04 SES 14 D, Promoting Inclusion by Improving Accessibility: Resources and tools
The study of mathematics is crucial in the preparation of students. Many sighted students feel stuck in its learning. For the visually impaired students, the obstruction is even higher, due to the additional difficulties they have to face in accessing mathematics. Presentation of written information to blind individuals has traditionally been accomplished through the use of Braille. Braille may not have been an ideal solution; however, it has been a satisfactory one for presenting texts. For documents containing mathematics, instead, it poses ever-bigger problems, such as the great number of characters required to write a simple formula or the fact that there is not a standard Braille alphabet for mathematics.
Nowadays, students with sensorial disabilities have new instruments at their disposal. Visually impaired people strongly benefit from speech synthesis software such as NVDA or JAWS. Blind people also use Braille displays, whereas partially sighted people may use any combination of screen magnifiers and colour customization. Assistive technologies perform satisfactorily with regard to texts, but they still have a long way to go as far as formulae are concerned. Indeed, these are usually represented in two dimensions, while language follows a one-dimensional construction.
Microsoft Word is the most widespread text editor. It has a graphical interface that allows to write texts and to insert formulae as images, which are clearly not accessible. HTML and MathML are markup languages that are used for creating web pages and are helpful to make available documents to a wide audience. Markup languages are suitable to be managed by screen readers and Braille displays. However, again formulae are generally inserted as images.
A system used by blind people is the LAMBDA system (Linear Access to Mathematics for Braille Device and Audio-synthesis). LAMBDA is composed of a markup language, a dedicated editor and a MathML converter. Mathematical language in LAMBDA is designed so that every symbol can be directly translated into words. This translation is implemented on the fly in the editor, so it can be used also by visually impaired people. Nevertheless, only visually impaired people use LAMBDA, and its list of mathematical symbols is neither complete nor adaptable.
Therefore, making mathematics accessible to the visually impaired students is a significant challenge that involves teachers’ pedagogical knowledge and the choice of an appropriate technology. To analyze the complex interaction of these domains that a teacher should possess, Mishra and Koehler developed the Technological Pedagogical and Content Knowledge (TPACK) framework. In our setting Content Knowledge is mathematics, Pedagogical Knowledge is inclusive methodology and Technological Knowledge is formed by the whole bundle of aforementioned technologies (Braille books, MathML documents, LAMBDA, …). An expert teacher is able to fruitfully interrelate these three domains, balancing each tool in his/her TPACK.
We pose the following research question: are there inclusive resources that teachers can use to prepare accessible mathematical materials to all students and especially to visually impaired ones?
A technology that meets these requirements and that can be added to the TPACK of each teacher is the markup language LaTeX. It is fully accessible and highly inclusive since it is widely used by the vast community of (not necessarily visually impaired) scientist and students of scientific disciplines throughout the world. Additionally, LaTeX compilers are free, open source and available for all operative systems. LaTeX can and should be learned by both teachers and students. Moreover, our research group is working on a LaTeX package, called “auto” (with an appropriate vocabulary) that allows the reading in the natural language of mathematical formulas written in LaTeX using JAWS.
This research is funded by the project “New technologies for disabilities” of Turin University.
A training course was organized for mathematics secondary school teachers from Turin that are sensitive to the issues of accessibility and/or that have visually impaired students in the classroom. It took place from November 24th to December 13th, 2017 at the Department of Mathematics “G. Peano” of Turin University. 13 teachers joined the course. 10 of them were teachers for students with special needs. The trainers were two researchers and a professor of the mentioned Department and they met the participants 4 times for 3 hours each time. The aim was making LaTeX known and promoting its dissemination. There are three valid reasons to pursue this. In fact, LaTeX is a markup language used by a large scientific community of different cultural and social extractions, so it has a syntax that is universally shared. It is a standard for scientific contents and it is open source. Some weeks before starting the course, participants received a survey electronically. It was useful to understand if the participants were familiar with LaTeX and if there were visually impaired students in their classrooms. The methodology of the 4 meetings has alternated moments of lectures to laboratory activities. The latter took place by dividing the participants into groups, who worked cooperatively on a laptop. In the first two meetings, in addition to giving a general overview of the problem of accessibility to documents containing mathematical formulas, the participants began to become familiar with LaTeX. In addition, there were moments dedicated to listening to 3 testimonies of visually impaired people, who collaborate with our research group. They have told their experiences of studies (two are graduates in Mathematics and one in Computer Science) and how LaTeX has been a valuable tool for them. They also answered participants’ questions about how they relate to mathematics in their student careers and in their current professional position. In the third and fourth meetings, the participants, divided into cooperative learning groups, were invited to produce inclusive educational activities to encourage their students to learn about LaTeX. Moreover, in the last meeting, the trainers took a document, containing mathematical formulas written in LaTeX, and JAWS read them once without and once with “auto”. At the end of the course, a questionnaire with 14 scale-Likert questions (from 1=insufficient to 4=excellent) was given electronically to the participants, to evaluate the course appreciation and understand what impact it had on their training.
From the first questionnaire it turns out that 8 out of 13 teachers has a visually impaired in class and their LaTeX knowledge was low or zero (answers: nothing = 7, low = 5, average = 1, high = 0). Until then, 3 used Lambda, while the other custom methods invented by them (e.g. for blinds: voice reading, graphs drawn on the back; for visually impaired: computer zoom and magnifying text with lenses). Only a blind student used speech synthesis. 9 replies from the final questionnaire were received. 78% was satisfied with the overall duration of the course compared to the topics covered. The same percentage positively assessed the training effectiveness. However, to use what has been learned with their students, the majority seems to show uncertainty: (1 = 11%, 2 = 56%, 3 = 22%, 4 = 11%). Surely having available “auto” will be a remarkable innovation on the theme of accessibility to texts containing formulas. The only “effort” required is the knowledge of LaTeX. One should not think that learning LaTeX requires the same effort that would require learning a new language. The commands have a syntax which is easily understandable. For example: the command corresponding to the fraction is \frac, \lim is for limit and so on. There is certainly an open question: what impact will these educational practices have? Some teaching experiment will be needed. The results will be seen in the long term, but in the short term it is interesting that there has been appreciation and interest in starting to follow this way. It is important to maintain a close collaboration between the research and the school, to support teachers in the acquisition of this powerful and versatile software, and to satisfy specific visually impaired students’ needs that developers may not have considered.
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