This paper wants to add the point of view of a professional mathematician (focused in geometry) in the field of education of blind people.
Indeed, several studies point out some specific difficulties of blind students, and in particular of those blind from the birth, in mastering geometric facts: they have problems in translating and transferring three-dimensional objects into two-dimensional iconic form, so that they cannot understand perspective drawings; also, they have problems in enlarging and minimizing even two-dimensional forms, so that they are not able to recognize different-sized shapes as being the same.
From several anecdotes and teaching experiences I collected, I arrived to state the following conjecture: lacking of (early?) geometric experiences in sections and projections is strictly related to problems of blind students (and persons) about the perception of geometric (mostly, but not only, 3-dimensional) facts.
To the best of my knowledge there are no manipulatives focused on offering this kind of experiences. Sometimes blind children are asked to cut some soft material, but nothing else.
Consequently, I realized several manipulatives purposely planned to offer blind students those geometric experiences they usually miss.
Indeed, manipulatives are commonly recommended and used in the field of education for blind children, for several teaching purposes. In particular, several authors stress the importance of this kind of tools for giving blind children the possibility of acquiring mathematical concepts though concrete activities (e.g., Del Campos, Russo, Tindell), and there is a large offer of concrete materials for blind students, but just a few are specifically planned for teaching mathematics.
And my feeling is that, despite the efforts, the manipulatives offered to blind children are often planned by sighted people, who didn’t recognize enough that it is not sufficient that a object “contains” an information. For that information to be received by a blind student, it has to be grounded on the experiences the student already knows,
The manipulatives already realized (by a brilliant student of mine) allow an haptic exploration of the meaning of “perspective”, showing (haptically) the simplest geometric facts about drawing (for example, drawing the same segment gives different-sized images depending of the distance of the segment from the point of view). A more complex manipulative shows how and why a circle is drawn as an ellipse.
The objects have been tested at the ICCHP-SU 2011, and the reactions and comments of blind people were very encouraging. The comment I like more: an university student saying “Ah, if I had this object during my high school years!”.
Bearing my conjecture in mind, I believe that a deeper reflection can help in designing better concrete tools, specifically planned to offer a concrete ground of experience as a surrogate for the visual experiences; so I am starting to re-read Euclid, from the very beginning, to realize an haptic collection of manipulatives to explore his journey through geometry.
Is this work worth trying? I suppose yes, and like to remind the story of Mademoiselle Melanie de Malignancy, blind from the birth, able to master geometric facts, as told by Diderot in his “Letter sour les aveugles”:
“Je lui disais un jour: «Mademoiselle, figurez-vous un cube. – Je le vois. – Imaginez au centre du cube un point. – C’est fait. – De ce point tirez des lignes droites aux angles; eh bien, vous aurez divisé le cube. – En six pyramides égales, ajouta-t-elle d’elle-même, ayant chacune les mêmes faces, la base du cube et la moitié de sa hauteur. – Cela est vrai; mais où voyez-vous cela? – Dans ma tête, comme vous.»”
