This one is on how it’s good when parents don’t understand their kids homework, and the usual folderol about how students used to learn via “tricks” and now it’s all about “understanding”.
They pulled out the old chestnut about the fractional division rule of invert and multiply. It starts out the same as it always does:
“Back when you were in school and when I was in school, the way we learned mathematics — and I’ll talk about the division of fractions — we all learned the trick. You flip (the fraction) over, then you multiply and that’s how you come up with the answer,” said Principal Fernando Hernandez. “It worked, but that didn’t mean that you understand the concept.
I have my own ideas about that but what caught my interest (and stopped further reading) was what came after:
“So something we would ask the students to do now is we might actually give them the answer. ‘One divided by two-thirds is one-half. Please justify that, prove to me that that is true.'”
In case you’re wondering, 1 divided by 2/3 = 3/2 not 1/2, but aside from that, what they’re trying to say is that they want students to be able to show that just as in dividing whole numbers, you can reverse the process and multiply the quotient by the divisor to get the dividend. Which doesn’t really explain why the invert and multiply rule works. But as I’ve said many times, if you give me two students of whom one knows why the rule works and the other doesn’t, but both can solve a word problem that requires fractional division, I can’t tell which one knows why the rule works.