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How much faster are various mathematical operations using a Trachtenberg method rather than a conventional method?

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If, like me, you had never heard of Trachtenberg, then you might find this article interesting: en.wikipedia.org/wiki/Jakow_Trachtenberg. In WWII Trachtenberg and his wife were placed in a concentration camp, but they managed to escape. (Wow.) –  Pete L. Clark Jan 9 '11 at 17:17
    
He actually escaped assassination, prison, and three concentration camps while creating the Trachtenberg system! How's that for awesome? –  Josh Aug 6 '13 at 17:01

3 Answers 3

From playing with the system a little myself, 20% sounds close for day to day use and not putting in much dedicated practice. As with most mental math (and most math in general) speed will increase based on practice. I enjoy that there are only a small number of techniques used for a large number of applications, rather than a large number of application specific techniques to memorize as in some systems.

The more extreme example mentioned sounds more like a stage demonstration than an average improvement.

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It depends on what area of arithmetic you are talking about

It's really useful in some places whereas at times it just involves a lot of learning by rote where normal conventional methods could have their way much more easily.

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I understand that speed will vary greatly, but I was hoping for a rough estimate or even some test results that would give me an idea of how much faster the Trachtenberg system is. –  Josh Jan 9 '11 at 18:49

According to the book 'The Trachtenberg Speed System of Basic Mathematics', "A thin, studious-looking boy wearing silver-rimmed spectacles was told to multiply 5132437201 times 452736502783. He blitzed through the problem computing the answer—2323641669144374101785—in seventy seconds. The class was one where the Trachtenberg system of mathematics is taught." The book also states that "Educators have found that the Trachtenberg system shortens time for mathematical computations by twenty percent.", although this statement does not seem consistent with the previous example.

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