Adaptation of Mathematical ALGorithms

When giving instruction, we often face the following task: how to adapt a given mathematical algorithm for a blind student. Our experience indicates several principles which should be taken into consideration. We will introduce them at first and then explain their meaning:

1. Respecting the blind people's manner of work
2. Eventual change of the arrangement of objects used during the computation
3. Effective processing of the algorithm with minimal time and memory requirementsas
4. Choosing suitable tools for manipulation with data and objects of the algorithm
5. The procedure and the result of the computation should be clear to the person who is responsible for assessing the work

A blind person perceives the information in a different manner than people who can fully use their sight. When following a given mathematical algorithm or text we usually prefer a suitable spatial arrangement of objects to

1. represent relations between them,
2. find them more easily and
3. examine their details promptly.

By contrast, for blind people such an arrangement often entails a barrier. When looking for a specific piece of information they spend a lot of time by following other objects and their details which are not important at that moment. They do not have the opportunity to work with objects generally without concentrating on their specific values or properties.

Example

We demonstrate the previous facts using the well-known algorithm for polynomial division. You can have a look at its description in the part Algorithms and their adaptations. One of the adaptations (Entering the polynomials into a spreadsheet using only their coefficients) strictly respects the original arrangement of the polynomials which is used when a sighted person performs the algorithm in the standard manner. Only particular results are inserted using coefficients of the polynomials' terms, see the following image.

Link to MS Excel file: polynomial_division_en.xls

Image 1: Entering the polynomials into a Spreadsheet using only their coefficients

If, for example, a blind user needs to divide terms of both polynomials with the largest degree (the divident $f$ and the divisor $g$ on the Image 1), he/she has to deal with several complications:

• Accessibility of the coefficients is not easy – blind students spend a lot of time moving between three objects and do not have an option to ignore specific values of the polynomials.
• Additionally, orientation is very difficult – the blind have to make sure very often which power corresponds to the coefficient they have actually reached.
• If they want to save some time, they are constantly occupied by holding semi-results in their memory as they are looking for a position where to insert them.

With respect to the blind person's manner of processing the information we have to ensure easy and quick access to the objects we actually work with during the computation. Therefore, in many cases, it is not useful to respect their traditional arrangement, although it can help the blind to understand single steps of the computation more deeply when getting to know the algorithm.

Besides choosing the method of adaptation we should also consider which (computer) tools are suitable for manipulation with data and the computation itself. Sometimes, it is enough to open a single file in the standard text editor. Alternatively, a blind student can use a spreadsheet which enables to organize data in rows and columns. In addition, one can work with more than one sheet located in one file. Naturally, this application is suitable for manipulation with matrices. There are other options – to mention just one, the special mathematical editor Lambda supports the speech and braille output and features useful accessibility functions for blind users which help them handle complex and structured expressions more easily.

Finally, it is necessary to ensure that the whole procedure of computation is clear also to the people who supervise and evaluate the work of the blind student. As mentioned above, the adaptation need not respect the original arrangement of objects: the blind student's solution is therefore not understandable to people who are used to the standard procedure of the algorithm. It is thus necessary to explain in advance any deviations from the standard procedure.