Not only is this wrong but harmful teaching of math. It is also false.
The following equivalence
5 x 3 = 3 + 3 + 3 + 3 + 3
is only true for Whole Numbers “when thinking of multiplication as repeated addition” but in abstract multiplication as a concept is much broader.
Multiplication of real numbers can not be “demonstrated” so easily in such groups.
5.0 x 3.0 = ????
Or can the that “concept” be applied to geometry which has an arbitrary orientation in multiplication.
5m x 3m = ??????
And most importantly multiplication as a function contradicts this logic.
Let X and Y be two sets. Let f:X→Y and g:X→Y be two functions. f=g iff f(x)=g(x) for all x∈X.
let f(x)=3 x x
let g(x)=x x 3
since f(x)=g(x) for all x∈X
f = g
then let x = 5
3 x 5 = 5 x 3:
therefore 3 x 5 = 5 x 3 = 5 + 5 + 5 = 15
this implies that 3 x 5 = 5+ 5 + 5 = 15 and it is EQUIVALENT as a function.
IN ABSTRACT MATH 3 x 5 represents many different things and it is important for the child to see MANY interpretations of this ABSTRACT concept .
Math Teacher please teach MATH as a Science and not as a Political Science.