[Blindmath] Working math homework and exams

[Tami Kinney]

Ben,

Thank you for this. In 2005/2006, I did look into taking the career 
advancement option through my VR agency to finish up my math degree... 
Since in the 7.5 years previously that I had been losing the sight to 
read print they had not gotten around to performing an on site work 
place assessment... When they failed to do their steps to go forward 
with the school plan or even answer questions, it occurred to me that I 
had best find better things to do. I have since learned that they do 
that to all of their consumers, and those who start school while waiting 
for the tools and texts they need end up pretty broken. Sigh.

Anyway, I would have been retaking calculus, which was fine because I 
needed to learn to conceptualize math non visually. Trying to figure out 
how to do that and still have time to eat and sleep made me hungry and 
tired. /smile/

For now, my plan is to rebuild the other foundations of my life and get 
back to work somehow in information management systems, then study math 
on my own until I get a tool kit built up and can just start taking math 
classes again without having to put up with a lot of hassle with VR or 
disability services...

So your explanations of the tool kit you use and your solutions to the 
problems of reading and homework production give me a lot of insight!

Best wishes for winter break and your next term.

Tami

On 11/19/2011 06:59 AM, Ben Humphreys wrote:
> 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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