Monday, February 22, 2010

Enlightened Exchanges Over Math Education, V

This time my critic is an anonymous commenter on the thread for last week's problem of the week.

Anonymous begins by taking issue with the idea of comparing specific problems. The several comments he/she makes--in reaction to several other commenters as well as to my original post--inspire me with a new thought. Besides comparing Reform Math with other curricula, it would be interesting to compare the different tones used by those on each side of the debate. 

With this in mind, I present my point by point reaction to various of Anonymous' remarks:
Anonymous: Your superficial analysis above (comparing one page of TERC with Singapore Math) is what parents should expect from a blog like this.
KB: "Superficial" is the wrong word. "Narrow" is better here. This blog has presented one narrowly-focused math problem comparison per week for over two years. Comparison of specific problems must absolutely be part of the debate over math curricula.
Anonymous: Maybe you should look up the last word in the Singaporean dictionary and compare it to zyzzyva.
KB: Dictionary entries are another source that come in handy, depending on what you are analyzing. If one's goal were to compare the English and Malay lexicons (there's no language called "Singaporean"), it's useful to compare specific entries in the English and Malay dictionaries. On the other hand, if one wants to make a more shallow comparison, one could compare the last two entries, as you suggest.
Anonymous: So according to bky and JC, 2nd grade should be only about teaching simple computation with number.
[bky wrote "Kids learning Singapore math are going to have a firmer concept of number, place value, and what operations mean"; and JC wrote "The focus should be on numbers. They are what math is about."]
KB: Here another comparison is in order: what bky and JC actually said about what aspects of number should be taught, with what Anonymous says they said.
Anonymous: Oh and by the way, Singaporean math pedagogy is much more about inquiry than direct instruction.
KB: I've often pointed this out on this very blog. There's a lot of Inquiry, in the best sense of term, built into the Singapore Math curriculum.
Anonymous: But you shouldn't let the facts get in the way of your rhetoric.
KB: Indeed.
Anonymous: The amazing paradox is that you support Singapore Math (which is fine with me) but you only want traditional drill with this text.
KB: Again, it's interesting to compare this characterization of bky, JC, and anonymous 2's comments with what they actually wrote.
[Anonymous 2 wrote: "I do Singapore math with my kids. It is largely direct instruction, at least in the early grades." JC added " Students from countries where direct instruction is used significantly outperform us. This is especially true on the PISA test, which tests the ability to apply knowledge." JC also cites Mayer on evidence that "unguided instruction" does not work.]
Anonymous: The majority of Asian students do their computational drills at home or afterschool but NOT in school.
KB: The book "The Learning Gap" argues otherwise.
Anonymous: School hours are for inquiry, problem solving, and critical thinking.
KB: As seen in this blog's weekly comparisons, inquiry, problem solving, and critical thinking are very present in the Singapore Math curriculum, and very different from the "inquiry," "problem solving," "critical thinking" seen in Reform Math.
Here ends this extended meta-comment, to which Anonymous did not reply. But either he or she or another Anonymous poster, in reaction to a subsequent comment by Barry Garelick on how "Discovery or inquiry based learning can be done well or poorly" begins with the following:
Anonymous (Anonymous 3?): Thanks for Garelick for admitting that discovery/inquiry learning can be done well. That it is not the cause of all America's woes as you read in the attack traditionalist blogs.
Which led me to the following question:
KB: Does anyone out there know which "attack traditionalist blogs" Anonymous is referring to? I.e., blogs that say that math should consist only of rote drills and that inquiry can't be done well?
Surely there there are more rational, less angry voices out there with criticisms of the various criticisms of Reform Math who are capable of reading and accurately characterizing those criticisms before they critique them.  

It's just that I haven't had the privilege of having an enlightened exchange with such people on this blog (hint).


Beth said...

Katherine, there are "attack traditionalists" who comment on kitchen table math. I've had run-ins with them myself. I totally get what anonymous meant by that.

Katharine Beals said...

Beth, There's certainly a belligerent--at time even astonishingly belligerent--tone in some of the ktm comments. I read those comments regularly and can guess what you're referring to. But I've never read a ktm comment that said either that inquiry never works or that math should only involve drill. Am I missing one that does?

Beth said...

Katherine, I don't know whether I can find a comment that says exactly that inquiry never works or that math should only involve drill, and the prospect of reading through all those comments looking for one is not a pleasant one.

But I have certainly read plenty of comments on ktm that shed a lot more heat than light. People write in, blaming shadowy "progressives" for educational practices that every progressive ed writer I know of is solidly against.

Anonymous is probably leaning a bit too far in the other direction, but I absolutely understand the impulse.

I'm not thrilled with people at either far end of the debate. I'm looking for the middle ground, where we can combine rigorous content with respect for the student as an individual.

Is that really impossible? I hope not.

Barry Garelick said...

I find that there are many people who mischaracterize traditional math as one that consists only of drill and "mindless rote". I went to school in the 50's and 60's and have looked at many of the textbooks in use at that time. Procedures are explained, in terms of what one is doing when executing a particular algorithm, as well as what types of problems are addressed by such procedure. Thus, multiplication of fractions is not simply left as an endless list of fraction multiplication problems, but includes word problems as well.

The anonymous commenter that Katharine talks about is saying that inquiry-based teaching is getting a bad rap. I would say that inquiry based teaching done wrong has become prevalent, and not just in math. Student-led teaching takes the form of students working in groups and helping each other "construct knowledge"--supposedly with teacher guidance. There have been attacks by reformers on the idea of students "sitting in rows with the teacher at the front of the class, teaching", as if sitting in rows stifles knowledge, that no "ah-ha" experiences can occur via direct instruction, and that the teacher never asks leading questions or scaffolds students. (Sherry Fraser's testimony to the National Math Panel comes to mind; she's a principal of the IMP math series.)

An interesting article on why minimal guidance in teaching is not effective can be found here.