Mathematics for Blind


Authors of mathematical, physical, and chemical texts rely on the usage of symbolic notation. For a better understanding of the structure of a mathematical expression, its syntax is visualised in 2D form and provided with elements which help with the perception of individual parts or the whole expression. Also in the case of performing several mathematical algorithms (e.g. multiplying two integers, one below the other) we place objects on the plane. Their arrangement respects the requirements on accessibility and effective handling in individual steps.

While reading and writing blind people rely on the Braille notation. They perceive Braille haptically and the method of reading is linear, therefore totally different in comparison with the visually based way of processing information by sighted. For clear encoding of a text into braille (whether it be a text from mathematics, physics or chemistry) the Guide book for transcribing a Latin text into braille was created in 1995 (W. Gonzúrová, 1997). It is the Czech national codification approved on 12 Septembre 1997 by Ministry of Education, Youth and Sport.

With the increased integration of visually impaired students into schools which are not specialized in teaching blind students, teachers are not acquainted with the Czech national braille codification and therefore are not able to read texts produced by their visually impaired students. Despite the fact that pupils of basic and secondary schools can use a Picht typing machine to write down their notes and make computation during science lessons.

Employees of the Teiresiás Centre aim to develop or localize computer-based tools which enable a blind person to write down symbolic texts in a correct form while allowing other participants to read and interpret them without the need to know the Braille norm.

Mathematical editors for blind

  1. BlindMoose – a Microsoft Word add-in developed at the Teiresiás Centre. The tool enables to write/edit and process the text with mathematical symbols while making it readable visually or haptically on a refreshable Braille display. You can find more information on the website of the BlindMoose editor.
  2. Lambda – a stand-alone commercial application for reading and writing mathematical symbols which was localised into Czech by employees of the Teiresiás Centre from 2005 to 2007. A tactile or speech output is available. You can find more information on the website of the Lambda editor.
  3. Chatty Infty – a stand-alone commercial application allows reading and writing mathematical expressions with the speech output support. During the years of 2015 and 2018 employees of the Teiresiás Centre prepared a Czech localization of the tool. You can find more information on the websites of the Japanese company sAccessNet.

Mathematics on the web

Because a range of information which blind people work with is available online, making symbolic texts accessible for blind users on the internet is as important task as their editing. Employees of the Teiresiás Centre are currently engaged in the development or localization of the following tools (both of them are available free or charge):

  1. Limpet – a Javascript library developed at the Teiresiás Centre which makes websites with mathematical expressions accessible for blind and partially sighted users. Individual mathematical expressions in the website source are represented by elements <img> which are supplied with alternative descriptions in the TeX format. When opening the page, Limpet renders 2D images of the expressions. The user of a screenreader can access the alternative description of the images in three formats: a text read by the screenreader, or a string which is presented on the refreshable Braille display in accordance with  the Czech Braille codification, or is presented in the original TeX format. You can find more information on the website of the Limpet library.
  2. MathPlayer – an add-in which enables reading of mathematical text in various applications, or websites. One can use it in the Internet browsers such as Mozilla Firefox and Internet Explorer, or the tools such as MS Word and MS Powerpoint. The add-in enables the speech output of mathematical expressions encoded in MathML by the screenreaders NVDA and Jaws. It was localized into Czech by the employees of the Teiresiás Centre. You can find more information on the websites of the MathPlayer add-in.

Mathematical Algorithms and their Modifications for Blind Students

Mathematics and the related domains are very visual. They often require observation of multiple objects concurrently while putting them into suitable positions in space and plane. This helps us to better understand the relationship between the elements, while working with them more effectively.

The Amalg project websites offers more information for blind students who work solely with the linear representation on the ways such algorithm can be used in reality together with specific examples.