I received a message from a TA at Berkeley with some questions about teaching
math to blind students.
I'm copying the NFB list on my reply.
Please feel free to add your comments )
--and don't forget to copy John if Flin if you have suggestions for him.
Hi John--
First off, note my current email address.
John Flynn writes:
> Hi,
> I found your AMS web page as I was searching for information on
> teaching math to visualy impaired studetns. I am a grad student in math at
> Berkeley and last semester I had a blind student in my class. It was a
> great experience to try to teach calculus and it raised lots of questions.
> Now I am trying to gather some information and make some records so that
> some of what I learned will beremembered in the department.
I'm glad you're doing this --it's a wonderful idea.
You may want to post your message to the NFB-RD (National federation of the
> blind ) list for additional feedback.
nfb research and development <nfb-rd@nfbcal.org>
> I would really appreciate if you have some comments to make or
> might point me to some resources or people which might help. I will
> outliine some of the issues I stumbled against.
Will do my best below.
Some background: I could see a little in one eye until the age of 14;
so I was blind by the time I got to Calculus. (this is relevant to some of the
issues you rraise e.g. spatial organization etc)
> I found that I had some things to overcome myself in interacting
> with my blind student as I had almost no interaction before with people
> with strong visual disabilities. It took me some time to get used to
> interacting but she helped me a lot and I learned a great deal from this.
This is usually the biggest first step.
>I
> am convinced that this "disability barrier" is commonplace and I think it
> made it hard in discussions to have an integrated classroom. It was almost
> as if my other students had to get through this too but because there wasnt
> as much contact it toook them longer. This is a big question; how to make a
> good classroom environment, what to do with the chalkboard, how to have
> everyone acting as peers.
I found little difficulty in interacting in an integrated classroom, both in
> India and here at Cornell.
The only adjustment I asked for (and always got)
was to sit in the front of the class (so the instructor would not forget me)
and also have the instructor speak aloud *everything* they wrote on the board.
During my college/university time, several instructors later commented to me
that they thought that doing the above in fact made their classes better
for all students as in their opinion it drew the students attention to the
thing that was the current focus of attention.
It also turns out to be helpful to all students when the instructor verbalizes
math --especially when new notation is being introduced.
> A constant question for me was the level of spatial intuition my
> studetn might have. In math we say that things are visual but I think we
> mean spatial. I wonder what you think about the spatial strengths of the
> visually impaired. I think that the great barrier is not spatial intuition
> but the communication of spatial information.
I think you're spot on.
How one successfully communicates spatial concepts will vary on the
individual's background; for instance, having been able to see, I think
very spatially and even point at my slides when I give talks.
>I am used to graphs and
> pictures. Soon my student educated me to the raised drawing kit and we made
> some progress at that. But I had no way of getting spatial output from her
> and this was a hugh drawback. (any ideas?)
Again, I never really used a raised drawing kit;
I used rudimentary things like pieces of cardboard and string back in India
when I was learning some of the more basic concepts,
but very quickly got past using those as aids.
Typically, when faced with a new concept, I had the person explaining it to me
phrase it in terms of things I had already seen or experienced. Here is an
example:
Consider the surface z = xy
When I encountered this for the first time the instructor said it's a saddle
...
I then mentally played with it some; taking specific slices of the surface,
xy=1 is a rectangular hyperbole
and as you increase or decrease the constant the branches of the curve move
closer to or farther from the origin.
I was then able to not only get a good visual picture of the surface; more
importantly, I had an accurate mental model of the surface in mathematical
terms, and given this could work just as well with that surface as any other
student in class.
For instance, it's easy to see with the above mental model that many if not
most functions will have a discontinuity at the origin when defined on this
surface (guess I'm getting into manifolds land)
> Then there were three dimensional problems involving rotating curves about lines
> and this was really hard to communicate, the best I could do was use balls
> of newspaper,and this was pretty bad.
Again, get the basic concept across and
and help the student do mental visualization exercises.
For instance, ask the student to take a small segment e.g. one joining (0,0)
and (1,1)
and ask what happens when that segment is rotated about the axis.
It is true that a blind student needs to do a bit more work than the average
student at this tage; but it pays off (believe me)
where the average student has a supposedly easier time because you can show
her a cone, the blind student has to do some work as pointed out above;
but when it comes to asking what is "S4" (the result of S2XS2
the blind student is better equipped because now neither the blind student or
the rest of the class can "see" S4 in practice, and the discipline of
visualizing things at a conceptual level really helps.
> There was a question of what should be expected from the student
> from the course, should we not examine her on "graphical" questions?
The student should be examined on *everything* that other students are
examined on.
This said, one needs to make sure that the student is properly equiped to deal
with the exam (by equiped I mean more than aids --I mean the ability to
tackle problems and think in specific ways --but of course that is the
purpose of the class)
> I think no?
> Then there is the question of technology. The other students have
> graphing calculators. There is technology for producing raised graphs but I
> didnt get to look at this (for example grafit).
> Any suggestions here?
You can look for "equality" and a "level playing field" in several ways.
In a sense a level playing field would imply that the blind student have a
graphing calculator --and there are people working towards this.
But lifting things up a level, I personally dont think graphing calculators to
be essential (either to the blind or sighted student).
Graphing calculators if well used are a good learning aid, but not a
substitute to learning.
> There is the question of the suitability of calculus as the first
> university level course in math for the visually impaired. Might a course
> which is more symbolic be more encouraging?
No. In principle I am opposed to blind students being offered courses that are
explicitly designed for them;
the resulting perception is always one of "the blind student has been given
something different (and consequently easier)"
--this leads later on to a feeling of inferiority and is a potential source of
discrimination.
> I appreciate any ideas you might have and any information you might
> point me to. Also if you know of any people who might be able to offer some
> support to visually impaired students and their teachers let me know.
I'm copying the NFB list on this.
>
> thanks
>
>
> John Flynn
>
-- Best Regards, --ramanAdobe Systems Tel: 1 (408) 536 3945 (W14-129) Advanced Technology Group Fax: 1 (408) 537 4042 (W14 129) 345 Park Avenue Email: raman@adobe.com San Jose , CA 95110 -2704 Email: raman@cs.cornell.edu http://labrador.corp.adobe.com/~raman/raman.html (Adobe Internal) http://www.cs.cornell.edu/Info/People/raman/raman.html (Cornell) ----------------------------------------------------------------------- Disclaimer: The opinions expressed are my own and in no way should be taken as representative of my employer, Adobe Systems Inc. ____________________________________________________________
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