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Needless to say, I was horrified by Elizabeth Green's Why Do Americans Stink at Math?, which is the single most breathless endorsement of constructivism I've ever seen in the Times. Actually, it may be the only breathless endorsement of constructivism I've seen in the Times.
I read it this morning, just before a meeting with Ed and his editors at Oxford, and as we were rushing to get ready I joked that Green was probably funded by Bill Gates.
Then tonight it occurred to me that I should check.
Chalkbeat: About Us
The Times has no business publishing an advocacy piece, albeit an advocacy book excerpt, without disclosing the Gates connection.
UPDATE 7/29/2014: Bill Gates is very likely the major funder of Elizabeth Green
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21 comments:
I had two people forward it to me.
I notice that she parrots what she got from a handful of common core advocates, reformers, and math constructivists...
There is no hint of any opposing view. No possibility that post-Sputnik New Math was something different from Common Core. No evidence that the author actually understands what she has written.
It is advocacy, disguised as journalism.
Is it possible for a non-specialist author to write about a specialized topic? I think yes. I see John McPhee generously quote his sources - but there is a clear sense that he did some real work, learning quite a bit about the places and people and forces he describes.
Here? There is no sign of synthesis.
The full book won't be any good, either.
Jonathan
The same argument - that the problem is teachers not doing XYZ constructivist reform correctly - was also used by advocates of the New Math in the 60s. I've also heard it used recently about Writers' Workshop (of course grammar is taught!) and about balanced literacy (of course phonics is taught!).
At a PD now. Incidentally, this is supposed to be about Singapore math. The guy just said this: "a lot of people say Singapore math is the opposite of TERC, but really the two are quite similar. If anything, TERC is more explicit."
Wow is all I have to say.
I tried to post the following a couple of times, but it was rejected by the Times.
"Instead of having students memorize and then practice endless lists of equations .."
This is a strawman. It never happened like this. Also, schools have been using constructivist techniques for at least 20 years. In our schools, it's been Everyday Math for the last ten years and MathLand before that.
Where are the results?
Nothing in this article is new. I've been fighting this vagueness for 15 years. People talk in glowing generalities about discovery, but nobody shows how the details work. I could define a proper constructivist curriculum, but it would require much more effort and be quite different than the silliness in this article. There is no engagement panacea for math, and mastery of basic skills is not some easy artifact of understanding. Problem sets in proper textbooks carefully lead students along a self-discovery path of deeper understanding. I find it incredible that educators typically define discovery by mixed-ability, in-class, group learning with the teacher as the guide-on-the-side. That's really what educators want. They don't want to hear about all of the understanding that happens with individual homework sets or with teachers properly trained as lecturers. And what about all of those concepts that you can't get to because so much time is wasted in class over very few constructivist group tasks - you know - the ones where the light bulb goes on for one student and she/he directly teaches it badly to the rest?
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What is almost worse are many of the clueless comments after the article.
Yes! Yes! Yes!
To all above.
re: Jonathan's observation that Green doesn't understand what she's written, the current book excerpt takes me back to Green's Building a Better Teacher story in the Times Magazine.
That story was fantastically influential (rightly so) because of its profile of Doug Lemov. I assume her book contract was based on that story.
But the story itself was confused.
It began with Doug Lemov, but it then moved on to Deborah Loewenberg Ball, who is the opposite of Doug Lemov (at least in the eyes of many of their beholders).
At the time I was slightly horrified .... how does an article on teaching move from Doug Lemov to Deborah Loewenberg Ball without batting an eye?
In light of the two new pieces by Green in the Times (she has one in Motherlode as well), it certainly appears that she doesn't really understand the arguments being made on either side.
Direct instruction **encompasses** inductive, trial-and-error learning. A teacher might teach-by-telling; s/he might teach-by-groups; she might teach by 'guided discovery,' etc.
But regardless of the method an instructivist is using, s/he assumes that it is possible to **transmit** knowledge from one mind to another.
Radical constructivism categorically rejects the possibility of "knowledge transmission."
You can't put these two together.
Catherine-
I wrote a story today on how CCSSO has an initiative called Innovative Learning Network that is actively working with the Global Education Leaders Program to drive a common global vision of education that is all constructivist.
The 2012 GELP Conference in Helsinki, Finland was also sponsored by the Gates Foundation. It made it clear that the real focus is students personality. Content, to the extent it's available still, is just about altering values, attitudes, and beliefs about real world problems.
I may not like living in one of the innovative school districts, but I am taking good notes.
"Even in Massachusetts, one of the country’s highest-performing states, math students are more than two years behind their counterparts in Shanghai."
I thought this article was comparing Japanese Constructivism vs. American something. What does Shanghai have to do with anything?
"Instead of having students memorize and then practice endless lists of equations .."
I wonder what would happen if we said that baseball pitchers need to understand the theory behind pitching, but should have to do "endless practicing of pitching"? No one would think this practice prudent. Why is math, which is a learned skill any different?
As a math tutor, who sees that memorizing the Times Table facts and understanding how to manipulate fractions leads to success in higher math, I don't understand this anti-practice and anti-memorization mentality. Ones long term memory is nearly unlimited, while ones working memory is small. By pushing out math facts to long term memory, one keeps the most amount of the precious and limited working memory available to do new concepts.
Sigh....
Anonymous said...
At a PD now...supposed to be about Singapore math. The guy...
Anonymous, who is "the guy"? I've never heard such claptrap before!
As something of a mathematician, but with very little to do with the United States... Out of curiosity, what is the sense of "Constructivism" in use in this present conversation? Is it emphasis of constructive mathematics, à-la Bouwer/Bishop/Martin-Löf? Is it a kind of deconstructionism, as I hear such folk as Anthony Esolen lamenting in the English CCSS? Is it a counterpart to legal Constructionism?
Because it would be nifty indeed if students had a good sense of mathematics as being playing with constructions (sometimes founded on the oracular...), but I doubt that's what's going on; and it would be horrendous if students were only given mathematics as a tool for superficializing their understanding of things; and it would be really really weird if that other thing... but this whole conversation here is opaque to me, orbiting around that black-hole word as it seems.
Elizabeth Green leaves out some details about Japan's math curriculum that are worth noting.
Japan had a "reform" jerk in 1998 that backfired and it quickly lurched back to basics in 2008.
See this article.
Belfry-
I use Constructivism in the sense explained by Jeremy Kilpatrick in his 1987 address to the Psychology of Mathematics convention in Montreal. That's why a quote from it heads up Chapter 3 of my Credentialed to Destroy book.
I also quote from Tom Romberg's definition of constructivism that he says guided his drafting of the original NCTM standards.
Since I wrote that book (it came out last October), I have moved on to tracking the Cybernetics angle for a subsequent book I am working on. One of the things that comes out repeatedly is that the Cybernetic theory of instruction requires constructivism. Otherwise, the goal of guiding perception of reality is not possible.
Constructivism is not about how to best teach academic content or reading. All of those things turbocharge what I call the Axemaker Mind after a James Burke book I have.
It's why the so-called innovative (as in League of Innovative Schools and EdLeader 21) district where I live only talks now of STEM and humanities. High schools are being restructured to center on 'problem-based learning' a la High Tech High.
I listen and take notes and research.
Well, Robin, now that we know you have written a book on ... something... that has been out for almost a year... in which you quote someone describing a thing they call "Constructivism", and one category to which it does not belong... can we hear what it is? Because, at the very least, it's an overloaded term already, and it may be suffering from blackwhite.
I also listen, and take notes, and research! But perhaps we belong to disjoint audiences?
Oh, Hm. here is something that looks like a transcript of that very speach. Here's a quick abstract, of my own concoction from that transcript:
"'Constructivism' is the name a [school of mathematics education] has taken to itself, which school attempts to understand how students 'construct' their knowledge of mathematics". Kilpatrick goes on to explain habits he has observed in that school.
OK. I won't need to buy your book anyway; I might suggest it to my library, though.
The thing I'm lamenting, in all of this, is the use of language not to convey but to elicit.
Speaking of math teaching in Japan, a book first published in 1999 (revised and updated in 2009) by Sigler and Hiebert, The Teaching Gap was a very thought-provoking look at what is needed and presents a very different picture than one would draw from Elizabeth Green.
Japanese math teaching, as described by the authors, was no simply rote learning (although it appears basic procedural knowledge is required) but also features a lot of teacher-directed problem-solving and students working in cooperative groups (Japan does not -- or did not then -- separate elementary students by ability).
IIRC, Sigler and Hiebert acknowledged the power of cultural factors in the differences they found between Germany, Japan and the U.S.
Would like to hear Barry's thoughts if he has read it recently.
I haven't read "The Teaching Gap" but it's on my list of things to do after I change out all the light switches in our house and finish my article on Common Core math standards for the HEartland Institute. In the meantime, there are two things to take note of. The first is my comment above with a link to an article about Japan going over to the math reform side back in 1998, how it backfired, and how they went back to basics in 2008. I have the link to the actual directive from 1998 should anyone be interested. The point being that Japan's math teaching while different in some respects from how it is taught in the US is more "directly instructed" than one would think. And Palisadesk, I wish people would stop referring to basic math teaching as "rote learning". It never was. It also wasn't "lists of equations" as Elizabeth Green proclaims in her paean to constructivism otherwise known as a NY Times article.
Secondly, I have linked to this before, but there was a paper written by Alan Siegel that blows out of the water the myth of Japanese teaching being all guide on the side and discovery oriented. I linked to this paper in a comment I left on Green's NY Times piece as well. I'm hoping this will dispel the notion that Japanese methods are US reforms done correctly and well.
As for cultural differences, yes those make a difference but such arguments serve mostly as red herrings. People always point to Singapore and say "Yeah, but culturally education is really important and parents pay for afterschool tutoring, plus drill their kids at home..." etc etc. All true. But the choice of the curriculum is culturally driven as well; Japan and Singapore didn't exactly pick Investigations and Everyday Math, did they?
it's Stigler, not Sigler.
To extend what Barry is saying, the Alan Siegel paper Barry is talking about is here:
http://www.cs.nyu.edu/faculty/siegel/siegel.pdf
with the meat in this:
http://www.cs.nyu.edu/faculty/siegel/ST11.pdf
The Siegel paper blows a number of things out of the water. First, that Stigler's work on the Japanese videos of instruction was high enough quality to draw the conclusions it did with any veracity.
Then, Siegel's paper blows out of the water the conclusions themselves.
The best way to understand the Japanese instruction is that it was *strongly* teacher led, using problems as a mechanism for teaching concepts, and in particular, for exercising repeated practice of the specific concept being taught. It is basically individual work to struggle and practice the teacher-taught concept, with an extremely small amount of group work, and
the group-work.
All of which depends on an incredible mastery of the underlying mathematical material, so as to guide continually, and often subtlely, through all sorts of pitfalls.
The videos available are here.
http://www.timssvideo.com/
Everyone should watch them.
To summarize one core element, Siegel shows that Stigler et al. mistakenly call *students solving problems using the method the teacher showed* discovery or inventing their own solution.
At best, this is because the people working on coding the videos *did not understand math well enough* to distinguish that a student being told "Here is a problem X; try to apply technique Z to solve X" is not coming up with their own solution.
Presumably, the people thought math solving is "here is problem C. We perform this set of steps." when in fact, solving a math problem involves seeing how that set of steps relates to the problem, and then the soution. Since the Japanese video left that as the exercise for the student, perhaps that looked like "inventing " a new or alternate technique.
To change the subject slightly, ignoring every other issue of culture, classrooms, policies, etc. between Japan and the US, let me say that the examples released to the public are content-wise, very impressive. The math lesson on inequalities for 8th graders used a technique (marginal cost) that I didn't see *until I was a grad student in CS theory at Cal.* (Meaning, never having seen it in any math, physics, or eng class I took at MIT let alone UCSD or hs.)
If you are presenting concepts to children *10 years earlier* than our brightest kids are seeing them, then the other issues don't even matter. They are rounding errors.
The article reminded me a bit of communist apologists in the 80s saying the USSR wasn't a true representation of communism.
'Really, constructivism would work great, but nobody is actually implementing it properly.'
Both arguments leave one asking what the difference really is. It's a failure but… versus it would be a failure no matter how you implemented it.
Perhaps the other points made in the piece - that math is taught in this country principally by people with very poor understanding of math and almost no training - could lead us, er, Bill, to improve on those matters. By the time anything actually changed, the constructivism fad would be over anyway (to be replaced by some new ism enthusing a small band of wide-eyed academic trotskyists).
Catharine, I agree with you that Elizabeth Green's reporting is horrifically bad. OK, now that we've gotten that out of the way: I checked, and Gates is one (two?*) out of over 25 contributors! It seems very misleading to say that she's "funded by Gates." One of the other donors on the list is the Walton Foundation . . . Can you imagine someone cherry-picking that particular donor to smear Green by association? (I can!)
*Bill & Melinda and Gates Family are both listed
I'm a little late to this, but we just returned from Shanghai, where we were guests of a Communist Party official who is a family friend. A couple of weeks ago, he was able to bring his son to a Saturday brunch with us. The son was able to come over from school and join us for part of the meal, because he'd managed to switch one of his Saturday morning classes into one of the few open slots he had on Sunday afternoon. He told us that the results had just been announced, and the Chinese national team had once again taken first place in the 2014 International Mathematical Olympiad. He had taken math classes from one of the Chinese IMO coaches but, like most of his friends, had too much competition to make it onto the team. One of his classmates had gotten onto the Chinese national team and had just scored a rare perfect score in the IMO competition.
Our friend's son then excused himself, and his mother drove him back to school, where he would sit in classrooms with neat rows of desks and would be intensively trained by intensively-trained trainers. Seven days a week of rigorous academic training (in all subjects, not just math). And group-based discovery is just not a part of his world.
There is a huge industry in afterschool schooling in Shanghai, Tokyo, and Seoul. I've been inside these schools many times as an unofficial observer (I lived in Tokyo and Seoul), and there is no trace of group discovery or constructionist fluff in the successful schools. These private schools face ferocious competition from other private schools for parents' voluntarily-spent (not taken and allocated by government) money. The schools compete by providing convincing evidence that THEY provide more advantage than other schools in the ferocious competition among students. They do so by touting the domain-specific qualifications of their direct-instructing instructors and by engaging in as much standardized testing as they can and broadcasting the results. These results are not just targeting some special test but include high school entrance exams, college entrance exams, national and international competition results, US elite university admission, and so on. These schools include many whose specialty is taking under-performing students and significantly improving their results. The successful schools want everyone to see their numbers, and those who hide their numbers don't succeed.
Any school that entered such a free market proclaiming the superiority of group discovery over direct instruction and claiming they "teach for understanding" while repeatedly trying to prevent objective, outside testing to confirm this "understanding" would be filled with the sound, not of engaged students, but of crickets.
If we think educational achievement would get a major boost from more group-based discovery and the like mandated in our schools, we should first explain why the schools forced to compete for their survival in fiercely competitive, educationally overachieving, free markets never voluntarily adopt this secret weapon.
Have you seen the criticism of Green's piece at http://jukuyobiko.blogspot.jp/2014/08/big-doubts-on-ny-times-article-why-do.html? It tears into her for not mentioning or considering juku (cram schools).
CT - thank you!
Yes, yes, yes!
That's one of my main complaints --- JUKU.
Plus her profile of the NCTM-style Japanese teacher includes the fact that he wrote **daily** newsletters home to parents because they needed to understand what he was doing in class.
I think that has to mean that parents were handling the reteaching & the 'rote' practice.
(I need to check that passage again.)
I'm a month late, but I see Belfry Bat wanted to know what constructivism was, so just in case s/he circles back:
Constructivism is two things. Constructivism as a learning theory says that we learn things by constructing the knowledge in our brain out of our experiences. This isn't a particularly radical idea, and is rarely what people mean when they say constructivism.
Constructivism as a teaching theory starts with the notion that teachers should give students experiences that will help them construct an understanding of the important concepts of the disciplines (so far so good). It then goes on to say that those experiences should be ones where students are solving problems using their informal knowledge to discover new ideas (sounds interesting, but difficult to implement). And next says that teachers shouldn't be telling children how to solve problems and giving them new knowledge by telling them things, but should instead arrange for all of the learning to come out of discovery and class discussion (difficult, inefficient, and with hidden pitfalls). It also claims that if children understand the concepts well enough by discovering them, then they shouldn't have to practice lots of problems to achieve memorization (probably not true).
Anyway, when people say "constructivism" they are usually referring to the last ideas: teachers shouldn't "tell" new things, instead children should spontaneously discover them, and children shouldn't need to practice very much in order to learn math. Both the people arguing in favor of constructivism and those arguing against are focused on whether or not it works to have students discover and teachers not tell what to do (constructivism) vs. having teachers explain and children practice (not constructivism).
I hope that's helpful for someone.
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