[Blindmath] Working math homework and exams
Bente Casile
bente at casilenc.com
Sun Nov 20 22:04:57 UTC 2011
Ben,
I totally agree that self paced calc I would not be good for someone on
your career path. As someone who worked on a math major I know the
courseload that is in your future. I just thought that I would offer it up
as possible accessible material that could act as a supplement. While I
have to admit it has been years I took Calc 1,2,3 Diff Eq, Linear Algebra,
Modern Abstract Algebra back in the day. If you ever need a set of eyes or
just want to "talk" through a concept contact me offline at
bente at casilenc.com I tutor math at a DSS office but I must admit precalc is
as high as I work with currently.
Bente
-----Original Message-----
From: blindmath-bounces at nfbnet.org [mailto:blindmath-bounces at nfbnet.org] On
Behalf Of Ben Humphreys
Sent: Sunday, November 20, 2011 8:04 AM
To: Blind Math list for those interested in mathematics
Subject: Re: [Blindmath] Working math homework and exams
Bente,
Yes, I looked into those online materials before starting at my
college, actually talked to Professor Blank who created much of it
back in the 1990s. He's now retired.
There were a few issues with this approach:
1. It was by definition self-paced and without the benefit of a
live-instructor
2. It covered about 75% of the content of a calculus I course
3. There was no path for the remaining 25% of calc 1
4. There was no path for calc 2 or calc 3
My feeling was that the lack of instructor-led support, the lack of
"college credit", and having no future path to the remaining calculus
required of an engineering student rendered this approach inadequate
for my needs. It would only have prolonged the inevitable, which is
the very cold plunge into a mainstream university math track.
Ben
At 06:56 PM 11/19/2011, you wrote:
>Ben,
>
> I know this is late, but check out the link. It is a calculus class
>specifically designed for blind/VI students. I have not looked at it in
>detail, but it could be worth a look. It might give you an option other
>than the learning ally book, at least for understanding concepts.
>
>http://163.238.35.147/CalculusForTheBlind/index.html
>
>Bente Casile
>
>-----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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