[Blindmath] Division of Polynomials

[John Gardner]

Hi Susan, I agree with you that it is important for students who need to
master the subject to be able to communicate with sighted peers.  Which
means that understanding standard visual layout is usually important even if
there are alternate ways to approach a problem.  For people fluent in
Nemeth, your references are very good, and most Nemeth-speaking students
would do well to follow your advice.

I will point out however that understanding visual layout does not
necessarily require Nemeth braille.  Or any braille.  Pranav's suggestion of
using Excel fulfills the same need of understanding layout and can be used
by braille readers or by audio speech readers.  Though braille is probably
faster.

Be well.
John 

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Susan
Jolly
Sent: Sunday, May 04, 2014 3:22 PM
To: blindmath at nfbnet.org
Subject: Re: [Blindmath] Division of Polynomials

Let me start by saying that I know from my own experience as a student, 
teacher, and parent that not all teachers fully understand their subject.  A

good teacher is able to communicate with a student and distinguish actual 
misunderstandings from the student's use of an alternate but valid approach 
to problem solving.

I also feel that educational materials in mathematics are often 
unnecessarily visually-based.  This can be true even in the lower grades 
such as when a child is asked to count the monkeys who are eating bananas.

Finally, I hope that students always have the goal of understanding the 
content of a course, not just figuring out some way of getting through the 
course without understanding what is being taught.  However, I am not naive 
enough to think the latter doesn't happen all too often.

Those of you were expecting that a "but" is coming were right.  But I do 
think that it is important for braille-using students to understand how and 
why common solution procedures work even if they choose to use alternate 
procedures.  One reason is communication.  There is important mathematical 
terminology that depends on spatial concepts.  The term "place value" is an 
example. Another reason is that you might need to teach this material to 
someone else.  After all, Dr. Nemeth taught university math for more than 30

years.

Back to the subject. My concern is whether there is a need to reinvent the 
wheel. The official document for Nemeth Braille was adopted in 1972 and  is 
available in both print and braille.  Its title is "The Nemeth Braille Code 
for Mathematics and Science Notation 1972 Revision." The print version of 
this book presents print math side-by-side with the corresponding simulated 
braille in a way that should be easy for any sighted person to understand. 
Section 180 gives two examples of braille spatial arrangements for division 
of polynomials. Section 182 explains synthetic division and gives four 
choices of spatial arrangements for the sample problem.

There is also a very thorough book on doing spatial math in braille that was

adopted in 1987.  The title is "Learning the Nemeth Braille Code" by Ruth H.

Craig although the book doesn't cover higher mathematics.

I am very sympathetic to those of you who are students and are having 
frustrating experiences. I'm happy for you to write me privately and ask 
questions.  I have a strong background in chemistry, math, computational 
math, and computer programming and at the very least know enough to know 
what I don't know!

Best wishes,
SusanJ



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