[Blindmath] [Blind math] Spatial Abilities

[Emanuela Ughi]

I am a professional mathematician, interested in teaching mathematics, and
in particular in teaching mathematics to blind students.
I made a whole exhibition with mathematical models to be touched,
assembled, manipulated in order to get some insight about mathematical
ideas and theorems.

I think that sighted people build their knowledge of geometric/spatial fact
over experiences that they have at very early age; early blind people often
simply miss those experiences, so that they miss the “bricks” to build
their geometric consciousness.
Perhaps some of them find themselves a way of getting these experiences by
exploring the world Nemeth tells that he explored a lot, during his
childhood, indeed.
Also,  I like to remind you of the story of Mademoiselle Melanie de
Malignancy, blind from birth, who was able to master geometric facts, as
told by Diderot in his “Lettre sur les aveugles”:
“I said one day to her: ‘Mademoiselle, figure to yourself a cube.’ ‘I see
it.’ she said ‘Imagine a point in the centre of the cube.’ ‘It is done.’
‘From this point draw lines directly to the angles: you will then have
divided the cube - ’ ‘Into six equal pyramids,’ she answered, ‘having every
one the same faces: the base of the cube and the half its height.’ ‘This is
true; but, where do you see this?’ ‘Inside my head, like you.’”

It is up to us (sighted mathematicians, I mean) to build a way to offer
them experiences that can surrogate the experiences they miss.
To translate an geometric fact in something that can be explored
haptically, a mathematician can better use all the knowledge he/she has
(for example, I have a whole “plan” about how to explore similarity between
planar figures, that requires the knowledge of theorems of 3-dimensional
geometry to be planned).
I had some thesis (in mathematics) on this subject. In particular, a thesis
was focused in finding a way to haptically explain the meaning of “drawing
in perspective”.
Another thesis re-read the first book of the Euclid's Elements, and made a
collection of  small tools to haptically offer the experience of the facts
Euclid stated.

I have shown and used these objects with (few) blind people. They were
thrilled to be able to discover new things, that are so obvious to sighted
people that the teacher don't even imagine that the blind student ignore
them.
In particular, a very brilliant girl, age 19, the best student in her high
school, discovered with me that... things fall along a straight line. She
didn't imagine that fact, and no one told her!
While touching my objects, her comments: I wish I had these objects when I
was 5, as a toy.

Unfortunately, in Italy, I had to almost give up this research, since I
didn't find a way to support a student of mine to continue this research
program (that seems very promising to me, not only to teach blind
students); also, I didn't find a way to test my objects with blind children
(it seems that the focus is on “assist” blind people, not in searching
innovative ways to offer them as much experiences as we can).

So, right now, I have some shelves with boxes of didactic objects that no
one uses.: I would be very happy to share my objects and my experience with
anyone could let them be as useful as they can.

Best regards
Emanuela ughi
Dipartimento di Matematica e Informatica
Università degli Studi di Perugia
Via Vanvitelli 1 - 06123 Perugia - Italy


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