Jakow Trachtenberg created the Trachtenberg system
of mathematics, whilst a political prisoner in Hilter's concentration
camps during the second world War. To keep himself sane whilst living
in an extremely brutal and harsh environment, Trachtenberg immersed
his mind in a world of mathematics and calculations. As concentration
camps do not provide books, paper, pen or pencils nearly all of his
calculations had to be performed mentally. This forced Trachtenberg
to develop methods and shortcuts for performing calculations mentally.
Trachtenberg developed his discoveries into a complete system of mathematics.
After the second world war, Trachtenberg started teaching
his system of mathematics. He started teaching the more backward children
to prove that anyone could learn his system. In 1950 he founded the
Mathematical Institute in Zurich, where both children and adults were
taught the system.
The system has been thoroughly tested in Switzerland
and is found to produce an increase in self confidence and general
aptitude to study, as the students prove to themselves what they are
capable of, by their accomplishments in calculating results to computations.
The Trachtenberg system is based on a series of keys
which must be memorized. There is no need for multiplication tables
or division as the system only relies on the ability to count. The
system also places an emphasis on getting the right answer and provides
a number of methods for checking the answers achieved by the system.
Research on the system, indicates that the system
shortens time for mathematical computations by twenty percent and
produces correct results, ninety nine percent of the time, due to
the checking method used as part of the system.
Instant Maths
Ann Cutler
Souvenir Press
A brief introduction to the Trachtenberg system. Introduces
the basic keys for multiplication by numbers from 2 to 11 and a couple
of other techniques. This book appears to be a simplified version
of 'The Trachtenberg speed system of mathematics'.
The Trachtenberg speed system of Basic mathematics
Translated and adapted by Ann Cutler and Dolph McShane
Souvenir Press
ISBN 0 285 629166
Introduces multiplication by numbers from 2 to 11.
Then goes on to deal with multiplying by 2,3 and any number of digit
multipliers. Methods of checking answers, division, squares and square
roots are covered. The book finishes with an algebraic description
of the Trachtenberg system.
