[BlindMath] synthetic division

Sun Feb 16 18:29:16 UTC 2025

Thank you to everyone who responded to this post. I am passing the
information, which for the most part aligns with my old school thoughts, on
to the TVI and math teacher who actually have this student now, as I am
only transcribing his materials at this point. But having had the student
for the last 12 years as his TVI, I know what his math skills are like and
what has worked well with him to this point. I feel pretty free to make
suggestions on what I think will be beneficial, whether they are taken or
not.

A quick story related to using a Perkins for math. Many years ago I had a
student who was incredibly good at math. We completed Algebra 1 when he was
in third grade. The summer after, he moved to Michigan. His TVI immediately
took him off a Perkins brailler and onto a BrailleNote  for math.
Ironically, he had moved within about 10 miles of Dr. Nemeth. As luck would
have it, a reporter who had covered the student for the Braille Challenge
knew Dr. Nemeth and put the two of them in contact. When they met, one of
the first questions Dr. Nemeth asked was what methods the student used to
work with and produce math. He told the mom to get the Perkins brailler out
again. I'm not sure what his thoughts would be today and technology has
improved considerably since then, but I could never wrap my brain around
doing anything spatial or extremely complex on only one line of refreshable
braille, particularly for young learners.

Thank you to those who shared their methods for doing this work.
Shelley

On Sun, Feb 16, 2025 at 1:00 PM Ken Perry via BlindMath <
blindmath at nfbnet.org> wrote:

> I have to speak up .  I took college in the 90's I lost my sight at 20
> going on 21.  I took my assessment test to go into college as a 100% blind
> person. I never used a braille display or perkins braille and did all my
> math with an editor on Dos first and windows later.  I took everything from
> Matrixes all the way up to the last Calculus without braille. Doing it in
> my own Ascii  like short hand.  I of course had a writer which was allowed
> back then. I could also do several pages of math in calculus in my head
> accurately.  There is something to be said about learning to do the math
> without a braille display. I used that rubber board and plastic to draw
> graphs which was not easy but I did it.  I did long division as a sighted
> person in High School but was able to do long division both regular and
> with polynomials all with an editor on the computer.  I wish we had more
> tools like the original Hinter Joice Pencil and Algebra with the new tools
> like Graphiti and monarch.    I code software for Braille and support
> braille but there are some of us out here that do math without it.
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Susan
> Osterhaus via BlindMath
> Sent: Sunday, February 16, 2025 12:34 PM
> To: Blind Math list for those interested in mathematics <
> blindmath at nfbnet.org>; peter.julien.rayner at gmail.com
> Cc: Susan Osterhaus <osterhauss at tsbvi.edu>
> Subject: Re: [BlindMath] synthetic division
>
> Yes John! Our students at TSBVI still use the Perkins braille writer for
> polynomial division and working matrices manually. However, we also let
> them use an accessible calculator such as the Orion TI-84+ or Desmos for
> working with larger matrices. We need to try using multi-line braille
> displays for polynomial division and solving systems of equations and
> inequalities.
> However, many cannot afford these yet, although there are programs in
> place for making some more affordable.
>
> Peter, I still remember having to teach division of polynomials on a
> braille writer to students who had never learned long division in the early
> grades.
> Yes, it is not easy teaching or learning long division for the first time
> in high school!! Nevertheless, my students got it!!
>
> Shelley, I wanted current blind users to speak up first before I answered
> you. I think the old fashioned method of using the Perkins braille writer
> is still the best method. Even if you do have a Monarch at your fingertips,
> starting on the braillewriter would probably be a good idea. Then, see if
> you can transition to a Monarch or other multi-line braille display.
>
> In addition to polynomial division, solving systems, and working with
> matrices, it is also difficult (if not impossible according to the
> single-line braille display users that I know) to create a number line
> graph unless you have access to at least 3 lines of refreshable braille at
> the same time. Again, start with the tried and true braille writer, and
> then try it on a multi-line braille display.
>
> The old, but still not retired,
> Susan
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of John Miller
> via BlindMath
> Sent: Sunday, February 16, 2025 10:25 AM
> To: peter.julien.rayner at gmail.com; blindmath at nfbnet.org
> Cc: John Miller <johnmillerphd at hotmail.com>; blindmath at nfbnet.org
> Subject: Re: [BlindMath] synthetic division
>
> Hello, I do polynomial division to this day using a Perkins braille writer.
> It is a key concept and data communications in engineering. Also finding
> the inverse of a three-dimensional or a four dimensional matrix is quite
> useful on a Perkins braille writer, despite having access to a single line
> braille display very best John.
> Sent from my iPhone
>
> > On Feb 15, 2025, at 1:38 PM, Peter Rayner via BlindMath
> > <blindmath at nfbnet.org> wrote:
> >
> > I'd never heard polynomial division called this before. I can imagine
> > doing this without some multi-line display by working out the first
> > term in the quotient, multiplying out the denominator, gathering
> > coefficients and subtracting then rince and repeat with the remainder
> > but good grief it would be horrible! Doing my own algebra is the last
> > major use case for my perkins and polynomial division is a good
> > example why.
> > btw, it wasn't until I learned polynomial division that I really
> > understood how long division worked.
> > cheers
> > Peter
> >
> >
> >
> > Shelley Mack via BlindMath writes:
> >> Greetings!
> >>
> >> If a student is beginning to learn synthetic division of polynomials,
> >> should the student begin on a Perkins brailler? Or I suppose a
> >> Monarch? I am transcribing for a student who does work primarily on a
> >> BrailleNote, but I can't envision a way to learn to do this one
> >> braille line at a time.
> >> (Sidebar: I am definitely old school when it comes to math in
> >> braille, being a retired TVI and certified transcriber. But if
> >> someone has a better way, please let me know.) Thoughts?
> >>
> >> Thanks,
> >> Shelley Mack
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> >
> > --
> > Peter Rayner (he/him), Honorary Professorial Fellow, University of
> > Melbourne mobile +61 402 752 379 zoom id 4431343191, join at
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> > Zz09>
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> > I acknowledge the Traditional Custodians of the land on which I work,
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