What is a good arithmetic textbook?

[Lockie123]

I am looking for an arithmetic book to use before going on to pre-algebra. However I don't want a book that says "28 + 53, add 8 + 3, carry the 1, etc). I'm looking for a book that has a better approach. For example, instead of that approach, saying "28 + 53 = 30 + 51 = 81" - something like that. I very rarely see this method in today's textbooks though, what a shame!

 

[NTW]

From the pre-calculator era, I remember a few books that explained 'tricks' of that sort. But they are now out of print, I believe...

 

[Lockie123]

@NTW That's a shame, perhaps I can find some of them online. Do you know the titles of some of the books? I hear a lot about old math textbooks, are they generally better than the textbooks we have today?

 

[NTW]

@NTW That's a shame, perhaps I can find some of them online. Do you know the titles of some of the books? I hear a lot about old math textbooks, are they generally better than the textbooks we have today?

I still have one in some cupboard around... 'Off the top', I can tell you now that the author was some 'Trachtenberg', and that the title of the book was 'The Thrachtenberg method of fast math' (or something like that). Sure you'll find more information un Google...

 

[Lockie123]

@NTW Yes, I've heard of that book! Did schools actually use that book in their arithmetic classes before moving on to pre-algebra?

 

[NTW]

@NTW Yes, I've heard of that book! Did schools actually use that book in their arithmetic classes before moving on to pre-algebra?

Schools used to be (and still are) conservative institutions... I believe that the 'Tracht' was used, outside schools, by people who needed to calculate quickly. For present-day students, it's difficult to imagine a physics examination with no calculators, and with the only help of log and trig tables... A fast way to do the calculations, and specially to check them, was highly valuable...

 

[Lockie123]

@ NTW Would there have been any disadvantage for students in later topics such as algebra and calculus if they just started with the 'Tracht' method for arithmetic though instead of adding and multiplying using tables?

 

[NTW]

No idea, but -in my opinion- the 'Tracht', being a mental method, is better suited as a complement of the usual written operations...

 

[Lockie123]

I welcome any further suggestions!

 

[Lockie123]

Does anyone have any suggestions at all?

 

[Mark44]

@NTW Yes, I've heard of that book! Did schools actually use that book in their arithmetic classes before moving on to pre-algebra?

As far as I know, very few if any schools used the Trachtenberg book in their arithmetic classes. In my own case, it wasn't published in the US until 1960, which was when I was already in high school.

Instead of looking for alternative approaches to arithmetic, which is pretty simple, I would advise just biting the bullet and getting some generic book on arithmetic.

I hear a lot about old math textbooks, are they generally better than the textbooks we have today?

They were certainly cheaper, since they didn't have any color illustrations, and were pretty sparse on even black and white illustrations.

 

[Lockie123]

Cheers @NTW and @Mark44!