Is 3x5 the same as 5x3?

[Ruken]

@Joey_P

Exactly. In fact, here’s a great example.
If the homework says (and the lesson plan for the day was about): Break down these addition problems to make them easier to work with (or however it should be worded):
17+3+100
The (most likely) proper answer would be: 10+7+3+100 = 10+10+100=120

If the kid wrote 20+100=120 (or worse, just 120), it would be wrong.
Why? Yes, he can do 17+3 (or just the entire problem) in his head, they were taught that earlier in the year, but it doesn’t teach them how to break down the numbers and build them back up into something easier to work with. It’s a building block to move forward with. Later in the year when some part of a bigger problem includes (probably on purpose) 143+157, they’ll quickly be able to say 200+43+57 and only have to work out the 43+57. The kid that was praised for jumping ahead and thinking outside the box and being super smarter than the rest of the class is going is the one that’s adding 143+157 by hand now.

Math isn’t like reading class. The goal isn’t to be the first one to finish the book or be the furthest ahead. It’s about fully understanding each concept before moving on to the next. Having a rocky grasp or no grasp at all of one lesson will just mean you won’t understand the next one at all.

Right now my kid is learning how to come up with a ‘guess’ as to what an answer should be by rounding all the numbers and then adding. They want her to be able to look at, say, 1233+885+17 and say “well, that’s about 1200+900+20 which means it’s going to be about 1120 (or 1100)”. What if her ‘trick’ was to just find the exact answer and then round to the nearest hundred? Right answer, wrong method. She’d never understand rounding that way. She’d never be able to guestimate that way. She’d never be able to get an idea if her answer is in the right ballpark that way (which is where they’re heading with it). What happens in the next lesson when they’re working on areas of shapes and the teacher say “Can you guess what this should be, it’s 9 x12”. She can’t do that in her head, but she can do 10x10. If she used her ‘trick’, she’d be lost.

My fourth grade teacher attempted these arguments. It even came up wrt rounding. We were going to be lost later if we didn’t do things her way. Fortunately, I and others ignored her. Because she was wrong.

[Left_Hand_of_Dorkness]

@Ruken

My fourth grade teacher attempted these arguments. It even came up wrt rounding. We were going to be lost later if we didn’t do things her way. Fortunately, I and others ignored her. Because she was wrong.

Indeed. A crucial component of teaching math is mindreading: as the teacher, I need to get into my students’ heads, understand how they’re solving problems. If they’re using a valid method, I should encourage them, reinforce them, and move them forward. If they’re using an invalid method, I should figure out exactly what they’re doing wrong, zero in on that, and help them fix their method. (This, by the way, is one reason why it’s so important to show your work–it’s for diagnostic reasons).

But if a student has a reasonable, valid method for getting a correct answer, and it doesn’t take them too long, and it’s extensible as they go forward, it’s obnoxious to deny them their favored method. It’s the opposite of good mathematical teaching: it teaches that math is all about method, not about reasoning.

[SmellMyWort]

@Grumman

If the teacher is trying to prepare them for future maths classes by falsely implying that 5x3 =/= 3x5, she needs to be fired.
Numbers are not matrices. Marking number multiplication wrong because it does not follow the same rules as matrix multiplication is as stupid as marking it wrong because number division does not follow the same rules.

I guess you fall into the author’s category of “The people complaining don’t know what is going on here.” The teacher isn’t implying that 5x3 =/= 3x5. The worksheet asked for these problems to be solved in specific ways and the student didn’t. The teacher didn’t mark the final answers wrong, but marked the process wrong and then showed how they should have been solved. Had the first question stated just “Solve 5x3” I would agree with everyone who thinks the teacher is an idiot. But it doesn’t. I wonder if everyone would be complaining if the student made the same mistake for problem #3 and drew 4 boxes of 7 cupcakes instead of 7x4.

@Left_Hand_of_Dorkness

Indeed. A crucial component of teaching math is mindreading: as the teacher, I need to get into my students’ heads, understand how they’re solving problems. If they’re using a valid method, I should encourage them, reinforce them, and move them forward. If they’re using an invalid method, I should figure out exactly what they’re doing wrong, zero in on that, and help them fix their method. (This, by the way, is one reason why it’s so important to show your work–it’s for diagnostic reasons).

But if a student has a reasonable, valid method for getting a correct answer, and it doesn’t take them too long, and it’s extensible as they go forward, it’s obnoxious to deny them their favored method. It’s the opposite of good mathematical teaching: it teaches that math is all about method, not about reasoning.

That’s fine if they’re just trying to solve a random set of problems, not if they’re trying to teach a particular strategy. Let’s say I’m taking a driving test and I need to show that I can parallel park. There are 3-4 open spots in a row on the street so instead of going through the motions I just whip into the spot. Should I pass?

[Muffin]

Customer: I think you entered the wrong number.
Cashier: Well, one cupcake plus one cupcake plus one cupcake . . .

[Muffin]

@SmellMyWort

There are 3-4 open spots in a row on the street so instead of going through the motions I just whip into the spot. Should I pass?

You shouldn’t even be driving when you are that young.

[SmellMyWort]

@Muffin

You shouldn’t even be driving when you are that young.

You’ve never seen Temple of Doom?