Customer Rating: 
Summary: a comment
Comment: some readers have commented that the method does not work with multiplication by 5. I am using the 1960 version and have found that the method does hold even for examples that I produce not from the book. I suggest you examine the algorithm more carefully.
In response to the 1 star review that claims this is not worthwhile for teaching mathematics and that reliance on calculators etc. is best while focusing on applied concepts is a good one, however, an overreliance on computational tools hinders mathematical thought since a student does not have a natural sense and intuition of the number system.
Furthermore, when numbers are simple to manipulate, the mental energy for such thought is reduced and enables a student to focus more time on the problem at hand without the interruption of using a calculator for input and computation.
I do agree with the businessman's comment that this is only a tool for teaching the operations involved with basic arithmetic and that it does not help with teaching word problems and cognitive skills. But, for anyone interested, this book will
aid them with proficiency in mathematical computation and hopefully give them tools that can help them tackle more challenging problems in mathematics.
Certainly, this system is far superior to conventional ones currently taught at the grade school level.
Customer Rating:
Summary: Superb method
Comment: I have been using this book for five days and it has significantly improved my basic maths and the speed at which I can make calculations. Initially one has to remember when to apply the correct rule given the numbers you are trying to calculate, but after some practice this becomes second nature.
The important thing about this book it that once you have learned the techniques, you can apply them to real world situations where you need to, for example, work out the area of a square (e.g. 48cm x 62cm) or where powers or logs have to be used.
What I've found the most useful is not purely improving the speed of calculating random numbers together, but realising how I can use these speed methods and weave them in to other unrelated calculations and dramatically speed up mental calculation. I think that's the key to promoting this method to anyone. Don't just look at it as a number crunching method (it's great for this if that's all you're concerned with), it's brilliant for applying to other maths problems.
This book is money well spent.
Customer Rating:
Summary: Mistakes
Comment: I have an old copy of this book, published about 1970, I believe. I've been working though it, and was very happy with it...until I got to multiplication by 5. I don't know if it's fixed later, but the method given is incorrect every time except the problem used as an example! I have triple- and quadruple-checked my answers and have come up with the exact same wrong ones every time I use the rule given. Somehow I doubt all those people who have written those glowing reviews have actually read all the way through the dang book. Either that or it was fixed in a later edition and I simply don't know about it. If anyone has some sort of answer for me, please email me at lady_michiko@yahoo.com. Thank you.
Customer Rating:
Summary: Brilliant book
Comment: This book makes numbers and playing with numbers fun. Most importantly, you get a very firm underlying knowledge of how numbers relate and work together. It's MUCH more useful than simply memorizing tables. And way more fun, of course. For children (and adults) who are either bored or too challenged by memorization, Trachtenberg's methods make the whole thing a delightful and exciting process. I demonstrated some multiplication to my niece and nephew, both high achievers in school... they were blown away with it... their parents ran off to buy the book.
Customer Rating:
Summary: Gotta love it...
Comment: I've used the system for years, since my father got me a copy from the Popular Science book club back in the 60's. You may recall that was the era of the "New Math".
Summary: a comment
Comment: some readers have commented that the method does not work with multiplication by 5. I am using the 1960 version and have found that the method does hold even for examples that I produce not from the book. I suggest you examine the algorithm more carefully.
In response to the 1 star review that claims this is not worthwhile for teaching mathematics and that reliance on calculators etc. is best while focusing on applied concepts is a good one, however, an overreliance on computational tools hinders mathematical thought since a student does not have a natural sense and intuition of the number system.
Furthermore, when numbers are simple to manipulate, the mental energy for such thought is reduced and enables a student to focus more time on the problem at hand without the interruption of using a calculator for input and computation.
I do agree with the businessman's comment that this is only a tool for teaching the operations involved with basic arithmetic and that it does not help with teaching word problems and cognitive skills. But, for anyone interested, this book will
aid them with proficiency in mathematical computation and hopefully give them tools that can help them tackle more challenging problems in mathematics.
Certainly, this system is far superior to conventional ones currently taught at the grade school level.
Customer Rating:
Summary: Superb method
Comment: I have been using this book for five days and it has significantly improved my basic maths and the speed at which I can make calculations. Initially one has to remember when to apply the correct rule given the numbers you are trying to calculate, but after some practice this becomes second nature.
The important thing about this book it that once you have learned the techniques, you can apply them to real world situations where you need to, for example, work out the area of a square (e.g. 48cm x 62cm) or where powers or logs have to be used.
What I've found the most useful is not purely improving the speed of calculating random numbers together, but realising how I can use these speed methods and weave them in to other unrelated calculations and dramatically speed up mental calculation. I think that's the key to promoting this method to anyone. Don't just look at it as a number crunching method (it's great for this if that's all you're concerned with), it's brilliant for applying to other maths problems.
This book is money well spent.
Customer Rating:
Summary: Mistakes
Comment: I have an old copy of this book, published about 1970, I believe. I've been working though it, and was very happy with it...until I got to multiplication by 5. I don't know if it's fixed later, but the method given is incorrect every time except the problem used as an example! I have triple- and quadruple-checked my answers and have come up with the exact same wrong ones every time I use the rule given. Somehow I doubt all those people who have written those glowing reviews have actually read all the way through the dang book. Either that or it was fixed in a later edition and I simply don't know about it. If anyone has some sort of answer for me, please email me at lady_michiko@yahoo.com. Thank you.
Customer Rating:
Summary: Brilliant book
Comment: This book makes numbers and playing with numbers fun. Most importantly, you get a very firm underlying knowledge of how numbers relate and work together. It's MUCH more useful than simply memorizing tables. And way more fun, of course. For children (and adults) who are either bored or too challenged by memorization, Trachtenberg's methods make the whole thing a delightful and exciting process. I demonstrated some multiplication to my niece and nephew, both high achievers in school... they were blown away with it... their parents ran off to buy the book.
Customer Rating:
Summary: Gotta love it...
Comment: I've used the system for years, since my father got me a copy from the Popular Science book club back in the 60's. You may recall that was the era of the "New Math".
Unlike what some other reviewers have said, calculation is NOT the least important aspect of mathematics. Mental arithmetic gives you a feel for the numbers, a familiarity with them. As a former math teacher myself, I wish I had a nickel for every kid who said "Well, that's what the calculator said" but had no idea whether the "answer" is reasonable.
Trachtenberg's system helps you to make the numbers your own and to make them serve you. While it's a shame about the current price, it's still a bargain if it helps you or your child.