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

[Smith, Andrew via Blindmath]

Amanda,
I'm curious, could you describe your algorithm?  I know some students
who are pretty much starting division; perhaps it could spare them the
hours and hours that we recall with such...fondness.
Thanks.


On 5/14/14, Amanda Lacy via Blindmath <blindmath at nfbnet.org> wrote:
> 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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