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""The teachers are eager and able to learn. I vividly remember one summer class when I taught why the multiplication algorithm works for two-digit numbers using

by JPKab 14y ago

""The teachers are eager and able to learn. I vividly remember one summer class when I taught why the multiplication algorithm works for two-digit numbers using base ten blocks. I have no difficulty doing this with third graders, but this particular class was all elementary school teachers. At the end of the half hour, one third-grade teacher raised her hand. 'Why wasn’t I told this secret before?' she demanded. It was one of those rare speechless moments for Pat Kenschaft. In the quiet that ensued, the teacher stood up." The "Secret": http://www.tech4mathed.com/MAT156/topics%20test%202/twodigitmultiplication.htm http://www.tech4mathed.com/MAT156/topics%20test%202/twodigit... Since there is a strong, strong chance that many of the readers who were taught in a U.S. classroom never saw this, I have the above link included.

svdad 14y ago
Thank you. I had no idea what the "secret" was myself. What would be meant, in the original article, by the "multiplication algorithm"? I know that's a bizarre question, but actually I don't think I could explain what that means to someone myself, so I'd better ask.
- anonymoushn 14y ago
  The multiplication algorithm I was taught in school was something like this: for each digit in the bottom number, starting with the ones digit: begin a new line beneath the current state. write a number of trailing zeroes equal to the number of digits of the bottom number you've already processed. for each digit in the top number, starting with the ones digit: write (carry + top digit * bottom digit) % 10 to the left of the leftmost digit on the bottom line of the state. the carry for the next digit of the top number will be (carry + top digit * bottom digit) / 10 use the addition algorithm to compute the sum of all the numbers you wrote this way. If you hard code it to only handle two digit numbers, it's a bit simpler. It computes the product of two numbers 10A+B, 10C+D for one digit A,B,C,D as (D * B + 10 * D * A) + 10 * (C * B + 10 * C * A). That sounds really confusing, because it is. The visual explanation relates it to something much less confusing in an obvious way.

by JPKab 14y ago

svdad 14y ago

Thank you. I had no idea what the "secret" was myself. What would be meant, in the original article, by the "multiplication algorithm"? I know that's a bizarre question, but actually I don't think I could explain what that means to someone myself, so I'd better ask.

anonymoushn 14y ago
The multiplication algorithm I was taught in school was something like this: for each digit in the bottom number, starting with the ones digit: begin a new line beneath the current state. write a number of trailing zeroes equal to the number of digits of the bottom number you've already processed. for each digit in the top number, starting with the ones digit: write (carry + top digit * bottom digit) % 10 to the left of the leftmost digit on the bottom line of the state. the carry for the next digit of the top number will be (carry + top digit * bottom digit) / 10 use the addition algorithm to compute the sum of all the numbers you wrote this way. If you hard code it to only handle two digit numbers, it's a bit simpler. It computes the product of two numbers 10A+B, 10C+D for one digit A,B,C,D as (D * B + 10 * D * A) + 10 * (C * B + 10 * C * A). That sounds really confusing, because it is. The visual explanation relates it to something much less confusing in an obvious way.