What a defense of nonsense. The marking punishes a student for achieving a correct answer in an appropriate way, regardless of pedagogical justification.
It's hilarious because I read 5x3 as "5, 3 times".
Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain. In my book, the kid demonstrated repeated addition and should have got the mark.
GP read it as: "5 x3", like he would read "copy x3", or "copy, three times". It's a natural way of reading "5x3", though I personally read it as "5x 3".
The meta-point here is that English (or any other language) is crap for math, which is why we use mathematical notation. And this bullcrap syllabus is trying to redefine the "x" operator, which gets my goat.
The definition of multiplication is indeed in the Wikipedia article, but if you reread it then you'll see it doesn't claim to be a Paeno axiom. A better article to read (after reading about Paeno axioms!) is here:
https://en.m.wikipedia.org/wiki/Second-order_arithmetic#Basi...
For example what if it was 11 x 3. It would make no sense to try to think of it as eleven groups of three, when you can easily derive the answer far quicker as 11 + 11 = 22 + 11 = 33.
If we're going to be pedantic, use this as a learning opportunity. "Actually, 5x3 is slightly different than 3x5. Multiplication has this property..." Some of the kids won't care, but some will be intrigued.
Teaching it this way is a gotcha.
Critics of this are missing that the teacher is not asking the student to find the correct result. Instead, the teacher is asking the student to apply a specific algorithm.
If the teacher asks to apply Merge Sort to a list, but the student applies Insertion Sort, both strategies will result in the same sorted list.
But only one will demonstrate what the teacher asked the student to demonstrate.
The definition of the algorithm given to the student may involve language like "take the first number and..."
The steps are the steps.
Secondly, a student that knows the difference between different techniques and can call them up at will (such as the difference between 5 sets of 3 and 3 sets of 5) is better off than a student that only knows how to produce a particular answer for a particular question.
But I am sure that a student who understands and can apply a specific process when required as well as produce a correct result is better off than one who can only produce a correct result.
Obviously I don't think that all of school should be rote application of techniques. But I've found that when you want to make sure your students have learned a specific technique, you sometimes have to create a somewhat artificial request. Have you taught enough to have found otherwise?
(I tutored math in college and did have the experience of helping people understand math...)
On the contrary, I think this student may be showing that he knew the two techniques, and that he is smart enough to pick the easier computation.
But yes, if your goal is to kill any creativity in intelligent should punish kids that deviate from the lines hard.
If a teacher asked "compute 1000 x 1", no sane kid would do "1 plus 1 equals 2; 2 plus 1 equals 3;...; 999 plus one equals 1000".
This teacher would have failed Carl Friedrich Gauss, too, for computing sum(1,100) in seconds.
Teaching and requiring that a commutative operation be ordered doesn't seem like it is going to contribute to that.
I was giving a different example of an algorithm than the one denoted by the assignment. "Use the repeated addition strategy..." is a clear call to demonstrate the application of a named procedure.
This is no accident, by the way. This is a deliberate design decision of those who created the common core standards. One of the goals is to teach algorithmic thinking.
It's pretty easy to google about if you can find your way through the reactionary hissy-fit memes.