average IBSLV falls behind their sighted peers. In the second, we found that augmenting this system with “coarse visual cues” (the highlighting of what is touched to allow IBSLV to take advantage of any vision they retain), allowed participants' to read, locate and relocate mathematical information faster than a keyboard system while also reducing participants' self-reported Frustration and Effort. In the third, we found that two multimodal approaches-one instantiated in our MathSTAAR system, the other instantiated in the Math Melodies application-allowed IBSLV to solve more than 90% of problems correctly. However, MathSTAAR did so while reducing both Frustration and performance time. We contextualize these findings in two ways. First, we show that even though many of those with sight consider reading mathematical expressions a trivial task, for IBSLV, this is not the case. Second, we employ Polanyi's ideas of particular and gestalt knowledge to show that both the nature of one's vision, as well as the tools one uses, greatly impacts what an individual might know and when they might know it.

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