Some regions have seen a trend towards multiplying numbers from left to right instead of right to left in recent years. An explanation of how this “works” and my own personal critique of the methods can be found here.

I would like to see the historical citations where you said this was tried before in the 1800’s. Not that I doubt you, but having this additional info would benefit people who want to refute this ‘new’ teaching method.
I totally agree wit your analysis as to the efficiency of this approach. We certainly do not need to further hobble our children’s learning.

First, let’s say I’m not a mathematician, nor a professionnal in education, so this is just my point of view (and experience).

You should make a difference between doing ‘mental maths’ and ‘written maths’.

Mental maths:

I’ve been reading quite a lot of books and discussions about mental memorization and ability to perform these operations only in your head, and everywhere I could see/read, was done left-to-right (‘Secrets of mental math, Arthur Benjamin & Michael Shermer, Chap 1’ for example).

About multiplication, the recommended way to calculate in you head is a little different from your examples:
For example, starting with a simple one: 42 * 7 would be done as 40*7=280 (put in memory, and although not necessary for this easy calculation, transformed in a memorable element using mnemonics (280=[infuse] for example), then 2*7=14 which would be immediately added to 280 which gives 294 (and which would get another mnemonic, but here we have finished the calculation, so we stop, and give the result). For more-digits-numbers, you have to decompose them in smaller numbers (if it’s a prime, you’re in deep trouble :-). Well, that’s just for mental calculation/simplification, and I agree, that can’t be made a ‘generic/automatic method’.

Written maths:

Historically, all additions/substractions were done left-to-right. For multiplications, there were matrix, right-to-left AND left-to-right ways to do it. Vedic mathemathics were/are done mostly left-to-right, and as you surely know, Indian nation (India) is the inventor of all modern algebra (arithmetics and 0, see http://en.wikipedia.org/wiki/Brahmagupta), not the Arabs as you stated. But you’re right, the Arabs took only the right-to-left part.

Also (if that counts as written calculation) all calculations on Abacuses/Soroban, especially as of today (Japan, China), are done from left-to-right. That’s not an option, that’s a requirement stated in the first section of every tutorial/lesson.

If the focus was on mental math, I’d agree that this has potential. In my particular region (curriculum spanning British Columbia, Alberta, Saskatchewan, Manitoba and all three territories by extension here in Canada) there’s a directive away from mental math and towards technology. Memorization of basic facts is no longer required. Furthermore, the curriculum explicitly states that, when multiplying by a number of three or more digits, or dividing by a number of two or more digits, use of technology is expected. Not even merely permitted, but expected. That blows me away.

As for the Arabs vs. India, it was my understanding that the actual base ten number system employed by most of the world today was developed by the Arabs, although the foundational algebra was developed in India. I may have the original region wrong, but the fact that the system was constructed with a right-to-left bias that is still present at higher grades remains true.

MrWin2kMan

July 25, 2011@ 10:46 amI would like to see the historical citations where you said this was tried before in the 1800’s. Not that I doubt you, but having this additional info would benefit people who want to refute this ‘new’ teaching method.

I totally agree wit your analysis as to the efficiency of this approach. We certainly do not need to further hobble our children’s learning.

lstep

July 26, 2011@ 4:36 amFirst, let’s say I’m not a mathematician, nor a professionnal in education, so this is just my point of view (and experience).

You should make a difference between doing ‘mental maths’ and ‘written maths’.

Mental maths:

I’ve been reading quite a lot of books and discussions about mental memorization and ability to perform these operations only in your head, and everywhere I could see/read, was done left-to-right (‘Secrets of mental math, Arthur Benjamin & Michael Shermer, Chap 1’ for example).

About multiplication, the recommended way to calculate in you head is a little different from your examples:

For example, starting with a simple one: 42 * 7 would be done as 40*7=280 (put in memory, and although not necessary for this easy calculation, transformed in a memorable element using mnemonics (280=[infuse] for example), then 2*7=14 which would be immediately added to 280 which gives 294 (and which would get another mnemonic, but here we have finished the calculation, so we stop, and give the result). For more-digits-numbers, you have to decompose them in smaller numbers (if it’s a prime, you’re in deep trouble :-). Well, that’s just for mental calculation/simplification, and I agree, that can’t be made a ‘generic/automatic method’.

Written maths:

Historically, all additions/substractions were done left-to-right. For multiplications, there were matrix, right-to-left AND left-to-right ways to do it. Vedic mathemathics were/are done mostly left-to-right, and as you surely know, Indian nation (India) is the inventor of all modern algebra (arithmetics and 0, see http://en.wikipedia.org/wiki/Brahmagupta), not the Arabs as you stated. But you’re right, the Arabs took only the right-to-left part.

Also (if that counts as written calculation) all calculations on Abacuses/Soroban, especially as of today (Japan, China), are done from left-to-right. That’s not an option, that’s a requirement stated in the first section of every tutorial/lesson.

W. Blaine Dowler

July 26, 2011@ 7:46 pmIf the focus was on mental math, I’d agree that this has potential. In my particular region (curriculum spanning British Columbia, Alberta, Saskatchewan, Manitoba and all three territories by extension here in Canada) there’s a directive away from mental math and towards technology. Memorization of basic facts is no longer required. Furthermore, the curriculum explicitly states that, when multiplying by a number of three or more digits, or dividing by a number of two or more digits, use of technology is

expected. Not even merely permitted, but expected. That blows me away.As for the Arabs vs. India, it was my understanding that the actual base ten number system employed by most of the world today was developed by the Arabs, although the foundational algebra was developed in India. I may have the original region wrong, but the fact that the system was constructed with a right-to-left bias that is still present at higher grades remains true.