29 Sep 2005 - 01:08

andy asks what constructivism is

AndyJoy asked on this thread: Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithm for a problem or make children memorize facts?

The short answer is yes, but for the record, here is a fuller explanation. I think the best quick introduction to constructivism and its recent history in U.S. educational practice is Barry Garelick's An A-maze-ing Approach To Math, which appeared in Education Next this year. I'll excerpt a little piece of it to answer Andy's question, entirely without Barry's permission (but hopefully with his blessing).

Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering (and taking ownership of) the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.

Texts that are based on NCTM's standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches "mathematical thinking" rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without first teaching him to swim.

The Standards were revised in 2000, due in large part to the complaints and criticisms expressed about them. Mathematicians felt that the revised standards, called The Principles and Standards for School Mathematics (PSSM 2000), were an improvement over the 1989 version, but they had reservations. The revised standards still emphasize learning strategies over mathematical facts, for example, and discovery over drill and kill.

So how does this fine-sounding idea play out in the classroom? Kids tend to spend too much deriving everything from first principles. What gets sacrificed is time spent learning advanced skills, as Barry shows:

Concept still trumps memorization. Textbooks often make sure students understand what multiplication means rather than offering exercises for learning multiplication facts. Some texts ask students to write down the addition that a problem like 4 x 3 represents. Most students do not have a difficult time understanding what multiplication means. But the necessity of memorizing the facts is still there. Rather than drill the facts, the texts have the students drill the concepts, and the student misses out on the basics of what she must ultimately know in order to do the problems. I've seen 4th and 5th graders, when stumped by a multiplication fact such as 8 x 7, actually sum up 8, 7 times. Constructivists would likely point to a student's going back to first principles as an indication that the student truly understood the concept. Mathematicians tend to see that as a waste of time.

Another case in point was illustrated in an article that appeared last fall in the New York Times. It described a 4th-grade class in Ossining, New York, that used a constructivist approach to teaching math and spent one entire class period circling the even numbers on a sheet containing the numbers 1 to 100. When a boy who had transferred from a Catholic school told the teacher that he knew his multiplication tables, she quizzed him by asking him what 23 x 16 equaled. Using the old-fashioned method (one that is held in disdain because it uses rote memorization and is not discovered by the student) the boy delivered the correct answer. He knew how to multiply while the rest of the class was still discovering what multiples of 2 were.

Now, consider the constructivists' argument for allowing this lack of 'domain knowledge' to persist -- kids develop deeper understanding, 21st century skills, bla bla bla -- after having read KDeRosa's "Terminator essay" on math education.

That essay just puts this nonsense to death, don't you think?

p.s. from Catherine

I found the smart constructivism post.

Here are the 2 best passages.

Smart constructivism says:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**

Radical constructivism says:

It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.

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Thanks! That helps. My teacher says that "the whole constructivism thing is highly politicized" but I don't think she knows about the radical view, because I don't think she would support that!

-- AndyJoy - 29 Sep 2005

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On the topic of what people think constructivism is, there is a paper that shows how the fuzzies conclude that the Japanese teach their students using radical constructivism. In fact, Japanese teachers rely on providing students direct information. True, they also make their students stretch and discover, but provide their students information rather than relying on them to discover what "took thousands of years to evolve". Please check out “Telling Lessons from the TIMSS Videotape: remarkable teaching practices as recorded from eighth-grade mathematics classes in Japan, Germany and the US” ; Alan Siegel; Department of Computer Science; Courant Institute of Mathematical Sciences New York University http://www.cs.nyu.edu/faculty/siegel/ST11.pdf

-- BarryGarelick - 29 Sep 2005

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Here is Thomas Sowell's take on discovery learning. I especially like:

It took more than a century of dedicated work by economists of genius to arrive at the analysis of supply and demand that is routinely taught in the first week of Economics 1. How long are novices in economics supposed to flounder around trying to "discover" these same principles?

-- KDeRosa - 29 Sep 2005

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Andy

She may very well have no idea there are radical constructivists saying it's possible for children to discover all of mathematics.

Talk about reinventing the wheel.

-- CatherineJohnson - 29 Sep 2005