How do I learn speed math? (Trachtenberg system)

[Matt Harrington]

A professor has recommended a book entitled the Trachtenberg System of
Mathematics, but all three copies from my library are missing. Is
anonyone familiar with this subject?

I am looking for techniques to improve my simple arithmetic. When I was
in grade school, I remember a fad where people could do complex
arithmetic by manipulating their fingers. Is this the Trachtenberg
system?

Any suggestions would be greatly appreciated. Thanks in advance.

Regards,

Matt Harrington

[Dave Joyce]

I have the book and read it many years ago. I does have faster algorithms
for multiplication and division. These algorithms are only slightly more
complicated than the usual ones, if that. Since the advent of calculators,
though, I don't think it makes any sense spending time learning how to
multiply and divide faster.

--
David E. Joyce Dept. Math. & Comp. Sci.
Internet: djo...@black.clarku.edu Clark University
BITnet: djoyce@clarku Worcester, MA 01610-1477

[John A Mess]

Matt Harrington writes:
>A professor has recommended a book entitled the Trachtenberg System of
>Mathematics, but all three copies from my library are missing. Is

>I am looking for techniques to improve my simple arithmetic. When I was
>in grade school, I remember a fad where people could do complex
>arithmetic by manipulating their fingers. Is this the Trachtenberg
>system?

The Trachtenberg System is a collection of techniques. Most of these have
appeared in various books: _Rapid Math_ by Sloan, as well as popular math
books. Most are based upon the "Principle of 9" though often not obviously.
For example, 7*9=63, 8*9=72, etc. notice that the digits sum to 9. That's
one trick. that 235*11=2585 where [2] [2+3] [3+5] [5] (ie., the consecutive
sums) is yet another. This is not to disparage the "system" because it does
provide a nice algebraic description of why the techniques work. He does
expand the principles to include integral long division, multidigit opera-
tions, and square root extraction. In all systems in my experience, the
key is practice. (I personally find that for anything over 4 digits, I'd
rather have a calculator :-) .) You will not become an instant math whiz.

As for the finger systems, there are at least two. In both cases, it was
again simple memorization and practice. In one system, the fingers code to
99; starting with the left pinky: 40 30 20 10 [50] [5] 1 2 3 4. The thumbs
are "5-markers" which, when down, add five (or fifty) to the count. The rest
is patterns and shifting. It does raise eyebrows at test time, however.

Now as for my method, I started by memorizing the 4-place log tables ....

[murdoch]

In article <15mjf9...@network.ucsd.edu>, m...@sdphu3.ucsd.edu (Matt Harrington) writes:
>
>
> A professor has recommended a book entitled the Trachtenberg System of
> Mathematics, but all three copies from my library are missing. Is
> anonyone familiar with this subject?
>
> I am looking for techniques to improve my simple arithmetic. When I was
> in grade school, I remember a fad where people could do complex
> arithmetic by manipulating their fingers. Is this the Trachtenberg
> system?
>

I tried to learn the Trachtenberg method butlost interest half way through
because i do not wish to impress others (i did it when i was a teacher and
wanted to impress my pupils, but now i teach education courses and so ...)
The chinese use fingers to count up to 100,000 eg. the litter finger is
used to stand for 1,2,3 (right side), 4, 5, 6 (middle joints), 7, 8, 9 (the
other side) but i did not learn how to use it to speed up calculations.

[David Bradley]

Article 22435 of sci.math - m...@sdphu3.ucsd.edu (Matt Harrington):

>A professor has recommended a book entitled the Trachtenberg System of
>Mathematics, but all three copies from my library are missing. Is
>anonyone familiar with this subject?

>I am looking for techniques to improve my simple arithmetic. When I was
>in grade school, I remember a fad where people could do complex
>arithmetic by manipulating their fingers. Is this the Trachtenberg
>system?

The finger fad is known as "Chisen-Bop" and is not the same as the
Tractenberg system. (I experimented with both back in public school).

My experience has been that _public_ libraries will sometimes carry the
book of Ann Cutler and Rudolph MacShane that you seek, namely, The
Trachtenberg Speed System of Basic Mathematics, to give its full title.

At one time I had mastered the Trachtenberg long multiplication technique,
where you write down only the answer to a problem such as 69854 x 379,
but it is now long forgotten. However, I still make use of the modulo
11 addition technique and "casting out 11's" when I tire of working mod
10 and casting out 9's.

Ann Cutler authored a kiddie version of the book, also published by Double
Day, in which she explains how to teach multiplication without memorizing
multiplication tables.

-D.M.Bradley

[alvara...@yahoo.com]

yo what the hel
l, 1992, shitttttt