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Information Technologies for Visually Impaired People
2. Preparation of mathematical information (presenting
school exercises, writing papers etc.).
3. Navigation in mathematical expressions and communication
between blind and sighted people.
4. Doing Mathematics (carrying out calculations and
computations at all levels, doing formal manipulation, solving
exercises).
We will present in Section 3 various published works
which address the first two problems at least in a satisfactory
manner (to some extent). In Section 7 we will focus on
a few approaches that are now addressing the third one.
Unfortunately until now almost nothing has been achieved
to support the target group in solving tasks relating to the
last category [16] [17] [18].
1.6 iGroupUMA
To address these challenges, 6 organisations having expertise
in the field of Mathematics for the Blind have decided
to join their efforts, creating the International Group
for Universal Math Accessibility (iGroupUMA). They have
been since joined by a seventh organisation.
The iGroupUMA members are:
University of Texas at Dallas, United States.
Dublin City University, Ireland.
University of South Florida at Lakeland, United
States.
Johannes Kepler University of Linz, Austria.
New Mexico State University, United States.
University Pierre et Marie Curie in Paris, France.
University of Kyushu, Japan.
2 Braille Mathematical Notations (BMNs)
2.1 General idea for BMNs
Braille is a linear writing system and consequently, it is
necessary to linearise formulas to represent them in Braille.
We have seen in Section 4 that the first "natural" way of
writing formulas is to translate them to a non specific linear
form, and then to use specific Braille characters for mathematical
symbols, however this method makes formulas very
long and quite difficult to handle for blind students.
In order to reduce the length of these formulas as far as
possible specific Braille notations for Mathematics, and
more widely for Scientific content, have been developed
during the second half of the twentieth century. These very
high level notations have been designed in order to improve
the readability for the blind, mainly by significantly reducing
the number of symbols necessary to represent a formula. To
achieve this brevity, they have been based on context sensitive
grammars which allow the use of the same symbol strings with
different meaning depending on the context.
In counterpart these notations are quite difficult to learn
(and to teach). The reason is that blind pupils have to deal
with 2 learning difficulties at the same time: the Mathematical
content itself and the Math code which is at least as
difficult as the content. Currently only very proficient Braille
users are able to do it, while average sighted pupils succeed
much easier.
To further complicate things, these Braille Mathematical
notations have been developed in different areas, according
to the linguistic and cultural history of these countries.
Therefore, while the mainstream (visual) representation
of formulas is identical in every language, the same is
not true for Braille notations. Indeed each Braille mathematical
notation is widely used in its zone of linguistic influence,
while it is completely unknown in other areas. In other
words, a Braille formula written using the British notation
is not understandable by a German speaking reader. This
problem is quite important since the number of available
Braille documents is very small compared to the number of
ordinary Maths books.
The main Braille Mathematical notations are the following:
In France, the Braille Mathematical code was first
adapted to Mathematics in 1922 by Louis Antoine. This code
was revised a first time in 1971. It was then deeply revised
in 2001[19], in the goal of improving the collaboration between
sighted and blind and facilitating automatic transcription.
Nevertheless a lot of Braille readers still use the version
devised in 1971.
Marburg is used in German speaking countries. It
was designed in 1955 in the Marburg school for the Blind
in Germany by Helmut Epheser, Karl Britz and Friedrich
Mittelsten Scheid. A heavily reworked and revised edition
was published in 1986 [20].
The Nemeth Code for Braille Mathematics was published
and accepted as the standard code for representing
math and science expressions in Braille in 1952. It was designed
in 1946 by Abraham Nemeth so that he could complete
his PhD in mathematics. The 1972 revision [21] is the
current official code in use in the US. Note that Nemeth
was adopted officially in a number of Southeast Asian countries
(like India, Thailand, Malaysia, Indonesia, Cambodia,
Vietnam).
The British notation [22] is used in United Kingdom
and in Ireland. It was first designed in 1970, and a deeply
revised version was published in 1987. This was slightly
revised in 2005.
The current Japanese Mathematical Braille notation
was published in 2001 by the Japan Braille Committee. It is
an important revision of the 1981 formal specification of
Japan Mathematical Notation, itself based on the notation
published in 1956 by Japan Braille Research Group ("Nihon
Tenji Kenkyukai’’).
Italy, Spain and many other countries have developed
their own Mathematical notations.
Additionally some countries where no specific notations
had been designed decided to officially adopt one of these
notations. For instance Greece is using the Nemeth notation.
Finally a set of countries does not use such specific notations,
like the European Nordic countries, but they use
simple linearisation of formulas, with a set of specific symbols
for Mathematical symbols that do not exist in the ordinary
alphabet.
UPGRADE Vol. VIII, No. 2, April 2007 33