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The Trachtenberg Speed System of Basic Mathematics, by Jakow Trachtenberg
Ebook The Trachtenberg Speed System of Basic Mathematics, by Jakow Trachtenberg
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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 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 These were children used to failure, shy and withdrawn; or at the other extreme, rebellious and unmanageable.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.
- Sales Rank: #294602 in Books
- Brand: Brand: Ishi Press
- Published on: 2011-08-08
- Original language: English
- Number of items: 1
- Dimensions: 8.00" h x .62" w x 5.25" l, .69 pounds
- Binding: Paperback
- 272 pages
- Used Book in Good Condition
About the Author
Jakow Trachtenberg (1888-1953) developed this system during the seven years he spent in Nazi concentration camps during World War II. He had been born in Odessa, Russia on June 17, 1888 and was recognized as a genius at an early age. When the First World War broke out, he was a Pacifist, opposed to the war, and wrote published articles attacking the war. When the Czar of Russia was overthrown, he had to flee to Germany. When Hitler came to power, he did the same thing again, writing magazine articles and books attacking the policies of the Soviet and German governments. His books included “Das Land das blutet. Bilder aus dem heutigen Russland” meaning “The country bleeds. Pictures from today's Russia” in 1928. In 1931, he wrote, “Das Problem der UdSSR”. In 1933, he wrote “Die Greuelpropaganda ist eine Lügenpropaganda sagen die deutschen Juden selbst” meaning “Atrocity propaganda is a Lügenpropaganda says the German Jews themselves” which stated “Some Jewish circles in Germany, who favored German nationalism, felt that the anti-Nazi reactions outside Germany had been exaggerated or distorted. They were afraid, that anti-Nazism would endanger the position of the Jews”. “Die Greuelpropaganda ist eine Lügenpropaganda sagen die deutschen Juden selbst. Atrocity Propaganda is based on Lies say the Jews of Germany themselves. La propagande d'atrocites n'est que mensonges declarent les juifs allemands eux-memes.” Nachdruck der Jakow Trachtenberg Verlag Ausgabe von 1933. Here he is defending the German government from attacks by Jews outside of Germany, calling it “Atrocity Propaganda”. This may explain why he did not flee to the United States as did so many Jewish intellectuals during this period. The immediate prewar years found Professor Trachtenberg living in Vienna and Yugoslavia - almost always as a fugitive. In Vienna in 1936 he wrote “Der russische Bauer heult unter dem Bolschewismus” meaning “The Russian farmer howls under the Bolshevism”. The police state finally caught up with him, and he spent a total of seven years in various concentration camps. It was during these years that Professor Trachtenberg developed his system of speed mathematics. Most of this was done without pencil and paper, since none were available. Thus the majority of the steps are performed mentally.
Most helpful customer reviews
2 of 2 people found the following review helpful.
Would recommend, but with a caveat.
By Goldeneye
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.
Amazingly, I managed to find a system that fit those requirements: The Trachtenberg Speed System of Basic Mathematics.
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. Perhaps the original version did have it, but it was mistakenly left out of the Ishi Press version. This is a shame, as the cover explicitly said it did have subtraction in the book, and everything else in the book is really good and well worth your money.
I would still recommend buying the book, even if the version you get doesn't have subtraction portion.
P.S: If you do know where to find a copy that has the subtraction, leave the information in the comments below.
1 of 1 people found the following review helpful.
Book's claims are misleading - BUT still helpful
By Micah Cowan
Disclaimer: stopped reading after ch. 4, due to irritation at misleading claims of the system, which is past all the parts covering multiplication, but falls short of applying to division, and square roots.
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. No, it just isn't. If you're examining carefully, the basic method taught in ch. 2 consists of ALL the same steps you would perform by writing out the product table, and then summing the results. 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. 3 is recommended as an alternative for use where the numbers involved contain a high number of high-value digits (such as 8s and 9s). 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. The main advantage is that you have less to "carry" from one digit of the answer to the next, which is why it's ideal for high-value digits; but the technique is probably actually _slower_ than school-taught methods, at least in terms of number-of-steps performed.
So how is the method faster? Basically: it isn't. If you can write figures out quickly, I suspect many people will get their work done _faster_ using the ordinary school-taught "tables" method. 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 2-3 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. 4 is neat, though.)
A note: the cool tricks in ch. 1 for multiplying numbers by a single-digit multiplicand, are completely discarded when it comes to doing longer multiplication, starting in ch. 2. You do not explicitly use those techniques past ch. 1, and in fact if you did explicitly use them, you would slow yourself down. It's not EXPLICITLY stated, but apparently the ONLY purpose of that chapter is to shore up your understanding of the times tables - that's right, you DO still need the times tables, despite misleading statements to the contrary in ch. 1. You can definitely use the chapter-one methods to shore up any holes in your recollection of the times tables - but ch. 1 only describes doing them on paper, usually with large, multi-digit multiplicands, whereas really, for effective use in later chapters, you'd want to just learn the rules as applied to single-digit multiplicands, and then drill them to the point that you've memorized the answers (so, times tables).
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.
But take my advice: learn the "rules" for multiplying by multipliers ranging from 5-11, but DO NOT BOTHER with learning the rules for 4 and (especially) 3. As the book states, they're included for completeness/rigor, but shouldn't be necessary for most people since everyone knows the 3's and 4's times tables (a baffling statement when I encountered it, as I thought the whole point was to eliminate the necessity of times tables - but when I realized in ch. 2 and beyond that you don't use these "rules" methods past ch. 1, it made a great deal more sense). 4's and 3's times tables are a snap, but the rules for multiplying them using the Trachtenberg chapter-one "rules" methods are more complex than any of the larger digits, and so making mistakes is easier. The rule for multiplying by 5 is _particularly_ easy, and everyone should learn to do that.
So, in summary, the book is helpful, it pretty much does what it claims (given a ton of practice)... but it's not really any different, in terms of numbers-of-steps to perform, than what you already know. 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. 1 "filled in", then erased. 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. :-p
A final word: don't listen to any reviews saying the techniques "don't work" for certain numbers, or certain situations. 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.
6 of 6 people found the following review helpful.
Just a bit of math fun...
By D. Knox
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! lol But it is very, very instructive and a great purchase for the middle school, high school, or college student. Certainly even math-oriented adults would enjoy learning tricks to make math easier. To me, a good part of the positive in it is just getting kids to *think* about how numbers go together, and how to manipulate them. If you make math fun and interesting, it can only be a plus for their overall education! :)
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