[Blindmath] [Blind math] Spatial Abilities

Sat Jun 7 18:53:55 UTC 2014

I am sorry, of course my attachments are just for sighted readers.

 I like this quotation by John Lennon: Life is what happens while you are
busy making other plans,

since in my “standard” professional life I am a researcher in Geometry,
with interests in finite fields and rigidity of graphs.

But, in 1998, I started to make mathematical models, in a very simple way,
using wood, plexiglass, wool treads, to better share my mental mathematical
images with my students; the objects have to be touched, moved,
disassembled... to communicate an idea or a theorem or an algorithm.
I was not aware, ad that time, of the consequences that this would have in
my professional life: in few years I built a mathematical travelling
exhibition that now is a permanent exhibition of my University.
It was clear to me that the success of my work is related to the fact that
students - and people, in general – deeply enjoyed the possibility of
understanding something new, improving somehow their self-esteem. This
approach to mathematics (and, in general, to science) from concrete
activities to abstraction seems useful in encouraging weak students, or
people not believing in their possibilities to understand, but also in
challenging skilled ones.

 A natural continuation of my work: to make object that contains geometric
information, to be used to offer haptic geometric experiences.

At the beginning, I made things “random”, following my interests and
curiosity.

Later, I decided to follow Euclid (Einstein said: "If Euclid failed to
kindle your youthful enthusiasm, then you were not born to be a scientific
thinker." ). Euclid's order can assure that we are covering all the needed
concepts.

 Example on Perspective

In the attached “Perspective” there are pictures of the objects I made
about perspective.

You can better see one of them at the following link

http://www.rai.tv/dl/RaiTV/programmi/media/ContentItem-e89a64e6-80d2-4803-80d0-1689cb398e98.html

The 15 minutes video presents some of my general work, but, at the time
10:58 there is the object that allow to explore the fact that a circle is
usually drawn as an ellipse (I think that it can be understood, even if the
interview is in Italian).

 Example over Straight Line

The attached picture “StraightLine” shows some of the objects related to
the concept of the straight line (I knew a blind woman, 60 years old, who
believed that a *straight* line is just the line – say on the floor – that
you walk through while walking *straight* in front of you . And no one ever
noticed that her use of the word was not the use of the teacher: quite
obvious that the teacher assumed that she couldn't understand the related
statements, since she was blind!)

We sighted people know that a straight line is the shortest path between
two points, that a line can “glide” over itself, that things fall along a
straight line. We don't know when we knew these facts, and in which order
we learned them.

These facts are not obvious to someone who doesn't see.

My objects simply want to offer haptic evidence of that: in the attached
picture,

. a line glides over itself

- a circle, too, glides over itself

- a part of a very large circle: it glides over itself, but it is not a
straight line (checking the fact overlapping a ruler over it or using and
elastic band between 2 points))

- a line different from a straight line and a circle CANNOT glide over
itself (if you try, the right and left part no longer touch perfectly).

(the next step would be to offer evidence of the fact that an helicoidal
curve glides over itself, too, in 3 dimensions – hard even for sighted
people)

 Example about similarity of planar figures :

The attached picture PuzzleSimilarity deals with the fact two planar
figures are similar (“the same, but enlarged” in the rough language of
sighted person) if and only if they can be obtained by cutting a
(generalized) pyramid by parallel planes.

A different object is shown, too, using threads to simulate lines, the
edges of the pyramid.

 As you can understand, every single object should be explained and clearly
connected with the geometric aspects it wants to offer.

In my opinion, all the objects (those already made, and those just
imagined) would form a “learning path” that should be offered to a blind
child, as soon as possible.

 I do hope that these few examples can give an idea of my work. I am
curious about your comments.

 Emanuela

2014-06-07 4:37 GMT+02:00 Susan Osterhaus <osterhauss at tsbvi.edu>:

> Yes, I agree with Maureen. Please share with all of us.
>
> Susan
>
> -----Original Message-----
> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of
> Emanuela Ughi via Blindmath
> Sent: Friday, June 06, 2014 11:58 AM
> To: Lewicki, Maureen
> Cc: Blind Math list for those interested in mathematics
> Subject: Re: [Blindmath] [Blind math] Spatial Abilities
>
> Maureen,
> I will try to collect some images, some links, and few words of
> presentation by few days.
>
> Anyway; I would like to stress that I don't believe that the "objects" can
> make miracles: they need to be used by a trained teacher, deeply conscious
> himself/herself about their geometric content.
>
> Ciao
> Emanuela
>
>
> 2014-06-06 12:52 GMT+02:00 Lewicki, Maureen <mlewicki at bcsd.neric.org>:
>
> >  Emanuela, I Would certainly like to see pictures of the objects, if
> > you would like to send them to me. There are organizations in the US,
> > primarily the American Printing House which  considers producing
> > things that might be of value to the blind population
> >
> > Maureen Murphy Lewicki
> > Teacher of the Visually Impaired
> > Bethlehem Central Schools
> > 700 Delaware Avenue
> > Delmar, NY 12054
> > http://bcsd.k12.ny.us/
> >
> >
> > On Jun 6, 2014, at 3:39 AM, "Emanuela Ughi via Blindmath" <
> > blindmath at nfbnet.org> wrote:
> >
> >  Emanuela
> >
> >
>
>
> --
> Emanuela Ughi
> Dipartimento di Matematica e Informatica Via Vanvitelli 1 - 06123 Perugia
> (39) 340 3341040
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-- 
Emanuela Ughi
Dipartimento di Matematica e Informatica
Via Vanvitelli 1 - 06123 Perugia
(39) 340 3341040
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