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Information Technologies for Visually Impaired People
Figure 1: Extra Graphics Used to Illustrate a Calculation.
of blindness, rather the biggest barrier is the notation used
for doing Mathematics. As this notation is essentially visual,
it is quite difficult to transmit its contents using other
modalities. Blind pupils often fail in Maths because of the
way information is presented. A key feature which is present
in the visual reading process is the role of the printed page.
This medium affords the reader not only the facility to act
as an external memory, but also facilitates a highly refined
control over the flow of information. In the case of graphical
content, tactile drawings can also be made. To some
extent, this applies fairly to representation of curves and bidimensional
geometrical figures. Even if great progress has
been made in the technologies that allow the production of
tactile drawings, there are limitations due to properties of
tactile sense. It is also possible to render a curve using audio,
by modelling a sound according to the shape of the
curve, or using an haptic device like the Senseable Phantom
[2].
In this paper we will focus on methods of access to mathematical
formulas, which are the basis for all calculations
and are used in all areas of mathematics and more generally
in the sciences. Considering the two communications channels
that have been cited above, formulas can be represented
is a tactile form, usually based on Braille, or they can be
spoken.
1.1 How People Read Mathematics
One of the key decisions which must be made when
considering the manner in which mathematics, originally
prepared using the visual modality, is depicted in either an
audio or tactile one, is to firstly ascertain what information
to present, followed by how to present this material. It is
therefore important to understand the reading process, in
order to fulfil the dual purpose of determining both what
and how to present the relevant information to the user. In
the subsequent paragraphs, the discussion is placed in terms
of both auditory and Braille reading. and where there are
discrepancies they will be highlighted.
A feature which is present in the visual reading process
is the role of the printed page. This medium affords the
reader not only the facility to act as an external memory,
but also facilitates a highly refined control over the flow of
x + 1 x + 1 / (x - 1)
x - 1
Figure 2: Linearisation of a Very Simple Fraction.
information. In his Ph.D. thesis, Stevens states that Rayner
[3] describes reading as: "... the ability to extract visual information
from the page and comprehend the meaning of
the text" [3]. Stevens [4] also tells us that reading can be
divided into three main domains.
1. The input of information from a physical, external
source, into the reader’s memory via the visual system;
2. The recognition of words and their integration into
higher level structures such as sentences;
3. The process of understanding what has been read.
It would appear that there exists a point at which the
process of listening and reading converge. This would seem
to indicate that, once the information has been absorbed by
the reader, it is both syntactically and semantically decomposed
in the same manner, though the processes of actually
retaining the material are quite different depending on which
means the reader uses to read. It would appear that many
readers hear a voice inside their head whilst reading. This
voice articulates what is being read, giving the reader both
a phonological and sub-localised impression of the document.
Stevens [4] defines the phonological code as "the auditory
image kept in working memory during reading". It can
be said that the written text is converted to this phonological
code, which contains all the features of natural speech,
such as pitch, rhythm etc. The notion of inner speech is
quite speculative, but Rayner states that "Some proponents
of inner speech have argued that reading is little more than
speech made visible" [3]. The above appears to suggest that
the visual component of reading is converted to an audio
version, seeming to suggest a point where the two converge.
After this point, the comprehension of the information
should be the same. It is clear that the only differences in
the reading process are the mechanical means of obtaining
the information.
One aspect in which listening and reading differ significantly
is the role of paper as an external memory. The manner
in which the eye can relate to this external memory is a
very powerful tool to aid in the retention and comprehension
of written information. It can rapidly scan over the
printed words, and by virtue of the juxtaposition of characters
or symbols on the printed page, semantically interpret
those symbols to produce the underlying meaning. Once
the information is lost from the short term memory, it can
be easily refreshed by the rapid movements of the eye.
There are a number of steps involved in the visual reading
of a document. A skilled reader will normally read at a
rate of 250-300 words per minute. The eye does not actually
start at the top of a page and continue in a linear fashion
until the end of the material is reached; rather the reading
process consists of several distinct movements. Stevens
tells us that there are a number of tasks which the eye performs
in order to gain informational input. The reading process
can be broken down into a series of sacades (jumps)
and fixations. He tells us that:
"The sacades move the point of fixation in accordance
with how much information has been or can be apprehended.
30 UPGRADE Vol. VIII, No. 2, April 2007 © Novática