Basic principles
LAMBDA (acronym of Linear Access to Mathematics for Braille Devices and Audio- synthesis) is an European research project that carried out an effective system allowing blind people to access scientific documents, above all in school and university environment.
The problem
Mathematics is often considered a quite difficult discipline for blind people. The reasons are generally due to the boundaries of aptic (i.e. touch) mediation and, often, to limited psychomotor experiences.
For younger children, the problem of mathematical notation, the main target of the LAMBDA project, is probably secondary, compared with the issues in developing suitable cognitive processes, without the support of visual experience. Yet, for the older students, as they become able to develop elaboration strategies, that lead to the abstraction process and to the consequent creation of mathematical concepts, the limits of Braille traditional notation become bigger and bigger and the need of more efficient tools increases.
The skilled students in computer science, those who have got good ability in using computer, vocal and Braille peripherals, are prone to extend to this field the well-tested advantages of the new access tools:
- greater functionality and speed compared with the traditional Braille instruments;
- access to all documents available in electronic format, not only to those produced also in Braille;
- accessible texts also for who does not know Braille.
In other disciplines (history, languages, literature, philosophy...) these results are well achieved and consolidated and the skilled student is no longer willing to waive them. Huge advantages in terms of functional efficiency ("Even if in a different way, I can do as much as my classmates do”), of autonomy ("I can do lots of things all by myself, I do not depend entirely on others"), of access to cultural and didactical tools ("With no or just a few adjustments, I can consult all by myself all the texts my classmates use”) and, finally, of communication with teachers and classmates ("Everybody can read, immediately and easily, what I write; the teacher can also follow my work and can really be my teacher").
Unfortunately, this is not true for Mathematics yet. In this environment, in fact, the computer advantages are quite uncertain.
Above all, there is the problem of the mathematical code. The peripherals for blind people, Braille and vocal ones, can only read linear texts (a sequence of known characters), but the mathematical document is not textual, nor linear. Indeed, it possesses a set of symbols much larger than the common use, and it assigns a meaning also to the position and dimension of the signs (above, below, index,…)
The mathematical codes
For sure, it is not impossible to create a textual and linear system for the mathematical writing. LaTeX is an efficient and complete system for linear writing, very popular in scientific and university environment, whose symbols and mathematical structures are indicated through short textual combination.
Currently, MathML is getting more and more important: the two final letters (ML stands for
Markup Language, language based on markers) clearly show links with XML and HTML and therefore with Internet. MathML is a code based on XML and approved by W3C, the world consortium that defines the rules of the web and internet.
Both LaTeX and MathML are based on a textual source code, very complex and verbose (above all for MathML), that can be transformed into a graphic mathematical text by a visualization software. Yet, it is not accessible by blind people, who can only consult and manipulate the source code. The use of LaTeX and MathML, by visually impaired users, is technically possible, yet it is very complex, above all in didactical field. The accessibility to screen readers is a necessary, yet not sufficient condition to have an efficient and really usable environment. But not only this. At school, the mathematical text is not only read or written: mathematical expressions are to be elaborated, analysed, transformed, manipulated, proved, solved and, in these situations, also LaTeX source code reveals itself absolutely inadequate.
Generally, writing and, above all, manipulating a mathematical text only using the computer keyboard is complicated, for sure harder than accomplishing the same operations using a pen and a sheet of paper. Let us think, for example, of how many calculations or reductions can be rapidly done on paper, just with a few signs, while the computer requires a series of complex steps, above all if it is necessary to keep track of intermediate passages, to correct the work done, in case of mistakes.