This reminds me of the time Feynman was teaching in Brazil and an abacus salesman cornered him. He could do the simple operations with simple numbers very quickly, but the harder the operation (multiplication, division, exponents, logs), the more Feynman pulled ahead. He tried to explain to the man how he did it, but the salesman couldn't follow. He just didn't understand numbers. This looks like it's doing the same thing -- setting students up neither to understand numbers in a way that aids learning more advanced operations nor to handle anything simple numbers. This is fine for the bottom 20% of the class but the rest of the class can, and needs to, take on a lot more so as not to do the sort of wheelspinning that forestalls preparedness for starting a STEM degree.
I never implied that the Japanese multiplication method is better. This post is about taking a second look at this well-known method, and showing that it’s a visual representation of long multiplication.
75 * 99 = (70 + 5) * (90 + 9). It is the same concept but 7-space-5 lines (one group) and then perpendicular group with 9-space-9 lines. Then, 7*9 = 63 but in hundreds; (7*9)+(5*9) = 108 but in tens; and 5*9 = 45. Final result is 6300 + 1080 + 45 = 7425. I think it's cool
Okay, now do 75x99.
This reminds me of the time Feynman was teaching in Brazil and an abacus salesman cornered him. He could do the simple operations with simple numbers very quickly, but the harder the operation (multiplication, division, exponents, logs), the more Feynman pulled ahead. He tried to explain to the man how he did it, but the salesman couldn't follow. He just didn't understand numbers. This looks like it's doing the same thing -- setting students up neither to understand numbers in a way that aids learning more advanced operations nor to handle anything simple numbers. This is fine for the bottom 20% of the class but the rest of the class can, and needs to, take on a lot more so as not to do the sort of wheelspinning that forestalls preparedness for starting a STEM degree.
I never implied that the Japanese multiplication method is better. This post is about taking a second look at this well-known method, and showing that it’s a visual representation of long multiplication.
75 * 99 = (70 + 5) * (90 + 9). It is the same concept but 7-space-5 lines (one group) and then perpendicular group with 9-space-9 lines. Then, 7*9 = 63 but in hundreds; (7*9)+(5*9) = 108 but in tens; and 5*9 = 45. Final result is 6300 + 1080 + 45 = 7425. I think it's cool