CNN has the video Bill Clinton concedes role in mass incarceration.

In listening to the justification that statistics show that a small number of criminals are responsible for a large number of crimes, does Bill Clinton show the tiniest understanding that many of the repeat offenses committed by these “criminals” are manufactured by the police? Like Sandra Bland’s great crime of not signalling a right turn, once you have been caught for doing something, you are forever targeted for anything else you might do that most people would never get charged for.

Think about the quote from a previous post Bad Science: Quacks, Hacks, and Big Pharma Flacks. The word “this” in the quote below could be equally well applied to the statistics that Clinton uses to justify why he thought at the time that mass incarceration was a good idea.

This breaks a cardinal rule of any research involving statistics: you cannot find your hypothesis in your results. … If your hypothesis comes from analyzing the data, then there is no sense in analyzing the same data again to confirm it.

Now you are ready to watch the following video and fully appreciate it.

None of the candidates can take great comfort from what Dr. Watkins says here. There is a temptation to feel that at least the other candidate is worse than you are on this issue, but nobody should be satisfied to be just the lesser of two evils. I suppose this also does not let us supporters of these candidates off the hook either.

The only thing to take away from this is to listen and learn, and then try to do something about it. Dr. Watkins has some suggestions. Maybe a candidate can pick up and run with some of them.

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.