I'm not even going to start on the stupidity of these sorts of 'plug and chug' assignments. This teacher is teaching something that goes beyond nonsense (just what is a "multiplication sentence" anyway?!?), and is just plain wrong! The phrase 'six times three' means the exact same thing as 'three times six'. Multiplication is (generally) commutative. Furthermore, the following should also be perfectly valid multiplication sentences deserving of full credit:
- 1*18
- 2*9
- (√18)*(√18)
- -18i*Exp[i*pi/2]
No wonder so many kids think they're "not good at math." They're being taught mindless drivel -- that doesn't even have the small benefit of being, at least, correct. And they've certainly never learned math.
Wait... You have the number 3, 6 times. So 3x6? Nope!
ReplyDeleteMaybe, they didn't learn that scalar multiplication is commutative. Which you can actually see from addition being associative. Which could actually be an interesting thing to show students. 3 + 3 + 3 + 3 +3 + 3 = (3 + 3) + (3 + 3) + (3 + 3) = 6 + 6 + 6. And then one of those is 3x6 and the other is 6x3, though which is which is entirely immaterial.
hm.... I would argue that there is, in fact a difference between 3x6 and 6x3 even though they come out to the same number. my intuition of the order, however, is the opposite to that of this teacher (and there seems to be some disagreement about this issue)
ReplyDeleteWhen I see "3 + 3 + 3 + 3 + 3 + 3", my first instinct is to translate that to "3 x 6", ie, "the number '3' six times", same as the student. However, I also realise that some people think of it as "6 x 3", ie, "six groups of 3", same as the teacher.
ReplyDeleteTo my mind, saying one way is more correct than the other is just quibbling.
Years ago, when my sister was in school, the students were shown 15 items on a page and were asked to circle them to show "5 x 3". My sister circled three groups of five. The teacher wanted five groups of three and my sister was marked wrong!
It's just quibbling.