Jessica Fairbrother Trent shared the video below on her Facebook page.

It comes from the article Arkansas mom destroys Common Core in four powerful minutes.

I was skeptical about the presentation that this “mom” made. I wasn’t sure she was giving the whole story. Before I got too excited about the push for the “Common Core”, I wanted more proof.

Ironically, a feature of Facebook, that I have been thinking of turning off, showed me a link to what it thought was a related story.

About That ‘Common Core’ Math Problem Making the Rounds on Facebook… This isn’t exactly the same example as discussed in the video, but I think it is close enough to make you want to reconsider what you think you may have learned in the video.

It is worthwhile to think about and discuss whether or not these new teaching techniques are the best way to teach these subjects. However, before doing that thinking and having that discussion, it pays to have some idea of what these techniques are trying to accomplish.

From my own experience, I did not learn the method of making change as described in the second article until I went to work in my father’s drugstore, and he taught it to me. I have noticed that there are very many clerks today who depend on the cash register to figure it out, and have no idea on their own of how to make change.

The classic case happened to me a little while ago. I bought something for $12.10. I handed the clerk a $20 bill and 10 cents. The clerk gave me back the 10 cents, and then proceeded to give me $7.90 in change. I don’t think I tried to mention to the clerk that $7.90 plus 10 cents is the same as $8.00. Rather than give me back my 10 cents, and then giving me $7.90, she could have just given me $8.00. (The trick my father taught me is to consider the 10 cents as paying for the $0.10 of the amount due, and then make change for the $12.00 that was left of the amount due out of the $20.00 that was left after taking care of the $0.10 I had handed to the clerk. Trying to do the math in your head, what is $20.10 minus $12.10, was too tricky in the situation where you were trying to make change quickly, and could not write the problem down on a piece of paper.)

The actual process of my education that I think is relevant to the discussion is what I did on my own while learning arithmetic and mathematics. I would frequently think about different ways to arrive at the same answer, and then ponder why these different ways always gave the same result.

When I started to learn about decimals, I would often think about working through the same problem by using fractions. It always amazed me that using different digits in the two processes, the results always came out to the equivalent answer. For instance we have the decimal “0.5” and the fraction ½. If you divide the number “1” by either of these two representations, you get the same answer.

The decimal algorithm I learned was 1.0 / 0.5 – shift the decimals in the two number to convert the problem into 10.0 / 5.0 = 2.0. For dividing by a fraction 1 / ½, you turn the fraction over, and multiply it by the dividend 2/1 X 1 = 2. One method used the digits 1 and 5. The other method used the digits 1 and 2, but either way the answer was 2.

So what I think the common core is trying do is to teach people to think about math in different ways, rather than leaving it up to the imagination of the few students who are interested enough or creative enough to think of these things on their own.

Whether that is a good pedagogical technique for all students, I cannot judge. I do not know the research that went into deciding that it was a good approach. I hope to heck that there is some research on the effectiveness of the technique that backs up the decision to introduce it into classrooms across the country. Do any of my readers know the nature of such research if it does exist?

When I cross posted this on Facebook, Facebook offered the interesting article, 2+2=What? Parents Rail Against Common Core Math, as related. It at least gives a hint that there is an answer to my question above the line.