[jasode]

>The point is that because the 5 is first, as everyone can see, it has a specific job in the repeated addition technique.

If you(royal-you) insist that the 5 being the first factor has a specific job and you teach such nonsense to a child, it means you're not teaching actual mathematics.

In _real_ math, the factors/mutiplicands have no notion of ordinal rank such as "first" or "second" or "specific jobs". Even if the child was not formerly taught The Commutative Law, it's not impossible for him to see multiplication tables[1]. (In fact, many are hung as big posters in elementary classrooms.) Any child with pattern recognition abilities beyond a chimpanzee would notice that the cells of XY have the same answer as YX. He/she would ask mom/dad/teacher "is xy always same as yx?".

In the world of _pseudo_ math that stresses bizarre hoop jumping, we overlay non-mathematical concepts such as "specific job" to factors. Maybe this skill is important and transferable to the enlisted man to make sure he makes his bed before cleaning his machine gun instead of the other way around so everyone in the squad doesn't get punished with 50 pushups. But don't pass it off as "teaching math."

[1]https://www.google.com/search?q=multiplication+table&es_sm=9...

[jmilloy]

I only have a bachelors degree in math, focusing on theory, but I think we have a different understanding of what actual mathematics is. For example, in some "real math", definitions, properties, and axioms are well-distinguished and mixing them up can get you in trouble.

More importantly, are we even trying to teach "real" math to elementary kids (I wish we did, but I don't think we do) or "computation"? Both are useful and interesting.

[chris_wot]

Yeah, but the problem is: repeated addition is attempting to take something very concrete like I give four children three marbles each, how many marbles does each child have?

You then use that addition technique to have them add up the number of marbles (in essence it's as if you are asking them to count on their hands, which is a valid technique at this level).

But that helps the child understand the concept of addition in a very literal and concrete fashion, because at the age of 4-5 years old (sometimes older), children don't think at a higher level of abstraction. And using symbols to represent multiplication IS a higher level of abstraction.

It seems to me, a non-educator, that the counting technique has value in word problems. But as soon as the child shows they understand the concept, then you introduce the notation (e.g. 5 x 3), explain the numbers can be added up either as five values added up three times, or three values added up five times.

That the test talked about a "strategy" is not really maths, and frankly it seems to be misapplying a solid teaching technique, leading to confusion, anger and a lack of confidence in the child. If that's happening, then I'd suggest the technique is not all that solid and teachers and other educators should seriously consider whether it is causing more harm than good.

P.S. If you have a Bachelors in Mathematics, then surely you can see that there is a fundamental problem if a child is taught that 5x3 is not the same as 3x5?

[jmilloy]

> P.S. If you have a Bachelors in Mathematics, then surely you can see that there is a fundamental problem if a child is taught that 5x3 is not the same as 3x5?

It's not the same. I'm not sure when that should be taught to a student.

[chris_wot]

It is the same!

[jmilloy]

Right, for different definitions of "same". I think that the OP attempts to explain that there are different definitions of "same" that are each valid.

[chris_wot]

I can't see how!