[Blindmath] Working math homework and exams

[Louis Maher]

Hello Ben,

Three comments.

1.  A Braille display would greatly lesson the memory issue.
2. You could open a second file for scratch purposes.  Alt-tabbing between
two files is faster than going up and down a single file.
3. Nemeth code is invaluable.

Braille will greatly simplify your scientific efforts.
 


Regards
Louis Maher
713-444-7838
ljmaher at swbell.net
http://www.nfbtx.org/localchapters/houston  


-----Original Message-----
From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] On
Behalf Of Ben Humphreys
Sent: Saturday, November 19, 2011 9:00 AM
To: blindmath at nfbnet.org
Cc: Doris Pichardo
Subject: [Blindmath] Working math homework and exams

Hi everyone on the Blind Math mailing list

Earlier in this term, we had a brief discussion on how to make use of a text
editor to take notes and do math homework.  At the time, the discussion
focused on how to represent math constructs like exponents, division,
special symbols etc.

I am now towards the end of my first calculus class, and my first math class
as a totally blind student.

Brief results: So far, have a B- in the class whereas I believe I would be
much closer to an A, homework and exams take 2-3 times longer to do than
other students.  Use of Tiger embosser invaluable for visualizing graphs but
a lot of extra prep work necessary to get math material and graphss in a
form suitable for embossing or reading and doing homework.

My instructor uses several formats for material.  Most often, she creates
material in Microsoft Word using Mathtype.  I obtain the Microsoft Word file
from her in electronic format, use Mathtype's convert to Latex feature, then
heavily process with a Perl script to remove all the extraneous junk and put
it in a straightforward format that I can read in Notepad.  Before I wrote
the Perl script, I required a human to remove all the extraneous Latex and
the human found it faster to type from scratch than to fixup the Latex.

Other times, my instructor scans in problems found on the web or out of
other textbooks.  These have to be typed in by a human so I can read them in
a text editor.

Finally, she solves class material and homework in handwriting and places
the scanned images of that online for the benefit of all the students.  The
format is scanned PDF. So I need a tutor to compare my homework with the
correct solutions.

Our "official" textbook is available from Recording for the Blind (Learning
Ally) but it's not only cryptic as most math texts are, but the readers are
aweful. While I appreciate the volunteers who record these textbooks, it's
an exceedingly hard thing to render a math textbook in audio format.  I get
stressed out just listening to those poor people trying to describe a crazy
equation or graph in words.

So that's the logistics of being a first-time blind calc student in a
university setting with no "inline" instruction such as might be provided
back in secondary school.


Back to the original story...

I planned to do my hhomework and exams in a text editor.  I choose this
approach for several reasons:

1.  I'm a good typist and excellent JAWS screen reader user

2.  Handwriting is out of the question

3.  I am just learning Braille and so I figured a text editor + JAWS would
be much more reliable.  If you've ever compared the 2, b, apostrophe, and ^
characters on a Braille display, you can easily see how a beginner would
completely blow an equation like 
y'=2b^2   because 5 of the characters are all two vertical dots in 
various configurations.  Recipe for disaster...

4.  I've heard in the past that folks used to use a Perkins brailler.  This
had the advantage that you could type your work in braille, and refer back
to previous work on the page relatively easily.

Unfortunately, this sounded like a heavy, noisy, and impractical solution
for me since I don't know braille that well.  And I was unsure how one makes
corrections (erasures or cross-outs) using such a method.

So I choose Notepad + JAWS as my solution.

I choose early on to use my own simplified expressions in lieu of
complicating my life with Nemeth or for heaven's sake Latexin a text editor.

So x-squared became x^2
a/b is a simple fraction
a+1//b was a shorthand to (a+1)/b and easier to understand
lim x->infinity-symbol (sideways 8)  became simply lim x~infinity

Then I used JAWS dictionary to redefine things like "^2" to be "squared", y'
to read "y prime", ~ for "goes to", and cos x to read cosine x.

My simple hybrid representations worked relatively well.

Now for the complications:

1.  When equations got long, it was really easy to get "dizzy" 
reading through them with a text editor.  Example:
4x^5 - (2x^2)(3x) + 45 = 16x^(4/3)


2.  As you work an equation with more than one or two terms, it was 
really easy to make a mistake:    Example:

2x^3 - 3x^2 = -5
could easily become
3x^3 + 2x^2 = 5

Because the human brain can only remember about 7 things at once, and if you
look at that equation, there are about 9 individual coefficients, exponents,
and signs to remember.  It's enough to drive you mad.  So you use copy and
paste as you work the problem and then change little pieces on each
iteration.

3.  The sighted students have the benefit of a scratchpad in the form of an
area off to the side of the page or on the back where "temporary"
calculations can be performed.  Then the result can be brought back into the
original problem.

I found I had to do my scratch work inline, which distracted me from the
original problem and forced me to scroll through long lists of calculations
to get to previous steps. this too was enough to make you dizzy and confused
just moving through all the math with a screen reader in your ear.

  So I started labeling my steps with comments like you might do in a
programming language.  Example:

# Original equation
4x^2- 400x = 0

# add 100x to both sides and cancel
4x^2= 400x

# Divide both sides by 4
x^2 = 100

# Solve for x
x=10

4.  The substitution problem - and this was the big one.  When you get a
problem with lots of variables, like in a word problem, you have to write
down all your variables, do some manipulation, and then substitute
everything back in.  Example:

A box has a base whose length is 10 and width is 5.  The height of the box
is 2.  Calculate the surface area of the box.

So you write down

l=10
w=5
h=2

s = 2lw + 2lh + 2wh

Now you have to ssubstitute in the values, which means you havfe to move
your cursor back up, memorize one or more variables, and then bring your
cursor down, place on the variable to be substituted, type the value, delete
the original variable, and repeat without blowing anything.

A sighted student does this completely intuitively because he or she
rewrites the surface area formula, substituting variables on the fly by
referring to them visually.

When you Add more fariables, fractions, exponents, and signs, the tendency
to blow it goes way up.

After taking a 2 hour exam that actually took me 7 hours, of going back and
forth dizzily within long problems, I figured there had to be a better way.

Enter the the Computer Algebra System.

I figured a Computer Algebra System could solve many of these problems for
me.  It could store and substitute variables, solve for x without using that
horribly error-prone quadradic equation, never blow an exponent or +/- sign,
produce graphs suitable for a tactile embosser, and give me the ability to
double check my answers, to say nothing of being a very capable talking
"calculator."

I started off with Maple and found the workbook and the other Java-based
user interface marginally to completely inaccessible.

Then I discovered the command-line version called cmaple.  that was much
more accessible.  I used the "interface(prettyprint=0)" command to force the
exponents into the same line as the equation instead of Maple printing them
above the equation.  And at that point, I had a pretty good solution.

Unfortunately, Maple suffers from several problems which make its use by a
blind student problematic:

1.  The two standard user-interfaces, workbook and Java-based, , are
marginally to totally inaccessible.  Use the command-line version for best
results.

2.  The program is costly even at the student price of around $100 and
requires a fair bit of fussing around to procure as a student.

3.  The installation program is a pig and requires sighted assistance and
many non-keyboard mouse clicks in certain places to complete.

4.  And here's the worst part -- you are granted a single license when you
purchase so operating on your home desktop, your laptop, and your school
workstation is going to be a problem.

Out with Maple, in with Maxima:

Once I discovered the potential of a Computer Algebra System (CAS), I was
hooked.  I then discovered Maxima and Axiom, two open-source programs simlar
to Maple but without the cost, licensing, or installation issues.

I've been using Maxima ever since.

Next steps:

I envision integrating the input and output of Maxima with my text editor so
I can do my homework in one seamless environment, capable of placemarkers,
cut and paste, variable substitution, calulations, etc

I will be switching from Notepad to Edsharp as my editor of choice since
Edsharp is so much more capable and extensible.  Creating the glue between
Edsharp and Maxima will be my project for the winter break.

A Potential Downside for CAS Use by Students:

A CAS is so capable, it introduces not only the time-saving features
described above, but the ability to solve some problems without doing the
real math.  Fortunately, most instructors would spot this by noticing you
haven't shown your work.  In addition, I've found the hardest work in math
is the problem setup and interpretation and the CAS can't do that for you.
Still, there may be some reluctance on the part of instructors to allow you
such a powerful calculator / programming language.

Next semester...

1.  An integrated editor / CAS
2.  Calculus II
3.  And in the future, maybe even Physics :~

I hope you all might find my experiments and hybrid solutions useful.  I'm
pretty sure Amanda and Dr. Baldwin will for sure.

Ben




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