What a defense of nonsense. The marking punishes a student for achieving a correct answer in an appropriate way, regardless of pedagogical justification.
I found this link interesting. Under this "Common Core" curriculum, apparently, students are trained to read 5x3 as "five groups of three" which is why 3+3+3+3+3 is right and 5+5+5 is wrong.
http://www.businessinsider.com/why-55515-is-wrong-under-the-...
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Anyhow, just goes to show Maths teachers have now been replaced by box tickers who refuse to apply their brain.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.
Paeno axioms do not define multiplication. Multiplication is considered to be part of second-order arithmetic, which includes Paeno arithmetic (which is a first order system) and augments it to form a stronger set of axioms, of which multiplication is one of them.
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:
Personally the way I learned to think of it was to read it in the order that organizes it into the fewest number of "groups". Afterall it is easier (and faster) to visualize three groups of five items, than it is to visualize five groups of three items.
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.
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".
Because where I come from, we use the English equivalent of "into" rather than "times". "5 into 3" roughly translates to "5, 3 times".
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 syllabus does nothing of the sort. The addition technique is a way of teaching very young children in a way they can grasp. However, it relies on using concrete objects and so far as I can see, should be used as a technique to aid understanding, and only then should the multiplication notation be introduced.
Agreed. Few children are going to get to the point where the commutative property is a concern, anyway.
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.
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 steps are the steps". Great advice if the purpose of school is to train people for rote factory work (we have robots for that). Not such a great way to prepare future leaders or creative problem solvers.
When are practising skills in school, sometimes we practice creativity and sometimes we practice techniques. Both are useful, and it's clear which is which.
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.
I seriously doubt this student "only knows how to produce a particular answer for a particular question". Are you claiming he could compute 3 times 5 but not 5 times 3?
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.
I agree with you. The learning objective is stated as "I can use multiplication strategies to help me multilpy", but it's important that the question asks about a specific multiplication strategy, and marks the question as partially correct because the specific multiplication strategy desired is used only partially correctly.
I don't think "merge sort vs. insertion sort" is a good analogy in this case. This seems more like the teacher is deducting points because of a wrong indentation or brace style.
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.
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.