The Medium has the article Why 5 x 3 = 5 + 5 + 5 Was Marked Wrong: Viral Common Core Math Problem Explained. My issue with the common core math is whether or not you can prepare teachers to teach it any better than (or even as well as) you can prepare teachers to teach math the traditional way.

I debunk the answer given in the article.

In this case, the answer was marked wrong by an ill-prepared teacher. The equals versus equivalency is a completely bogus justification for marking the answer wrong.

Use the repeated addition strategy to solve 5 X 3.

5 x 3 = 3 x 5 = 3 + 3 + 3 + 3 + 3 = 5 + 5 + 5 = 15.

Of the five ways of expressing the number, all five are equivalent. There is no core mathematics principle that says adding 3 five times is more right than adding 5 three times. The order of scalar multiplication is commutative. Teaching that all five are equivalent, or letting the student find out that they are all equivalent is a very important underlying mathematical principle, called commutivity, that is essential for students of more advanced math to know.

The order of matrix multiplication is not commutative. That is an important distinction to recognize. The matrix multiply example below shows that changing the order of multiplying two matrices changes the result. This example can be downloaded into Microsoft Excel or other spreadsheet program to check the formulae to see whether I have done the multiply correctly.

So what is true about one kind of multiplication is decidely not true of the other. To use one to show the principle of the other is to misunderstand matrix arithmetic.

This is a definite example of why we shouldn’t have math phobic teachers trying to teach math. They can see the examples in the teacher’s guide, but they really don’t understand the principles.

Note: Using matrices is a good way to express the solving of simultaneous equations. It is something that I spent half of an electrical engineering career doing. That is, I maintained and modified a computer program that solved the circuit equations of integrated circuits. Just about every integrated circuit design has been analyzed by a computer program like the ones I was responsible for. First I did it in several IC design companies and then I did it in companies that sold this type of software to these IC design companies.

If you do find an error in my math, don’t worry. I am retired, and don’t do this kind of work anymore. I assure you that when I did this kind of work, I had the math right.