[Blindmath] Working math homework and exams

[Ben Humphreys]

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