Tuesday, June 16, 2015

Common Core -- "and the brains of Isadora Duncan"

Mathematics educator and blogger Gary Rubinstein has been doing some extraordinarily important work on the Common Core beat. There's a lot of confusion about the boundaries of the discussion, and they have a way of shifting between and sometimes even within arguments.

A great deal of that shifting centers around exactly what constitutes Common Core. Proponents will often fall back to the "just a set of standards" definition and claim that criticisms involving implementation are invalid. That's a difficult position to hold since the standards without implementation aren't that meaningful, particularly considering that schools already have state or district standards in place that aren't all that different from Common Core.

A much more tenable defense is that the bad examples circulating online aren't really aligned with Common Core and we should wait until there's a faithful implementation before judging. This is the argument Rubinstein goes after, starting with this analysis by Education Week.

[Eureka Math is more or less the same as EngageNY. I'm still looking for an official statement but you can pretty much use them interchangeably.]

I volunteer with an after school tutoring program here in LA.in a program that largely focuses on language arts, my role is designated math guy. I go from table to table answering any algebra/geometry/calculus questions that that the regular tutors can't handle. Sometimes this is because the tutors have forgotten what similar triangles are or how to apply the quadratic formula, but just as often, the problem has less to do with math and more to do with Common Core. It is not unusual for a volunteer who happens to be an engineer or a computer scientist to wave me over because he or she has no idea what the question is asking. In these cases, I noticed that the EngageNY logo often appeared at the bottom of the worksheet.

Rubinstein has dug deeply into the EngageNY materials being given to students and what he has found is not good.
First of all, some lessons are full of errors.  Second, some lessons are unnecessarily boring, and third, some lessons are unnecessarily confusing.

I should note that I have not gone through every module in every grade.  I also did not search through to cherry pick examples that were particularly bad.  I just randomly picked some important topics to see how they covered them and either I just happened to find the only four bad lessons in my first four tries or there are so many flawed lessons in this project that randomly selecting a bad one is quite likely.  It’s a bit like evaluating a singer and the first few songs you listen to are out of tune.  How many more do you have to listen to before you can safely assume that this is not someone with a lot of talent?

Exhibit A is the first lesson in the first module for 8th grade, exponents.  On the second page, they introduce the concept of raising a negative number to a positive integer.  Every real math teacher knows that there is a difference between the two expressions (-2)^4 and -2^4.  The first one means (-2)*(-2)*(-2)*(-2)=+16 while the second one, without the parentheses around the -2 means -1*2*2*2*2=-16.  I have checked with all the math teachers I know, and none have ever seen -2^4 interpreted as (-2)^4.  Yet, here all over lesson one module one for 8th grade EngageNY teacher’s edition, we see this mistake.

And from the 8th grade EngageNY teacher’s edition

According to Rubinstein, this mistake is made eighteen out of the twenty times the topic is addressed.

I'll be coming back to this later but for now I'm going to close with a couple of paragraphs from the my Monkey Cage piece on Common Core and the New Math of the Sixties.

One of the best summaries of these criticisms came from Pólya, who alluded to the famous, though probably apocryphal, story of Isadora Duncan suggesting to George Bernard Shaw that they should have a child because it would have her beauty and his brains, to which Shaw is supposed to have replied that it could well have her brains and his beauty.

Pólya suggested that new math was somewhat analogous to Duncan’s proposal. The intention had been to bring mathematical researchers and high school teachers together so that the new curriculum would combine the mathematical understanding of the former and the teaching skills of the latter, but the final product got it the other way around.
The sad part is this time they found someone with far less mathematical understanding than the high school teachers.

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