Multiplication table posters - Some are wrong!

[IraHayes]

Popped round to a house where my children were playing with their son and while we were chatting about the water festival holiday I noticed the multiplication poster they had on the wall was wrong.
The poster was of the form ...

2 x 1 = 2
2 x 2 = 4
2 x 3 = 6 etc etc

Now I didn't even bother trying to explain why it is wrong but i do know I have seen this mistake before, albeit a fair while ago.

The correct way is of course,

1 x 2 = 2
2 x 2 = 4
3 x 2 = 6 etc

Expressed as a verbal notation what we are doing is saying
1 group of 2 equal 2
2 groups of 2 equal 4
3 groups of 2 equal 6 etc

Thus, the following becomes weird..
2 groups of 1 equal 2
2 groups of 2 equal 4
2 groups of 3 equal 6

Euler set the rule back in 1795 in his book "Elements of Algebra"
** disclaimer: ok I had to google the date and the book name but thanks to my old A-level maths teacher I knew it was defined this way because of Euler.

Has anyone else been irked by this error? Or did you just see it and think what an odd way to express a times table??

[Alex]

It might be "weird", but it sure isn't "wrong", because:

N x M = M x N

End of.

[Cooldude]

What's strange about this is I've known several female Khmer over the years who never went to a day of school in their lives, yet when I quiz them on multiplication tables, they all knew the correct answers.

[Roryborealis]

It might be "weird", but it sure isn't "wrong", because:

N x M = M x N

End of.

Doesnt the Reflexive Property of multiplication just make it a matter of perspective?
(No offense to Euler)

[John Bingham]

In Khmer things are phrased differently. For example it's houses two, not two houses.

[IraHayes]

It might be "weird", but it sure isn't "wrong", because:

N x M = M x N

End of.

You got 2 likes for this??
Hmmmm
Yes, while 2 groups of 3 is the same as 3 groups of 2

but you are missing the fundamental principle here. JB also misses it with this comment

In Khmer things are phrased differently. For example it's houses two, not two houses.

Euler wrote, in the chapter "Multiplication of Simple Numbers"
When there are 2 or more equal numbers to be added together, the expression of their sum may be abridged to the following:-

a + a is the same as 2 x a
a + a + a is the same as 3 x a
a + a + a + a is the same as 4 x a

In this manner we may form an idea of multiplication, and it is to be observed that:-
2 x a signifies 2 times or twice a
3 x a signifies 3 times a or thrice a etc

No one has ever been taught simple algebra where we express 2 or more equal numbers to be added together as

a2 or b5 ... We all express them as 2a and 5b and you can thank Euler for this.

[Alex]

It might be "weird", but it sure isn't "wrong", because:

N x M = M x N

End of.

You got 2 likes for this??
Hmmmm
Yes, while 2 groups of 3 is the same as 3 groups of 2

but you are missing the fundamental principle here. JB also misses it with this comment

In Khmer things are phrased differently. For example it's houses two, not two houses.

Euler wrote, in the chapter "Multiplication of Simple Numbers"
When there are 2 or more equal numbers to be added together, the expression of their sum may be abridged to the following:-

a + a is the same as 2 x a
a + a + a is the same as 3 x a
a + a + a + a is the same as 4 x a

In this manner we may form an idea of multiplication, and it is to be observed that:-
2 x a signifies 2 times or twice a
3 x a signifies 3 times a or thrice a etc

No one has ever been taught simple algebra where we express 2 or more equal numbers to be added together as

a2 or b5 ... We all express them as 2a and 5b and you can thank Euler for this.

I'm talking about a fundamental rule in mathematics, the commutative property of multiplication ("the order of numbers being multiplied does not change the product"). You simply cannot say that those posters are "wrong", because from a mathematical point of view, changing the order changes nothing.

You're talking about how mathematics is being taught. And I conceded that you can rightfully claim that those posters are "weird" or unusual. Wrong they are not though.

That distinction actually matters. In mathematics, using unambiguous language is of the utmost importance. Which is also an important aspect of teaching mathematics.

When you wrote "wrong", I thought you found a genuine error such as "2 x 4 = 9". You didn't.

[IraHayes]

It might be "weird", but it sure isn't "wrong", because:

N x M = M x N

End of.

You got 2 likes for this??
Hmmmm
Yes, while 2 groups of 3 is the same as 3 groups of 2

but you are missing the fundamental principle here. JB also misses it with this comment

In Khmer things are phrased differently. For example it's houses two, not two houses.

Euler wrote, in the chapter "Multiplication of Simple Numbers"
When there are 2 or more equal numbers to be added together, the expression of their sum may be abridged to the following:-

a + a is the same as 2 x a
a + a + a is the same as 3 x a
a + a + a + a is the same as 4 x a

In this manner we may form an idea of multiplication, and it is to be observed that:-
2 x a signifies 2 times or twice a
3 x a signifies 3 times a or thrice a etc

No one has ever been taught simple algebra where we express 2 or more equal numbers to be added together as

a2 or b5 ... We all express them as 2a and 5b and you can thank Euler for this.

I'm talking about a fundamental rule in mathematics, the commutative property of multiplication ("the order of numbers being multiplied does not change the product"). You simply cannot say that those posters are "wrong", because from a mathematical point of view, changing the order changes nothing.

You're talking about how mathematics is being taught. And I conceded that you can rightfully claim that those posters are "weird" or unusual. Wrong they are not though.

That distinction actually matters. In mathematics, using unambiguous language is of the utmost importance. Which is also an important aspect of teaching mathematics.

When you wrote "wrong", I thought you found a genuine error such as "2 x 4 = 9". You didn't.

Point taken about unambiguous language when discussing mathematics.
I should have added ".. using the repeated addition strategy"
Though I fear almost none of the respondents would have understood that this strategy is a rewording of what Euler wrote all those years ago. The people who designed the posters that set all this off certainly didn't.

[Kammekor]

Popped round to a house where my children were playing with their son and while we were chatting about the water festival holiday I noticed the multiplication poster they had on the wall was wrong.
The poster was of the form ...

2 x 1 = 2
2 x 2 = 4
2 x 3 = 6 etc etc

Now I didn't even bother trying to explain why it is wrong but i do know I have seen this mistake before, albeit a fair while ago.

The correct way is of course,

1 x 2 = 2
2 x 2 = 4
3 x 2 = 6 etc
<cut>

I think the creators missed the didactics for the multiplication tables.

[barang_TK]

I remember learning tables as :
2 repeated once, 2x1
2 repeated twice, 2x2
2 repeated 3 times, 2x3
etc.
If you google "multiplication tables", you'll find both forms in math scholar manuals, i don't think there's a wrong one.