[BlindMath] I need some ideas and encouragement for doing braillecalculus
Angie Matney
angie.matney at gmail.com
Fri Sep 20 12:41:51 UTC 2019
Aqil makes some very good points about LaTeX. I started learning it during freshman year, and it helped me get through undergrad and graduate school. I happen to be someone who "thinksst" in braille, and using LaTeX with a braille notetaker helped me do that. I found that in some cases, I could use a braille 'n Speak (I am dating myself) or a Braille Lite to write in a slightly stripped-down version of LaTeX. The fact that my fingers still made braille shapes for numbers and letters was helpful to me. Not sure this makes sense, but it's how my mind processed information. There were some times, like with some chain rule problems and some matrices, where I did find hard-copy braille essential. But I have been reading braille since I was four years old. So for me, using hard-copy braille, or in some cases just being able to type on a braille keyboard, feels the way that I imagine a pen and paper would feel to someone who first learned to write that way. I think I would have had a very difficult time and would have been much slower if I had been forced to use a QWERTY keyboard without a braille display. As Aqil says, it's about understanding how you process information.
Good luck.
Sent from my iPhone
> On Sep 20, 2019, at 7:26 AM, Aqil Sajjad via BlindMath <blindmath at nfbnet.org> wrote:
>
> Hi Emily,
>
> I don't have too much to add to the excellent responses from several other people. Just one thing, it is very important to have an "ends justify the means" approach when it comes to deciding how you're going to deal with accessibility issues. Some people find that braille helps them do math more efficiently. Others find that it's more of a hindrance and they can do better by using some other method. Since you're having some difficulty with braille, you might like to try doing this without braille. And see how it works. It may or may not work, but it's worth exploring.
>
> I lost my eye sight during high school and soon learned braille in the hope that it would help me with math. But I soon came to the conclusion that it was too slow and cumbersome, and was therefore not the solution for me. I went on to do a phd in physics without it. If I had stuck to braille, I would have struggled to pass even a high school level exam! Again, the point of this example is not to preach that you ditch braille, but that you explore other alternatives and find what works best for you if your current method isn't working out that well.
>
> Since you are proficient with LaTex, you could for instance just try working out a few problems just by working in that with a screen reader. Or in some cases you can use your own condensed or relatively simplified version of LaTex. One possible advantage of this will be that you will easily be able to copy and paste your equations on to a new line for further manipulation in the next step.
>
> For the chain rule, you could try writing the different pieces in separate lines. That is, the derivative of the outermost function in one line, then the next one in the second line with a multiplication sign in front, and so on.
>
> Overall, the absence of a good pen and paper alternative for math remains a challenge. If you're familiar with LaTex, then that can help.
>
> Aqil
>
> -----Original Message-----
> From: BlindMath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Emily Schlenker via BlindMath
> Sent: Friday, September 20, 2019 4:05 AM
> To: Blind Math list for those interested in mathematics <blindmath at nfbnet.org>
> Cc: Emily Schlenker <eschlenker at cox.net>
> Subject: Re: [BlindMath] I need some ideas and encouragement for doing braillecalculus
>
> Thank you so much! I will definitely change to direct braille, and I am already fairly proficient in laTex. Emily
>
> Sent from my iPhone
>
>> On Sep 20, 2019, at 2:22 AM, Radu Vasile via BlindMath <blindmath at nfbnet.org> wrote:
>>
>> Hello,
>> I am Radu Vasile from Romania and I have graduated in Math and Computer science.
>> I am now working as a software developer and I have my own business in this at this moment.
>> Also, right now I am enroled in a phd in Math.
>>
>> I had no Braille Display in my studies.
>> I have recorded courses on tapes and in the evening I have transcribed them in Braille using a Perkins like machine.
>> During exams, I have used my Perkins machine to write down problems and exercises, and then solve them.
>>
>> Nothing is better for a big math problem than to have all the information, from different parts of the page, at your disposal in the same time.
>> A Braille display will never do the job.
>> Using direct Braille, you can have several pages of informations around you, checking them in the same time.
>> Using a Braille display, to see what is in the previous pages, you must navigate back and forth and you loose focus.
>>
>> Now, in my PHD studies, I take latex sources from my professors and print them using a Braille Printer to be able to read them.
>> To write, I use Latex, or latex like expressions, so my professors can read what I write.
>> Most of the time we communicate using latex like language, because even sighted persons do this between them when they communicate by writing on social media accounts, or other online tools.
>>
>> Using latex like language, I was able to do computations in notepad using a screen reader.
>> I move expressions by cut and paste.
>> And from step to step I write what transformation I apply there.
>>
>> The main Idea is that you need direct Braille to be able to follow big computations, or a procedure like mine using a latex like notation.
>>
>> I am able to do computations directly in my head too, but it is better on the paper, because some times I found my self computing the same thing again and again, because I have forgoten it.
>>
>> The second main idea is that calculus is no so hard as it appears in the beginning.
>>
>> Best Regards
>> drd. Radu VASILE
>> e: rvasile at gmail.com
>> t: +40722614784
>> -----Original Message----- From: Emily Schlenker via BlindMath
>> Sent: Friday, September 20, 2019 3:36 AM
>> To: Blind Math list for those interested in mathematics
>> Cc: Emily Schlenker
>> Subject: Re: [BlindMath] I need some ideas and encouragement for doing
>> braillecalculus
>>
>> Hi. You have really inspired me, and now that you mention it, I am much calmer when I’m doing math mentally. The problem is, it is hard for me to keep track of problems where I do three or 4 chain rules and one or two product rules, and then I have to put it all together. I also get very lost with implicit differentiation. These often have fractions with different denominators and ugly numerators. I would love to have a little bit of tutoring on the weekends. I really think this will make my brain better overall if I can do more and more in my head.
>>
>> Sent from my iPhone
>>
>>> On Sep 19, 2019, at 7:25 PM, David Moore via BlindMath <blindmath at nfbnet.org> wrote:
>>>
>>> Hey guys!
>>> I majored in mathematics at the Ohio State University!
>>> I loved calculus, because the disability office did such a great job a converting all graphs into tactile form.
>>> Also, I had an Optacon.
>>> The Optacon allowed one to run a small camera over the page, and I could feel exactly what a sighted person could see as a vibration on my finger tip of my left hand.
>>> I traced graphs, and learned what all of the symbols look like in print!
>>> I used tapes from the Recording for the Blind, which is now Learning Ally!
>>> I would hear the function on tape, and I would take the derivative or the Integral in my head, and I would check the answer that was read to me on the tapes from the back of the book!
>>> Also, I spent time with many sighted engineering majors, and they took my hand and traced all kinds of graphs with my hand.
>>> They explained how a simple graph can be moved around, stretched, and made fat or skinny to make the graphs of much more complicated functions!
>>> The derivative
>>> Is slope, and the second derivative tells you where the graph changes from curving upward, to downward, the inflection points on the graph!
>>> I did so many of my calculations in my head, and never in Braille!
>>> Braille just slowed me down.
>>> I wrote my math for my professors by writing a symbol in words!
>>> For example,
>>> The derivative of (X^2 + 1)^2
>>> Requires the chain rule giving!
>>> And then I just kept writing each step out like that!
>>> They understood what I was writing.
>>> For example,
>>> Integral of E^(x^2) does not have an anti-derivative!
>>> Take care, guys, and I will help you and tutor you for free over concepts that are giving you problems!
>>> Have a great day!
>>> David Moore
>>> Sent
>>> from Mail for Windows 10
>>>
>>> From: Nicolas Spohn via BlindMath
>>> Sent: Thursday, September 19, 2019 8:01 PM
>>> To: Blind Math list for those interested in mathematics
>>> Cc: Nicolas Spohn
>>> Subject: Re: [BlindMath] I need some ideas and encouragement for
>>> doing braillecalculus
>>>
>>> Hi Emily,
>>> I think it is interesting that I got your message today because today I have been thinking a lot about how frustrating calculus is. I am a high school senior taking advanced placement calculus. My blindness occurred a few years ago so I am not up to par with braille. I have been using math player to read my equations. One of my biggest struggles is interpreting tactile graphs. Another one of my struggles is making sure I am typing my work on Microsoft word in a way that my teacher understands it. Keep putting forth the effort with calculus! I always say to give something a try and figure out whether or not it’s possible or whether or not it’s something worth trying. Keep at it! I’ll try to keep at it too!
>>>
>>> Nick
>>>
>>> Sent from my iPhone
>>>
>>>> On Sep 19, 2019, at 7:05 PM, Emily Schlenker via BlindMath <blindmath at nfbnet.org> wrote:
>>>>
>>>> Thank you so much. I am very lucky in that we have an office at my university where I get all of my tactile diagrams done for all of my classes. They also do my braille, and if I need a graph at the last minute, they will make it. Awesome idea about the calculator.
>>>>
>>>> Sent from my iPhone
>>>>
>>>>> On Sep 19, 2019, at 5:36 PM, Doug and Molly Miron via BlindMath <blindmath at nfbnet.org> wrote:
>>>>>
>>>>> Dear Emily,
>>>>>
>>>>>
>>>>> When I learned calculus I was a low vision person, not totally blind. I did not use braille. Now that I am totally blind I can understand the desire to work in braille, but there is a problem in that so much of calculus instruction is based on graphs, which are poorly supported in the tactile display world. One thing you have described is a shortage of braille display space for your equations. There are several braille displays available that will handle many lines of braille that might ease your problem. The TI84 graphical calculator abailble from APHB might help also. Good luck.
>>>>>
>>>>>
>>>>> Regards,
>>>>>
>>>>> Doug Miron
>>>>>
>>>>>> On 9/19/2019 2:52 PM, Emily Schlenker via BlindMath wrote:
>>>>>> Hi, everyone. I am in first semester calculus, and I am really
>>>>>> struggling. I understand the processes, but I am having trouble
>>>>>> staying organized while working problems in braille. I use a
>>>>>> braille notetaker with 32 cells, and I am having trouble with
>>>>>> things like the chain rule that require lines and lines of
>>>>>> equations. The actual line on my braille sense is not long enough
>>>>>> to accommodate some of my equations, and I get flustered and lost
>>>>>> scrolling between so many lines. Ho do those of you who are
>>>>>> braille users stay organized? Do you have any strategies for
>>>>>> keeping parts of the same problem organized? I am not opposed to
>>>>>> breaking out the Perkins Brailler with wide paper, but I am also
>>>>>> wondering if there is anything else I can do to be successful. I
>>>>>> have a great instructor who always goes step by step and doesn't mind repeating things, but I always get lost about half way through big problems.
>>>>>>
>>>>>> Thanks for any help you can give me.
>>>>>>
>>>>>> Emily
>>>>>>
>>>>>>
>>>>>>
>>>>>> ---
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>>>>>
>>>>>
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