The Boston Globe has the article Are teachers really ready for the Common Core?

This article adds some information that is needed in this debate, but it is only a piece of what is needed.

In reading some recent articles and seeing some videos, I have started to gain an understanding of what the Common Core is trying to achieve in math.  (See my previous post, Arkansas mom destroys Common Core in four powerful minutes)  That understanding alone does not answer the question about how much research has gone into figuring out if the new teaching methods work.  As I keep reading, I find that research has been done, but I haven’t yet read enough details on what research was done and how it was carried out to know if I think the research was sufficient.

Questions I would like answered include the following: Have the new methods been tested on a broad range of students to see if the new method works for all, for most, for many, or just a few?  Has the research included a study of how to train teachers to teach the new method?  Again all, most, many, or none.  Has the research analyzed the impact of parents “helping” their children with homework for all kinds of parents.  Different kinds of parents might include the highly talented mathematicians who learned by different methods, to the average parent, to the parent with not enough time, to the uneducated parent. Has the research studied the best methods to roll-out the new program – all at once, a little at a time, school by school, city by city, state by state, or the whole country all at once.

Changing the education system of an entire country requires much more thought than changing how one teacher teaches a course.  Has the thought been done at the top, through the middle, and down to the bottom of the implementation pyramid?

I was intrigued by the following example question.

A right circular cone is shown in the figure. Point A is the vertex of the cone and point B lies on the circumference of the base of the cone.

The cone has a height of 24 units and a diameter of 20 units. What is the distance from point A to point B?

____ units

It took me a few seconds to see that this was not as complicated a question as I first thought.  It took me a few more seconds to figure out how to do calculate the answer in my head without any difficult arithmetic.

To check your answer with the right one, see the answer on the PARCC web site.

Perhaps this isn’t as controversial a question as the examples in my previous post.

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.