The Trachtenberg System is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp. This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplicands. This is held as a temporary result.

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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 kid when asked to multiply times simply wrote on the blackboard the answer, 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These were children used to failure, shy and withdrawn; or the other extreme, boastful and unmanageable. The children's response 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 unhappy traits. Equally important were the by-products the pupils garnered while learning the new system.

As these youngsters became proficient in handling numbers, they began to spurt ahead in all their studies. Their IQs went up too! To prove the point that anyone can learn to do problems quickly and easily, Trachtenberg successfully taught the system to a ten-year-old-presumably retarded-child. Not only did the child learn to compute, but his IQ rating was raised. Since all problems are worked in the head, he acquired excellent memory habits and his ability to concentrate was increased.

The Trachtenberg system, once learned, can take the drudgery out of the arithmetic that is part of your daily stint. Experts believe that the Trachtenberg system could have far-reaching an effect on education and science.

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How does Amazon calculate star ratings? The machine learned model takes into account factors including: the age of a review, helpfulness votes by customers and whether the reviews are from verified purchases. Review this product Share your thoughts with other customers. Write a customer review. Most helpful customer reviews on Amazon. Verified Purchase. Disclaimer: stopped reading after ch. First of all, I want to answer the question: will this book help you be faster with arithmetic?

Very likely yes, particularly if you practice, a LOT. However, if you have been lead to believe that this system is an entirely different approach from the lengthy "tables" method of multiplying large numbers together No, it just isn't.

If you're examining carefully, the basic method taught in ch. The difference is, you do them in a different order completely resolving a single digit at a time, rather than waiting for a later sum , and you do it all in your head. Seriously, that's the entire difference. The "two-finger" method taught in ch. It's a different method, but it's still the same deal: you're performing ALL the same steps you're already accustomed to in long-form multiplication, just in your head, and in a different order.

In this case, there's potentially less "math" to keep in your head at a time, but keeping your place in where you're working your problem becomes more challenging part of why it's called "two-finger" - people end up using their fingers to track where they are in the problem , and you're actually REPEATING some of those steps.

So how is the method faster? Basically: it isn't. The difference will be in how much work is shown on the paper, not in the speed of the results. Moreover, the school-taught method requires far less concentration keeping far less in your head at a time , and makes it a good deal easier to check your work for mistakes.

Of course, if you can think your answers far quicker than you can write digits, then provided you have a decent memory and can maintain concentration, this method may well be quite a bit faster than you. That's really where the "speed" tricks of this book come into play: they encourage you to perform arithmetic steps at a time, practicing towards "thinking" only the final result of those steps.

You still DO all those steps, but much of it becomes less conscious - and in that way, you work faster because you're not slowed down by explicitly thinking it in your mother tongue. So, YES, this book can make you faster at arithmetic. But it will take an awful lot of drilling before that can happen, or I suspect before you can even come close to matching your speed with the tables method. In the meantime, it also demands much more concentration, and provides more opportunities for mistakes, at least until you've gained quite a bit of mastery through practice.

The checksum method for sanity-checking answers, taught in ch. A note: the cool tricks in ch. You do not explicitly use those techniques past ch.

You can definitely use the chapter-one methods to shore up any holes in your recollection of the times tables - but ch. But they ARE cool techniques, and even if you don't end up using them much directly, they're still useful to know, and as the author states in the book, they may just rekindle your interest in arithmetic in general.

So, in summary, the book is helpful, it pretty much does what it claims given a ton of practice Mainly, it teaches some fresh ways of looking at the subject, and makes a great platform for drilling and practicing - but you could probably get similar results from drilling and practicing the school method, too. Edition notes: latter editions of this book appear to have some of the problems in ch. It could lead some to suspect they received used copies when they ordered new: nope, if you look very closely, you'll see that the erased figures are printed in "silk screen" dots, a tell-tale sign that they were actually PRINTED that way.

Such reviewers either haven't gotten to the final set of rules for a given digit in chapter one there are some cases where it gives an "incomplete" list of rules at the start, along with some carefully-chosen examples that will work, and then follows on with the "real" list of rules , or they're forgetting one of the rules they were meant to perform, or else they're forgetting that they have to perform the steps one final time when they reach the invisible "zero" to the left of the multiplicand.

At any rate, there are algebraic proofs of the techniques at the end of the book of all the techniques taught. I haven't looked through those, but they're not difficult to prove for yourself if you're comfortable in algebra. I've been good in math but always had trouble with mental math. I stumbled across this book while looking for ways to improve.

I really enjoy the concepts and think the book is well written. Being able to see the patterns behind the methods really helps. I think the book has good explanations and tries to present things in a systematic way. I would suggest people that are interested in learning to be better at math give this book a shot. I actually had a copy of this book when I was a child, and took great pleasure in learning some of the tips'n'tricks.

I was so pleased to purchase this other copy in order to allow my son the same opportunity now. I guess the enjoyment you get out of it would greatly depend on how much you enjoy math games. If you don't, I sure wouldn't buy this! Certainly even math-oriented adults would enjoy learning tricks to make math easier.

If you make math fun and interesting, it can only be a plus for their overall education! I get bored with doing math. This has nothing to do with an inability to do math and more to do with the fact that a lot of the work required to do it is tedious.

Because of that fact, I've been looking for a easy and fast mental math system to take out the menial work out of doing basic math. First off, let me state that all the 5 star positive reviews are justified.

This is, in fact, an amazing mental math system that goes a few steps beyond what's necessary for a mental math book. If it had merely given you a quick way to do addition, multiplication, division, subtraction, and square roots, it would have been a good book, if somewhat indistinguishable from all the other mental math books. There are two things that set it apart from other systems: 1.

It gives you a way to check your answer that's quick and works for all operations 2. It's a complete system, not just a set of tricks, thus it anchors it self in your brain. However, while I do like this book, I have to give a caveat that forces me to knock this book down from five to four stars. For whatever reason, my version of this book as published by Ishi Press International and fulfilled by Amazon, appears to not have subtraction part of the Trachtenberg method.

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## Trachtenberg System

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## The Trachtenberg Speed System of Basic Mathematics

Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? 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 kid when asked to multiply times simply wrote on the blackboard the answer, 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.