[Blindmath] Linear formulas for synthetic division algorithm available in Nemeth braille

[Amanda Lacy via Blindmath]

I've taken math through calculus 3 and can't exactly remember how to do 
long division. I have an algorithm I use in my head that works. I have 
painful memories of those hours and hours I spent on the Purkins trying 
to line up rows and columns when I was in the third or fourth grade, but 
those aren't useful memories which enable me to solve anything. As soon 
as I found an algorithm that made sense to me I must have used it and 
forgotten the rest.
On 5/14/2014 4:37 PM, Jonathon Yaggie via Blindmath wrote:
> Susan,
>
> My inability to read braille in general hinders me from actually being able
> to read what you wrote very well.  But a couple important notes on the
> mathematics of the division algorithm which I think should be noted to
> students if plan to use it.
>
> 1) One does not need to add zeros when using the division algorithm as one
> does in the spatial version
> 2) It works for all polynomials e.g. synthetic division is a special case.
> 3) it is important also to note that this is the long division algorithm.
>   How do blind children learn long division? or dont they?  Such a simple
> thing I have never even considered.
>
> In addition, are there example in there?  i had written out some examples.
>   I will attach them (tex and pdf) if you want to use them.   It makes me
> feel like the 40 pages of background I wrote for my MA thesis was not a
> waste :)
>
> Jon Yaggie
> EYH Volunteer Coordinator
> UIC Mathematics
>
>
> On Wed, May 14, 2014 at 4:17 PM, Susan Jolly via Blindmath <
> blindmath at nfbnet.org> wrote:
>
>> I have written and posted an article which gives the formulas for the
>> algorithm on which synthetic division is based. The article is in print but
>> all of the formulas and other math are written in Nemeth braille. My main
>> intent is to be of benefit to braille users who prefer not to use standard
>> spatial algorithms.
>>
>> The formulas are given at the start of the article and are followed by
>> background material including an explanation of the notation in the
>> formulas.
>>
>> I would like to thank Jon Yaggie for making me think more carefully about
>> the importance of understanding division of polynomials.  My article
>> includes a reference to an article by two college math professors which
>> explains the importance to higher math of a good understanding of long
>> division.
>>
>> Here is the link to my article:
>> http://www.dotlessbraille.org/SyntheticDivision.htm
>>
>> I welcome feedback as to errors or material that isn't clear.  I'm also
>> glad
>> to answer any questions about the topic.
>>
>> Some of the students on this list have indicated that they've been having
>> some difficulties in their math classes. My hope is that studying my
>> article
>> can help students to identify some particular reasons why. It might be
>> useful to take notes whenever having problem understanding the article.  It
>> could be lack of ease with Nemeth math, forgetting or not knowing certain
>> definitions, poorly written explanations on my part, lack of familiarity
>> with assumed background material, or any number of other reasons.
>>
>> Best wishes,
>> Susan Jolly
>>
>>
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