[Squeakland] Panel discussion: Can the American Mind be Opened?

mmille10 at comcast.net mmille10 at comcast.net
Wed Nov 21 22:23:35 PST 2007


Re: Constructivism, where to start?

I'm not real clear myself where it came from. My introduction to it was reading up on Kay's vision for educational computing, and watching some presentations of his on the same topic.

Citing some things from the article you referenced. I didn't read the whole thing. I was primarily interested in the section on constructivism:

"Included on the list for decreased attention in the grades K-4 were 'Complex paper-and-pencil computations,' 'Long division,' 'Paper and pencil fraction computation,' 'Use of rounding to estimate,' 'Rote practice,' 'Rote memorization of rules,' and 'Teaching by telling.' For grades 5-8 the Standards were even more radical. The following were included on the list to be de-emphasized: 'Relying on outside authority (teacher or an answer key),' 'Manipulating symbols,' 'Memorizing rules and algorithms,' 'Practicing tedious paper-and-pencil computations,' 'Finding exact forms of answers.' ...

The variant of progressivism favored by the NCTM during this time was called 'constructivism' and the NCTM Standards were promoted under this banner."

Some of what's described here is what I've been hearing about through other venues. The only characteristic that was news to me was the de-emphasizing of "manipulating symbols". Wow. Does this mean they weren't going to teach algebra somewhere in grades 5-8? One of the benefits I've heard about for learning advanced math, even it is by rote learning of algorithms or rules, even if the student never uses it again, is it at least teaches symbol manipulation and logical thinking.

I get the sense with the way that various reform efforts have played out though is they've thrown the baby out with the bathwater, or maybe the "baby" wasn't there to begin with and the reform methods just expose that more. There was a fairly recent video I saw by M. J. McDermott, a meteorologist, expressing her concern about the state of math education in Washington State's public schools (at http://www.youtube.com/v/Tr1qee-bTZI). She said that when she went back to school to become a meteorologist she noticed a lot of the freshmen were struggling with the math that was being used. She also heard complaints from professors about this. She attributed it to a lack of basic mathematical knowledge, and made her own determination that it was the "new math" they were learning in the public schools. She said that all they knew how to do was use calculators, and work in groups. She spends most of the video demonstrating the new methods they're using for multiplication and division, both t
he "reasoning" and algorithmic methods. I agree with the "reasoning" cluster problems approach, because I've developed similar methods for "calculating in my head", but the algorithmic ones seemed overly complicated. Personally I'd prefer the standard algorithms to the new ones. I get the sense she missed the boat in her emphasis on these methods. I think the real deficiency she was noticing was the lack of ability in symbolic computation, which she only mentions. She said the students lacked understanding of algebra and trigonometry. This is probably because they just let their calculators do it. The ones that most students have access to now can even solve Calculus problems, I think.

I happened to look at the comments for this video on YouTube and I found that people were calling what McDermott was describing "constructivist" education, though she doesn't use this label. Whether that's an accurate label or not, that's people's impression of it.

As I researched constructivism some more, it began to sound like teaching methods that have been discredited, such as "whole reading" and "whole math", particularly the discovery aspect. I happened upon a couple of old articles by Lynne Cheney (yes, the wife of the current Vice President), back when she was Chair of the Endowment for the Humanities. She harshly criticized constructivism, associating it with these methods. I can't find the original article now, but I remember one where she talked about an instance in a "whole math" course where the kids were supposed to be learning about the Pythagorean Theorem. They were expected to create a right-triangle out of 3 rectangles of graph paper of different sizes (the triangle is the space created by the rectangles placed at different angles to each other). The goal was to get the kids to see the relationship between the rectangles, representing "squared" values. A few would understand that the combination (sum) of two of the smaller s
quares was equal to the area of the largest square, realizing the proof of the theorem: a^2 + b^2 = c^2. The teachers thought they were not supposed to say that any student's result was wrong for fear of damaging their self-esteem, and since this was the case there was no follow-up for those who didn't get it. What this appeared to create was classrooms with lazy teachers, because they barely played a role in the students' education. She said that in that particular classroom, when the students were later tested on their knowledge of this theorem, most didn't understand it.

I found a counterpoint to Cheney's article at http://www.mathforum.org/kb/plaintext.jspa?messageID=712380 from Tim Craine, an education professor who taught geometry. My read of his analysis is it's likely the problem with the classroom Cheney described was due to the teachers not following through. He doesn't say it, but I think what he means is it takes a teacher who's fluent in math and cares about educating kids to really make this exercise work. He agrees with something I've thought about, which is once a student has made their discovery, the teacher can come in and help the student analyze it, so they can see the implications. The phrase that came to mind is, "Once you've got something, understand what you really have."

Quoting from Craine:

"These discoveries, however, cannot be left to chance, but are more likely to take place under the guidance of a teacher.  Contrary to Gardner's assertion, cooperative learning does not imply that children receive 'no help' from the teacher, nor that there are 'winners' who discover what they are supposed to and 'losers' who don't. A skilled teacher guides the entire class in a discussion of what they have observed and in formulating the appropriate generalizations."

It's looking like what is probably also a problem is something Alan Kay has talked about just generally with math and science teachers, which is that many are not fluent in math or science, and further have an aversion to it. I had the thought today that perhaps one reason why rote methods are used is that the teachers don't have to understand it to present it and make it look like they're teaching something. And maybe some students get the material anyway, though they'd probably do just as well not having such a teacher and just reading the math text.

What's apparent to me as I've done a little more research into this to write my response here is it appears constructivism can be misapplied in unskilled hands.

Personally I agree with what I've heard about constructivism from Kay, since I always learned best through doing. I remember that I always did better in science classes where we frequently did labs. I think that's one reason why I liked computer programming and later computer science so much. I spent some time thinking and theorizing about computing, but it was mostly hands-on work.

Re: It seems like education is largely done by anecdote, rather than scientific research

In terms of scientific education studies, I don't know of any either. There may be some scientific studies on cognition, which would relate well to education. I imagine they would be more general, just focusing on how the mind understands concepts, learns them, thinks about them, etc., not specific to certain areas like math and science. There may be some that are specific to language, for example.

mmille10 at comcast.net

>Date: Wed, 21 Nov 2007 17:32:37 +0000
>From: "David Corking" <lists at dcorking.com>
>Subject: Re: [Squeakland] Panel discussion: Can the American Mind be
> Opened?
>To: squeakland at squeakland.org
> <f7a24bea0711210932l68da94f3y194ae1d0ae13df14 at mail.gmail.com>
>Content-Type: text/plain; charset=ISO-8859-1
>Mark wrote:
>> Re: attempts with constructivism
>> I hope you're right. I have heard criticisms of constructivism, based on
>> anecdotes, but I've always wondered whether what's been evaluated is
>> actually constructivism or just some group's ideological interpretation of
>> it (the group that says they're implementing the pedagogy, that is). I
>> haven't studied it in detail, but the ideas behind it, as presented by Kay,
>> make sense to me.
>I think it is worth studying in detail, but I am not sure where to
>start.  First I think we need to learn to distinguish among
>1. constructivism the psychological hypothesis - as proposed by Piaget
>as I understand
>2. constructivism the pedagogy
>3. constructionism - another pedagogy - and a word coined by Seymour
>Papert.  Note the 3rd syllable.
>(There is also constructivism the epistemology, which I can't even
>spell, that also originates with Piaget.)
>I recently read this unsympathetic 2003 article on the US history of
>constructivist pedagogy in maths
>But it is largely anecdotal (which is fine for a historian, but not
>when we are responsible for the education of the next generation.)
>However, beyond such material, I get thoroughly confused by an
>inability to distinguish proven knowledge, accepted wisdom, and pure
>pseudo-science.    It seems that a lot of educational research is done
>by anecdote rather than by controlled blind large group studies.  Any
>pointers to the good stuff?  Or tips to help a natural scientist to
>understand the research methods of the social sciences?
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