[Blindmath] Working math homework and exams

[Amanda Lacy]

Indeed I will appreciate this.

Amanda
----- Original Message ----- 
From: "Ben Humphreys" <brh at opticinspiration.org>
To: <blindmath at nfbnet.org>
Cc: "Doris Pichardo" <pichardo.doris at gmail.com>
Sent: Saturday, November 19, 2011 8:59 AM
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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