What is a good arithmetic textbook?

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Discussion Overview

The discussion centers around the search for a suitable arithmetic textbook that offers a more conceptual approach to arithmetic, rather than traditional methods. Participants explore the merits of older textbooks and specific methods, such as the Trachtenberg method, in preparing students for pre-algebra.

Discussion Character

  • Exploratory
  • Debate/contested
  • Historical

Main Points Raised

  • One participant expresses a desire for an arithmetic book that emphasizes conceptual understanding over rote methods, citing an example of an alternative addition approach.
  • Another participant recalls older textbooks from the pre-calculator era that included similar 'tricks' but notes they may be out of print.
  • There is a request for specific titles of older arithmetic books and a discussion about whether these older texts are generally superior to modern ones.
  • One participant mentions the Trachtenberg method as a notable book and questions its use in schools for arithmetic instruction.
  • Another participant reflects on the conservative nature of schools and suggests that the Trachtenberg method was more commonly used by individuals needing quick calculations rather than in formal education.
  • A question is raised about potential disadvantages for students who might rely solely on the Trachtenberg method for arithmetic when progressing to algebra and calculus.
  • One participant suggests that the Trachtenberg method could serve as a complement to traditional written operations rather than a replacement.
  • Several participants express a desire for further suggestions on arithmetic textbooks.
  • One participant advises against seeking alternative approaches and recommends obtaining a generic arithmetic book, while also commenting on the cost-effectiveness of older textbooks.

Areas of Agreement / Disagreement

Participants express differing opinions on the value of older arithmetic textbooks compared to modern ones, and there is no consensus on the effectiveness of the Trachtenberg method as a primary instructional tool. The discussion remains unresolved regarding the best approach to teaching arithmetic.

Contextual Notes

Participants reference the historical context of arithmetic education, noting the differences in teaching methods and materials over time. There are unresolved questions about the impact of alternative methods on later mathematical topics.

Who May Find This Useful

Individuals interested in alternative approaches to arithmetic education, educators seeking textbook recommendations, and those curious about historical methods of teaching mathematics may find this discussion relevant.

Lockie123
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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!
 
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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...
 
@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?
 
Lockie123 said:
@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...
 
@NTW Yes, I've heard of that book! Did schools actually use that book in their arithmetic classes before moving on to pre-algebra?
 
Lockie123 said:
@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...
 
@ 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?
 
No idea, but -in my opinion- the 'Tracht', being a mental method, is better suited as a complement of the usual written operations...
 
I welcome any further suggestions!
 
  • #10
Does anyone have any suggestions at all?
 
  • #11
Lockie123 said:
@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.
Lockie123 said:
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.
 
  • #12

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