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[xk0sm0sx]

When I read about it obviously I was furious. After all, the commutative property is such a basic understanding of mathematics.
But this article written in English talks about it and explains the situation, and I sort of understood the rationale:

http://d.hatena.ne.jp/takehikom/20131117/1384646400

"There are 5 cars. How many tires do you have altogether?" is the word problem which is presented first. Sharing a tip that each car has 4 tires, the pupils are expected to write "4 x 5 = 20." If someone wrote "5 x 4", then the expression would represent "4 five-wheeled vehicles" or "4 houses each of which has 5 cars". They can understand visually that either situation is not what is shown in the original problem.

To the best of my knowledge, the oldest example is found in the prototype of Elementary School Teaching Guide for the Japanese Course of Study, Mathematics, published in 1951 [URL 5]. It is reported that more than a few pupils replied the incorrect expression in calculating the number of pencils using multiplication, where the writer inferred from their reactions that they lined the two numbers up and sandwiched in the times sign without thinking deeply, and that they were incapable of organizing the situation for a valid choice of operation. The teacher told the pupils that the expression did not fit in with the problem because it would yield the number of persons. Here B-4 was adopted.

Mod Edit:

The answer is circled as correct but the formula is circled as incorrect.

 

[The Technomancer]

Sharing a tip that each car has 4 tires, the pupils are expected to write "4 x 5 = 20. If someone wrote "5 x 4", then the expression would represent "4 five-wheeled vehicles" or "4 houses each of which has 5 cars".

...no it wouldn't.

 

[triplestation]

They're doing matrices already daaaaaaaa

 

[shanshan310]

Eh, I guess I can understand the rational but marking a student wrong for thinking a different way is ridiculous (5x4 could just as easily represent 5 cars with 4 wheels rather than 5 wheels on 4 cars). The Japanese education system is stupidly rigid and this kind of crap does not surprise me.

 

[Cerity]

I don't mind this, teaching it this way leads more naturally into further maths.

 

[The Technomancer]

A-4. We can recognize the number of dishes as the multiplicand (or the basic quantity) and the number of apples per dish as the multiplier.

I mean this. Its really this. Its this simple.

 

[m3k]

Yeah, nah

maybe in Japanese the language of the car prioritises an order but in English... Nah

 

[Uncle Rupee]

Math teacher needs to be fired

 

[xk0sm0sx]

Eh, I guess I can understand the rational but marking a student wrong for thinking a different way is ridiculous (5x4 could just as easily represent 5 cars with 4 wheels rather than 5 wheels on 4 cars). The Japanese education system is stupidly rigid and this kind of crap does not surprise me.

The expression is based on having the subject of the first be the subject of the result.

Hence
"4 tires * 5 cars = 20 tires" vs "5 cars * 4 wheels = 20 (cars)"

 

[akira28]

where does "4 houses each of which has 5 cars" come from?

I mean I see the benefit of imparting some kind of logical order in the factors but saying that if you don't order them immediately = chaos?

 

[The Technomancer]

The expression is based on having the subject of the first be the subject of the result

Hence
"4 tires * 5 cars = 20 tires" vs "5 cars * 4 wheels = 20 (cars)"

Which is entirely arbitrary. The "reasons for incorrectness" don't actually provide a single reason why the result label should be derived from the label of the first term.

 

[Zoator]

This is pretty awful. Why force students to think so rigidly, especially when the distinction in that example is so arbitrary. The word problem even states that there are 5 cars first, so why on Earth would 5 (cars) * 4 (tires on each) be incorrect? This is blatantly disregarding the commutative property of multiplication, and forcing children to think in rigid terms, when there are other ways to approach the problems that are just as correct.

 

[DominoKid]

but the numbers don't change...

 

[Somnid]

Bullshit, this is trying to pull language constructs into math which is highly irrelevant.

 

[xk0sm0sx]

This is pretty awful. Why force students to think so rigidly, especially when the distinction in that example is so arbitrary. The word problem even states that there are 5 cars first, so why on Earth would 5 (cars) * 4 (tires on each) be incorrect? This is blatantly disregarding the commutative property of multiplication, and forcing children to think in rigid terms, when there are other ways to approach the problems that are just as correct.

I've read that this is only enforced for lower grades (seems to be grade 2 and below). It's said to meant to help children give more thought into their answers. Ha.
Also, it's said multiplication questions at that grade are always structured in such a format. So that format of answering has a 'certain meaning'. :/

 

[Zoator]

The expression is based on having the subject of the first be the subject of the result.

Hence
"4 tires * 5 cars = 20 tires" vs "5 cars * 4 wheels = 20 (cars)"

Except even that way of thinking teaches incorrect usage of units and dimensional analysis. The correct usage would be:

4 tires/car * 5 cars = 20 tires or 5 cars * 4 tires/car = 20 tires

In both cases, the "cars" unit cancels out, and the result is consistent. Teaching children otherwise is just wrong.

 

[alekth]

Sounds entirely arbitrary to me.

OK, after reading the whole article, I get where they are coming from, but I find the reasoning unnecessary, and even more unnecessary I find teaching little kids the sort of rigid thinking.

 

[James-Ape]

5 plates each with 3 apples.
3 apples on each of the 5 plates.

I don't understand the reasoning at all. Both are right and it just depends on how the student mentally constructs numbers. Wouldn't this be forcing students to think in a way that might be as natural to them?

 

[m3k]

When I read the question I could easily think 5 cars with 4 tires each... This is weird, you can't force someone to interpret a question like this

this makes no sense to me

 

[Octavion Rex]

I don't see any difference...besides the fact that the car comes first and not the wheels.

 

[DJ_Lae]

Four tires on each of five cars, or five cars with four tires each.

Their explanation is arbitrary bullshit.

 

[NotMyRealName]

The expression is based on having the subject of the first be the subject of the result.

Hence
"4 tires * 5 cars = 20 tires" vs "5 cars * 4 wheels = 20 (cars)"

dumb question, but what happens to the cars on the right side of the equation?

Except even that way of thinking teaches incorrect usage of units and dimensional analysis. The correct usage would be:

4 tires/car * 5 cars = 20 tires or 5 cars * 4 tires/car = 20 tires

In both cases, the "cars" unit cancels out, and the result is consistent. Teaching children otherwise is just wrong.

edit. Ok , that explains it.

 

[Devolution]

All I'm seeing is some weird distinction that doesn't change the math. Why make it more complicated than it needs to be?

As others have said

5 cars with 4 wheels or

4 wheels per car, and 5 cars

Who gives a shit?

 

[Oxirane]

Take half a point off for not including units.

 

[xk0sm0sx]

Haha one reason I see from the author is basically saying you have to think with the mindset of a 7 year old kid.

You have no concepts of units, no concepts of arbitrary numbers (It always involves a real world situation).
You are given a question which involves you writing an equation that makes sense to get the answer.

One of the ways is 3 apples * 5 dishes
Another way to think about it is you are giving 3 apples to 5 dishes, as compared to giving 5 apples to 3 dishes.

Yeah it's language, but at that age, they seem to think it was the better way for a kid to learn how to multiply :/.

 

[ShinNL]

I do not agree, because the question refers to cars, which all have four wheels.

By typing 4x5, like 1x5, 2x5, etc. you suggest the number of tires is what changes. But it's more likely the number of cars change, so it's much better to type 5x4, because the number of tires will always be in factor of 4.

Basically if this was programming and you don't have time to make everything a variable, it's much more likely to type:

cars x 4 = totaltires

rather than

tirespercar x 5 = totaltires

Haha one reason I see from the author is basically saying you have to think with the mindset of a 7 year old kid.

You have no concepts of units, no concepts of arbitrary numbers (It always involves a real world situation).
You are given a question which involves you writing an equation that makes sense to get the answer.

One of the ways is 3 apples * 5 dishes
Another way to think about it is you are giving 3 apples to 5 dishes dish, as compared to giving 5 apples to 3 dishes.

Yeah it's language, but at that age, they seem to think it was the better way for a kid to learn how to multiply :/.

It's so much easier to picture 7 baskets, all filled with 4 oranges, than counting the 4 oranges in a basket, then do it again 6 more times.

 

[Devolution]

I do not agree, because the question refers to cars, which all have four wheels.

By typing 4x5, like 1x5, 2x5, etc. you suggest the number of tires is what changes. But it's more likely the number of cars change, so it's much better to type 5x4, because the number of tires will always be in factor of 4.

Basically if this was programming and you don't have time to make everything a variable, it's much more likely to type:

cars x 4 = totaltires

rather than

tirespercar x 5 = totaltires

4x = answer

you don't write x4.

see? completely arbitrary.

 

[Zoc]

Outstanding example of Japanese traditional-culture idiocy.

No explanation is needed why this is wrong, it is prima facie ridiculous. I'm certain that the teacher only graded that answer wrong because that's what the answer book said.

 

[Napoleonthechimp]

I get that it isn't the answer to the question but I still don't understand why those two things aren't the same.

As a pupil there's no way I'd accept that from a teacher.

 

[xelios]

Sharing a tip that each car has 4 tires, the pupils are expected to write "4 x 5 = 20. If someone wrote "5 x 4", then the expression would represent "4 five-wheeled vehicles" or "4 houses each of which has 5 cars".

4 [wheels on] x 5 [cars]
5 [cars with] x 4 [wheels]


They're the same. This is just stupid and pointless.

 

[Yoshichan]

Already way too complicated for me...

 

[lazorexplosion]

Yeah that's simply flat out wrong. 5*4 = 4*5 = 20, period. Anything else is fucking crazy.

 

[PdotMichael]

4 x 5 or 5 x 4 are without using units just numbers.

 

[DJMicLuv]

The question was asking how many apples, so the answer was 3x5 - 3 apples times 5 bowls, the number of apples being questioned meant that the 3 had to come first, 5x3 would read as if there was 5 apples in each of 3 bowls.
It's pedantic but it makes sense.

 

[Memento_Mori15]

I don't mind this, teaching it this way leads more naturally into further maths.

Perhaps because it's late, but I don't see this.

Kid should have stated he was using the commutative property.
5 plates * 3 apples/plates
3 apples/plates * 5 plates.
...
yeah, not really seeing the difference.

 

[You Are Viewtiful]

You don't mix math and language. Sorry Japanese teacher, you have brought shame to yourself.

 

[Devolution]

The question was asking how many apples, so the answer was 3x5 - 3 apples times 5 bowls, the number of apples being questioned meant that the 3 had to come first, 5x3 would read as if there was 5 apples in each of 3 bowls.
It's pedantic but it makes sense.

5 bowls full of 3 apples.

How many apples.

It's completely meaningless to me.

 

[Timedog]

This makes no sense whatsoever. If you're worried about them possibly not getting the concept, make them apply labels, THEN mark them incorrect if they mess up the order. Don't teach them some weird shit that will only confuse them later.

 

[shanshan310]

Outstanding example of Japanese traditional-culture idiocy.

No explanation is needed why this is wrong, it is prima facie ridiculous. I'm certain that the teacher only graded that answer wrong because that's what the answer book said.

Pretty much.

 

[xk0sm0sx]

This makes no sense whatsoever. If you're worried about them possibly not getting the concept, make them apply labels, THEN mark them incorrect if they mess up the order. Don't teach them some weird shit that will only confuse them later.

I think your suggestion was the best one they could use. Teach kids the concepts of arbitrary numbers, while teaching them how to count.

 

[ShinNL]

4x = answer

you don't write x4.

see? completely arbitrary.

While programming I always write the variable name first, otherwise it would be rather hard to read if the readable part wasn't always at the beginning of the line.

And yes you can write x4, we're not talking about a variable x here with 4x as a shorthand (aka 4.x)

 

[hipbabboom]

All I'm seeing is some weird distinction that doesn't change the math. Why make it more complicated than it needs to be?

As others have said

5 cars with 4 wheels or

4 wheels per car, and 5 cars

Who gives a shit?

English can be highfalutin as you describe and still make sense but are we to assume Japanese language can be restructured in the same manner? Could it be their grammatical structure dictates that they think in this manner?

 

[You Are Viewtiful]

English can be highfalutin as you describe and still make sense but are we to assume Japanese language can be restructured in the same manner? Could it be their grammatical structure dictates that they think in this manner?

No I'm pretty sure the teacher is alone in his/her thinking. Japanese or non-Japanese.

 

[AbortedWalrusFetus]

I do not agree, because the question refers to cars, which all have four wheels.

By typing 4x5, like 1x5, 2x5, etc. you suggest the number of tires is what changes. But it's more likely the number of cars change, so it's much better to type 5x4, because the number of tires will always be in factor of 4.

Basically if this was programming and you don't have time to make everything a variable, it's much more likely to type:

cars x 4 = totaltires

rather than

tirespercar x 5 = totaltires

It's so much easier to picture 7 baskets, all filled with 4 oranges, than counting the 4 oranges in a basket, then do it again 6 more times.

As a programmer I have no idea what you are talking about.

 

[Lord Ghirahim]

Could it be their grammatical structure dictates that they think in this manner?

No, it does not. This is just good old idiocy.

 

[Cerity]

Perhaps because it's late, but I don't see this.

Kid should have stated he was using the commutative property.
5 plates * 3 apples/plates
3 apples/plates * 5 plates.
...
yeah, not really seeing the difference.

What I'm saying entirely depends on how both multiplication and vectors/matrices are taught, but even then 5*3 and 3*5 are very different things.


You can do;

3
3
3
3
3

or

3 3 3 3 3

or

5 5 5

or

5
5
5

or even

1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

and so on.

But again, it entirely depends on how they're taught multiplication in the first place. As far as I can tell, in the west we're taught with the 'groups of" mentality and so we've stuck with that logically in our heads.

 

[Devolution]

What I'm saying entirely depends on how both multiplication and vectors/matrices are taught, but even then 5*3 and 3*5 are very different things.


You can do;

3
3
3
3
3

or

3 3 3 3 3

or

5 5 5

or

5
5
5

or even

1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

and so on.

But again, it entirely depends on how they're taught multiplication in the first place. As far as I can tell, in the west we're taught with the 'groups of" mentality and so we've stuck with that logically in our heads.

It's 4 4 4 4 4 in one of the examples but that still doesn't mean 4 or 5 should come first.

4 tires per car
5 groups of 4

 

[YoungFa]

They should just teach set theory in grade school. Everywhere.

 

[xk0sm0sx]

No I'm pretty sure the teacher is alone in his/her thinking. Japanese or non-Japanese.

No, this is actually practiced generally in the Japanese education system. It is not the fault of just one teacher.

The japanese wiki about this problem : http://ja.wikipedia.org/wiki/かけ算の順序問題

 

[lazorexplosion]

If you're teaching anything other than 4*5 and 5*4 aren't equal and identical you aren't teaching multiplication because multiplication is commutative. You're teaching japultiplication cauue it aint multiplication. You can't attach meaning to the order of multiplication when the order of multiplication doesn't matter, and if you're saying otherwise you don't understand the commutative property of multiplication.

That means at some stage they then have to unlearn japultiplication and learn multiplication as soon as they get to larger and more abstract applications of multiplication where the commutative property is needed. Is that sounding like a simpler way off teaching multiplication? Hell no.

It's just crazy.