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The Trachtenberg Speed System of Basic Mathematics
The Trachtenberg Speed System Of Basic Ann The Trachtenberg Speed System Of Basic Doubleday & FIRST First Edition, First Printing. Not price-clipped. Published by Doubleday & Company, 1960. Octavo. Hardcover. Book is very good. Dust jacket is very good with edgewear/tears. 100% positive feedback. 30 day money back guarantee. NEXT DAY SHIPPING! Excellent customer service. Please email with any questions. All books packed carefully and ship with free delivery confirmation/tracking. All books come with free bookmarks. Ships from Sag Harbor, New York.Seller 321328 Science & Nature We Buy Books! Collections - Libraries - Estates - Individual Titles. Message us if you have books to sell!
256 pages, Hardcover
First published January 1, 1960
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Displaying 1 - 23 of 23 reviews
June 10, 2009
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.
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.
April 16, 2020
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
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August 12, 2014I know it was not part of the brief of this book, but I really would have liked to know why these methods work.
December 24, 2010
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
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
November 14, 2017
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.
July 19, 2019
My dad showed it to me in primary school and I was entranced.
January 11, 2017
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!
June 19, 2016
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.
November 3, 2012
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.
November 29, 2021
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.
July 13, 2021
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.
April 4, 2022
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.
Regardless, a must read book id say.
May 30, 2023
A practical guide for basic arithmetic. The multiplication chapters were particularly useful.
August 28, 2024
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
July 16, 2013
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.
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.
February 25, 2009
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!
August 10, 2020
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.
September 4, 2011
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.
July 16, 2013
best one
September 12, 2013
KKJK/IOOI
This entire review has been hidden because of spoilers.
March 28, 2016
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?
Want to read
May 20, 2017It is very good
Displaying 1 - 23 of 23 reviews