The Trachtenberg Speed System of Basic Mathematics

by Jakow Trachtenberg, Ann Cutler (Translator), Sam Sloan (Introduction)

The Trachtenberg Speed System of Basic Mathematics is a revolutionary system for calculating and teaching basic math. Children, who had repeatedly failed in arithmetic until their parents sent them to learn this method, were able to perform amazing calculations within seconds. In one demonstration, a ten year old child, when asked to multiply 5132437201 times 452736502785, simply wrote on the blackboard the answer, 2323641669144374104785, in seventy seconds. He never set up the basic and familiar line by line chart, multiplying and adding each row of numbers. Instead, he just wrote down the answer without any of the intermediate steps. To demonstrate his method, Trachtenberg chose children who were doing poorly in their school work. These were children used to failure, shy and withdrawn; or at the other extreme, rebellious and unmanageable. The children's responses to the new, easy way of doing arithmetic was immediate. They found it delightfully like a game. The feeling of accomplishment soon made them lose their disagreeable traits. Equally important were the by-products the pupils attained while learning this new system. As these youngsters became proficient in handling numbers, they began to spurt ahead in all their studies. Their IQs went up as well! Not only did the child learn to compute, but his IQ also went up. Since all problems were worked out in his head, he developed an excellent memory and his ability to concentrate was increased. The Trachtenberg system, once learned, can take the drudgery out of the arithmetic that is part of everyone's daily stint. Experts believe that the Trachtenberg system could have far-reaching effects on education and science.

Genres: Mathematics, Nonfiction, Science, Reference, Education, Puzzles

272 pages, Paperback

First published January 1, 1960

About the author

The late Jakow Trachtenberg, founder of the Mathematical Institute in Zurich, Switzerland, and originator of the startling new system of arithmetic, was of firm opinion that everyone comes into the world with 'phenomenal calculation possibilities.'

Trachtenberg married Countess Alice, a member of the [German] aristocracy. An outspoken pacifist, Trachtenberg wrote Das Friedensministerium, a widely read work, which brought him the plaudits of such statesmen as Roosevelt, Masaryk, and Van Zeeland.

Trachtenberg, a brilliant engineer with an ingenious mind, originated his system of simplified mathematics while spending years in Hitler's concentration camps as a political prisoner.

Trachtenberg died in 1953.

Reviews

[Michael · Rating 1 out of 5]

I'm a math major in school. I'll be applying to graduate school for math in a few months. I'm taking the General GRE in a couple weeks and the Math Subject GRE not long after. So, to help me prepare I bought a few books on... arithmetic?

Yes. See, I have a problem. I screw up arithmetic constantly. I have actually written the following on a Calculus test: "6 + 3 = 8." Usually I'm not quite that bad, but when adding/multiplying large numbers, chances are extremely high I will make a mistake.

So I thought maybe there were other algorithms out there that could improve my accuracy here, and I ordered some books. Unfortunately, I don't believe this system is helpful. It mostly consists of reworkings of the standard multiplication/division algorithms. They are described in such a way that it may not be immediately apparent that that's what they are. For instance, instead of memorizing, say, the times table for 6, you memorize a rule for how to multiply a digit by 6. This really doesn't buy you anything.

The methods usually involve less writing down intermediate steps, but all the same calculations are there.

One very good thing mentioned in this book is the error checking method "casting out nines," here called the "digit sum method." However, this is not original to the system; it has been around for hundreds of years (as the book admits). Plus, unfortunately, the book does not make clear that it is possible for a calculation to pass this error check and still be incorrect; that is, when the check says you're wrong, you're wrong, but when it says you're right, you're only *probably* right. In fact, the book strongly implies the contrary.

The foreword claims that students using this system faced off in a test of arithmetic against "mechanical brains" (did people really call computers that??) and the students won. Hmm. Well, the mechanical brain sitting on my desk right now can do millions of arithmetic operations per second. This kind of statement may have *almost* made sense in 1960, but today...

Lastly, I have to complain about one more thing. This book strongly encourages a misconception that some people have about mathematics. I'm referring to the idea that arithmetic IS mathematics, and that being good at mathematics means being good at arithmetic. Arithmetic is to mathematics as spelling is to poetry.

[Sana · Rating 4 out of 5]

I can't compare this to the other books I've read, but I can definitely say that I enjoyed every minute of this. Scribbling down numbers, getting calculations right and not being dissapointed in math was fun

[Yingtai]

I know it was not part of the brief of this book, but I really would have liked to know why these methods work.

[Richard Craig · Rating 5 out of 5]

If you or perhaps your child,has difficulty with mathematics,the Trachtenberg system is well worth a try.
Trachtenberg developed a clever system of mental mathematics and arithmetic whilst he was being held as a prisoner in a Nazi concentration camp.Trachtenberg was an outspoken pacifist and openly condemned Hitler and the Nazi regime.
The Trachtenberg method is not only speedy but simple.There are no multiplication tables and no long division as we know it.To add long columns of numbers we need not count higher than eleven!In fact one needs only to count to eleven to master the entire system!It is quite simply brilliant.A book I would recommend to any one who has difficulty with maths or those who simply want to increase the speed of there mental calculations.Every home school should own a copy.
R.E.Craig

[Nicholas Martinez · Rating 5 out of 5]

An incredible alternative to multiplicative operations. I had to read this one twice to qualify a full understanding--each time taking some time to practice the techniques for an hour or two after learning them. That being said, this reframed my mental concept of multiplication, division, and back of the envelope calculation in general, complete with practice problems and a sensible teaching slope. The more I learn about mathematics and science, the more alive it seems to be, with breathing, symbiotic relationships. In my opinion, this book is another window to that perspective. Any student of math or science, formal or lifelong, can benefit from this book.

[Frank Ashe · Rating 5 out of 5]

My dad showed it to me in primary school and I was entranced.

[Mainak Jas · Rating 5 out of 5]

I read this book long ago (more than 10 years ...). Yet, it is still crystal clear in my head as if it was yesterday. What I really love about this book is not just the methods but the fact that the author offers proofs in the book's appendices. This is in sharp contrast to many books on Vedic mathematics which also dealt with speed mathematics, but the reader is left to trust the author without any proofs. The techniques themselves are rather ingenious. He not only offers methods to compute the result quickly but also how to check if the result is correct. The pen and paper version of checksums in computing :) This, combined with the backstory of all this being developed in concentration camps makes it such an inspiring read!

[Smallllama · Rating 5 out of 5]

Outstanding. This man should have universities and cities and libraries named after him. Nonetheless, I would not give this book to a child. Its methods could greatly speed up the child but, until a person is sophisticated enough to understand what is going on behind the scenes and WHY these things work, learning to do math this way provides a weak foundation for learning higher concepts. This system's weakness is that it makes math seem like mystical powers.

[Adrian Goh · Rating 1 out of 5]

Didn't really find the system effective or quick. Neither did I find it intuitive. The traditional system was more intuitive and more efficient it seems.

[Chelsey · Rating 5 out of 5]

This book contains educational information that will change the way a person looks at mathematics. Developed by Jakow Trachtenberg, he explains the simplified version of completing mental math. Born in Russia, he created a system while captured in Hitler's concentration camps and later on taught students the system. If mathematics is difficult, this book will help you to see a different way that is not taught within the school systems of America.

[Colin · Rating 3 out of 5]

I'd rate this as 'slightly interesting, but a bit self-important' -- the method itself seems to be a few tricks hacked together. (There is a section on the algebra at the end, but it's very much tacked on as an afterthought). I find it hard to imagine anyone taking this book and learning to do arithmetic from it.

[Michael Hooper · Rating 4 out of 5]

A very good book with a very good system. My only complaint is that the examples are a bit muddled, the author will give two example and work through them both concurrently, so it can get confusing as to which example one should follow.

Regardless, a must read book id say.

[OmAr Alex]

!!

[Mister Oolong · Rating 5 out of 5]

A practical guide for basic arithmetic. The multiplication chapters were particularly useful.

[Dhruva Choudhary · Rating 5 out of 5]

A book that will explain to you how to multiply faster without any mistakes, so far I have been unable to find any exceptions for the methods this book has given

[Priyank · Rating 4 out of 5]

Simplified techniques to solve the basic day-to-day mathematical problems. Very good book to read at an early stage to get a glimpse of the magic of arithmetic!!!

Although most of the methods need some practice to get a hand-on, some methods are very natural, that we might be doing without consciously knowing about it.

[Hilary · Rating 5 out of 5]

Genius book! Trachtenberg devised a new system of teaching mathematics while incarcerated in a Nazi concentration camp -- true story! The system works! It is more efficient, effective, and accurate than anything else I have ever seen. This approach should be used in every public school!

[Polar Bear · Rating 5 out of 5]

Very interesting review of how we perform basic mathematics. I learned this system long ago so I've forgotten everything except multiplication by eleven (the easiest trick). Just add each digit to its neighbor and some other stuff. It's worth reading in my opinion.

[Michelle · Rating 5 out of 5]

Very interesting, somewhat useful. Seems like the authors exaggerate the benefits of the system though. Explanations of the methods are very thorough. A fun read. Lots of cool arithmetic tricks.

[Mazhar Shakeel · Rating 5 out of 5]

best one

[Pandu Reddy · Rating 2 out of 5]

KKJK/IOOI

[Tushar Gargava · Rating 3 out of 5]

I'll re-read it. But in one read, it seems more complicated than what I'd expected it to be. Maybe once I start working on the methods mentioned, I might understand the significance of it better?

[Giang Nguyễn Ngọc]

It is very good