There are a number of issues with this explanation.

Firstly, as we know, multiplication and addition are associative, which means if you ever teach a child that 5 x 3 is different to 3 x 5, you are imparting wrong information.

The issue is that the question asks the child to "use the repeated addition strategy to solve: 5x3". The reason this is a problem is because "repeated addition" is indeed a strategy to teach children the concept that if you take a multiple of some number the. It is like repeatedly adding that number of items, a number of times. It is used as a stepping stone towards fully understanding multiplication,after on, and takes into account that young children think I terms of what they see. So for example, they see that a dog has 4 legs, and if you have 3 dogs then you add the four legs together three times (one for each dog).

Notice that it's madness to teach this as a. "addition strategy", because at that age "strategy" is far too abstract a concept for most children to grasp. The irony is that teachers then attempt to teach using a technique that uses a low level of abstraction, but when they call it the "addition strategy" they have just attempted to teach this technique that is using a more concrete methodology via language that uses concepts that are arguably more abstract than the concept they are attempting to teach!

You can see that the whole point of that technique is missed completely on that exam because of the question being asked. In fact, to have a student demonstrate understanding the I fact the question should be "I have five jars of Jellybeans. Each jar has 3 Jellybeans in them. Show me how you would represent the number of jars times by the number of Jellybeans in each jar, using addition."

You see, the point of the strategy is entirely being missed here. The author protests that the child will get confused because if they rely on the law of association with subtraction and division they will get the answer wrong, and be confused. But that's not what is happening. The child has clearly understood that actually, 3+3+3+3+3 is the same as 5+5+5. In actual fact, the student has shown a clear understanding of multiplication via addition.

If you think that child will be confused, wait till they get to fractions and numbers with decimal places! Because at that point, you can't use addition to explain multiplication and then you need to explain multiplication in terms of scale. There's actually a case to answer that the entire technique of teaching multiplication via addition is fundamentally flawed and it's better to teach in terms of scale anyway. I don't subscribe to that view, but I can see why it might be held.

I have to also take issue with using the definition from what looks like the Cambridge Dictionary's noun definition is that this is NOT the same precise meaning as equivalence in mathematics. In fact, if you were to use first-order logic, then it would be:

iff 5x3=15 then 5+5+5=15

or,

(5x3=15) ≡ (5+5+5=15)

That satisfies the two expressions logical equivalence. So the statement that this is NOT logically equivalent is entirely wrong.

Furthermore, the author has not read the definition on Wikipedia carefully enough. It says:

The multiplication of two whole numbers is equivalent to adding as many copies of one of them, as the value of the other one

The assumption being made here is that Wikipedia is saying that the number that is to be added up multiple times is the leftmost number in the expression, but it does not in fact say this at all. It says to add "as many copies of one of them", which means it could be referring to the left or right hand value in the multiplication expression.

The common core and the techniques used to teach young children are solid. Unfortunately, it looks like the way they have been used and taught to educators is the problem here! The fact that you can see the framework leaking into a test question shows that there is a fundamental flaw in the pedagogy of whoever is teaching that class.