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.
