# When “a x b” is not equals “b x a”…

When I first saw this article on how some apparently correct answers were marked wrong, my first thought was “what rubbish is this?”.

More recently though, my wife talked about the incident in which a colleague of hers will be switching her kids to private school because her kids was deducted points for not showing the steps, even though their answers were correct. Is this justified?

If this is what is resulting from “Common Core”, I will dare say that the next generation of US-educated kids may just end up being the laughing stock of the world. And this is my take on it.

Math the Universal Language

Math defines operators that work using a certain set of rules and properties. For simple arithmetic, we know these rules instinctively. Take addition for example, we know that “1 + 2 = 2 + 1”. It is commutative. Multiplication is a little bit more involved. It is commutative on numbers but is not on matrices. “3 x 5 = 5 x 3”. Order does not matter.

Regardless what language Math is taught in, you get the same answer, hence Math is also known as the universal language. We expect aliens in space to know this too, because Math describes the underpinnings of nature.

Now in “Common Core”, “3 x 5” is taught as 3 sets of 5, and “5 x 3” is 5 sets of 3. This is a reasonable way of understanding the question. To teach the math, we impose a context on the operation by expressing in English. Now herein lies the issue; The rules changed… 3 sets of 5 is not the same as 5 sets of 3, even though the underlying Math is commutative.

By penalizing a child on it, we are now teaching kids the wrong basic mathematical rules which can be detrimental when solving equations which rely on these properties. To me, “preparing them for matrices in High School” does not fly as a reason. It is easier to teach something new than to correct a misconception. Here, we are simply teaching the wrong fundamental.

And it matters to me as a parent, because I have to go in and correct all the bad knowledge for my own kids.

Hence this is what I think teachers should do. In the absence of a clear context, a student should not be penalized for invoking the commutative rule. In other words, if a question is given as simply: 5 x 3. Then solving the question as 3 x 5 is correct. However if we ask a question along the lines of: “A grocer has packed 5 bags of 3 apples…How many are there in all?”. Then solving for 3 x 5 in this case should be penalized.

In the viral image, a question is given as “Draw an array to show and solve: 4 x 6”. The student is penalized when he drew a 6 by 4 array. This is retarded, because an array can look 4×6 or 6×4 when we simply turn the paper 90 degrees. In my definition, this is a “vague context” and so the student should not be penalized.