This is how they're teaching fractions?

[AWB]

@Musicat

Before looking at your answer, I just did it in my head, like this: 2 1/2 times 1 3/4…take the 2 times first…2 times 1 is easy, 2 times 3/4 is obviously 1 1/2, so that much adds up to 3 1/2. Now take one half of 1 3/4. Easy-peasy…half of 1 is 1/2, and half of 3/4 is 3/8. 3/8 plus 1/2 is 7/8.

Now add 3 1/2 and 7/8 to get 4 3/8 (7/8 is 1/8 short of 1, so 3 1/2 plus 1 is 4 1/2, take away 1/8 to make 4 3/8.)

Somehow I don’t think this problem needs to be written down or formalized. It’s too easy.

Besides, why is Mary making a half batch of cookies? Doesn’t she know that the dough will be eaten before it gets to the oven? And is it white sugar or brown? Make 5 batches, like Og intended!

Y’know, once students get the concept, it doesn’t matter how they get their answers. I once had a student that would do FOIL expansion to do this type of mixed-fraction multiplication. It made sense to him.

But while they’re still learning what it means to multiply fractions, an easy-to-understand process should be applied. And common denominators for fraction multiplication is just confusing. (The division version of this did seem to work well, creating a shortcut that eliminated the denominators. But then that’s a “shortcut” method that some would decry.)

[AWB]

@constanze

Couple problems here:
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3) Children parroting mulitplication tables don’t understand math better. They get another “Black Box”, and if they slip up, they are capable of saying that 4x4 is 64 without realizing why that might be odd. The problem is that too many strategies are perceived by the children as black box: put the problem in one end, crank the handle, out comes an answer which is submitted to the oracle (Teacher) for checking. Realizing what’s really going on, checking your own work and so on would be a better step towards understanding of math.

I agree that creating little “black boxes” isn’t desirable. But at the same time, it helps if you can spit out the answer to basics, which I feel multiplication (at least 10x10 tables) is. It’s akin to memorizing the order of the alphabet: it should be automatic to know L comes after K.

[AWB]

(Just an overall comment: I really didn’t expect this long of a message thread. Y’never know what’ll click in Dopers’ heads. )

[AWB]

sigh Make the 2[sup]nd[/sup] sentence’s verb in post #80 read “aren’t”, not “are”. Kinda takes the wind out of my sails.

[Boyo_Jim]

We should be happy the students don’t attempt 2nd Amendment solutions to such problems.

[Sam_Stone]

@asterion

I blame Canada.

Don’t blame us - we kick your ass in math.

We do, however, teach our kids that beavers are amphibians…

As for the op, how much do you want to bet that this technique was implemented to give kids more exercise in finding least-common denominators? It’s a traditional trouble spot for a lot of kids. I’m not saying it’s right, I’m saying it’s a likely justification for an idiotic way to teach multiplying fractions.

[Left_Hand_of_Dorkness]

@Sam_Stone

Don’t blame us - we kick your ass in math.

We do, however, teach our kids that beavers are amphibians…

As for the op, how much do you want to bet that this technique was implemented to give kids more exercise in finding least-common denominators? It’s a traditional trouble spot for a lot of kids. I’m not saying it’s right, I’m saying it’s a likely justification for an idiotic way to teach multiplying fractions.

I’d bet a significant amount* that it’s some ignoramus somewhere on the chain of command. It could be one teacher who taught the assistant a dumb way to do it. It could be a tyrannical department head. It could be a foolish principal. It could be a terribly-conducted professional development session that confused the teachers who attended it. It could even be a lunatic who was removed from the classroom and stuck in central office to head up curriculum and who sent out a loony email about How We Will Be Teaching Fractions From Now On.

But I have a very hard time believing it’s a deliberate pedagogical choice. There are plenty of dumb teachers out there, no doubt, but they tend to be dumb in other ways.

*No I wouldn’t, this is a lie, I don’t bet. But if I did I would.

[septimus]

@Malacandra

Good luck working out 1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7 x 7/8 x 8/9 by the common denominator method.

Simplify the following polynomial
(a-x)(b-x)(c-x)…(z-x)

My wife’s college-bound students in Thailand came to me for some math refresher tutoring. I decided to start with exponentiation. (That the nature of negative and fractional exponents can be readily deduced seems like a good way into the beauty of math.) “We’ve already studied exponentiation” was their bored reply. “Good, this will go faster then” was my response. But it turned out “already studied” meant crammed, took the test, and then forgot everything because they didn’t need it anymore.

“What’s 2 to the 3?” “6?”

One of these students is intelligent and is working toward a Comp Sci degree. When he was taking calculus I quizzed him again and found he still couldn’t do simple arithmetic.

It’s reassuring to learn American schools are as bad as Thai schools!

[Malacandra]

@septimus

Simplify the following polynomial
(a-x)(b-x)(c-x)…(z-x)

That’s an old one, that is. 0

[Shot_From_Guns]

@AWB

Y’know, I take serious offense to the “just a sub” comment.

I think you’re taking it out of context. What **rachel **said was: “Being realistic, you’re just a sub at this school and have no power to change their curriculum.” She’s not belittling the work you do–she’s saying that you have no power to fix this. You yourself said it: you follow the lesson plans left by the teachers you’re subbing for.