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 PressA 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 629166Introduces 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.
http://hucellbiol.mdc-berlin.de/~mp01mg/math.htm
Explanations and examples.
http://www.shermankeene.com/tracten.html
Free Trachtenberg Mathematics Software.
http://www.ecis.org/profdev/newsletter/aug96/maths/maths6.htm
Simple school project on Trachtenberg.
http://forum.swarthmore.edu/dr.math/faq/faq.trachten.html
Dr. Math's FAQ on Trachtenberg (rules and examples).