[tremendo]

When I learned English (second language) I remember thinking "wow, wonderful, the language of multiplication tells you exactly what to do!" which I read as, in this case 5 × 3 => "[five times] three" 3+3+3+3+3, as the teacher illustrated, but here the student apparently answered "five [three times]".

In my first language (Spanish) the multiplication is read as "five by three" which conjures up rectangles or lists, which can be vertical or horizontal oriented, and in either case, less clear and unambiguous than the English version.

Still I believe it's certainly teaching the wrong lesson to mark the answer as incorrect, especially when the red mark comes without explanation. Even if the problem states "Use the repeated addition strategy". The author mentions it's crucial to understand this but I don't believe important enough to discourage a young student this way. The explanation of what was requested and the method of arriving at it should be made explicit, and it may have happened in class, we just don't know.

[mattmcknight]

I feel the opposite way about the English reading "5 times 3". In English, the subject comes first, so I would expect the sentence to mean take 5, use "times" as a verb, and 3 as the adverb. Likewise, if you read it as "5 multiplied by 3", you would expect to take five, three times.

[signal11]

Exactly. And this is why we use math operators rather than English terms for math operations. If you want to specifically mean 5 times a group of 3, define a new operator for it, like 5 ○ 3. Don't 'overload' the x operator with your own arbitrary meaning.

[chris_wot]

Ummm... I think you just overloaded the x operator yourself!

[newjersey]

If you look at the next question, they go over the five by three in a rectangle approach.

Maybe we should do away with grading students based on exam performance altogether.

[chris_wot]

My wife is a teacher in the NSW education system (Australia) and I've seen her use the rectangle system. However, the rectangle system is used to also show that if you take the same rectangle with the items placed in it in a uniform distribution, the rotate the rectangle and its contents by 90 degrees the the number of items are the same, but the row and column numbers swap around.

If anything the rectangular system shows that multiplication is commutative, which I feel is its real value. Interestingly enough, that isn't ever explained to most teachers so I'm not surprised if it's being misapplied as a technique for learning!

[vixen99]

As against what happens out there in the tough world of work.