February 10, 2009

The Cheese Stands Alone

Stephen Downes has finally seen the light as to the benefits of worked problems examples for inducing learning:

Today's newsletter is delayed a bit because I could not tear myself away from this wonderfully detailed set of instructions on how to make cheese. Makes me just want to go out and get myself some rennet. You'd probably have to practice a bit to really learn how to make cheese, but these instructions really look like all you'd need to get going. It's also important to have previously seen and tasted cheese, so you know what success looks like. (emphasis added)

At least when it comes to novice cheesemakers learning how to make cheese.

But apparently not for learning academic content which seems to require a more constructivist approach, according to Stephen.

Wouldn't the budding cheesemaker learn more from being handed all the necessary cheesemaking ingredients and provided the wonderfully engaging opportunity of floundering around making cheese on their own with some minimal guidance provided by the instructor.

I guess not. It doesn't work for chick-sexing apprentices? Why should it work for novice cheesemakers?

And for that matter why should it work for novice students of algebra?

Here's the analog in the algebra world. Behold Algebra: Structure and Method, Book 1, Dolciani (1981 Ed.). (Click to enlarge)

The classic worked product example for teaching how to solve simple equations using the multiplication property of equality (a page I selected randomly).

The "lesson" is followed by a few more example and then the student is provided the opportunity to practice what has been taught by working various oral, written, and open-ended problems, relevant to the lesson so they can " practice a bit to really learn" it.

This is the traditional way algebra is taught. Apparently, it's only "tedious lecture" and "rote learning." Of course if it were rote learning the student would only be able to solve 4x = 52 and would have to be taught 5x = 50 and 3x = 36. But as any good connectivist will tell you, the student should be able to generalize a solution for any similar problem fitting the pattern of the worked problem example after sufficient practice.

It seems to me that the primary difference between this method of learning and the constructivist method of learning is that the "wonderfully detailed set of instruction instructions" isn't provided to the student beforehand. The student is supposed to figure them out (i.e., construct) this knowledge for himself. At least that's the theory.

Of course, in the real world, even the constructivists would rather see the instructions beforehand.


Anonymous said...

Alfie is intellectually dishonest.


He's bright enough to know better than to post the following in the comments. Yet he seems to really believe it:

"It is frankly incredible that DI’s defenders are still circulating the canard that Follow Through demonstrated the superiority of this approach, when in fact it did no such thing. The study’s primary researchers reported that the “clearest finding” of Follow Through was not the superiority of any one style of teaching but the fact that the variation in results of a given model of instruction from one site to the next was greater than the variation among the models. And a group of experts commissioned to review the study discovered that this was just the tip of the iceberg. Their overall conclusion, published in the Harvard Educational Review, was that, “because of misclassification of the models, inadequate measurement of results, and flawed statistical analysis,” the study simply “does not demonstrate that models emphasizing basic skills are superior to other models.” Indeed, numerous studies since then have found that DI is actually ineffective, if not counterproductive. (For more, see www.alfiekohn.org/teaching/ece.htm).

Anyone who has read the research literature on DI yet continues to claim that it has been proven superior to more developmentally appropriate approaches to early-childhood education really has something to apologize for."

KDeRosa said...

Anon, you are a post or two ahead of me.

Stephen Downes said...

> Wouldn't the budding cheesemaker learn more from being handed all the necessary cheesemaking ingredients and provided the wonderfully engaging opportunity of floundering around making cheese on their own with some minimal guidance provided by the instructor.

Nothing I have ever proposed resembles the description above. You are confusing my theory of learning - which I have detailed in numerous articles on my own site - with some fabrication that exists only in your own fantasies.

We could discuss my criticisms of 'worked examples' (especially as they pose for direct instruction) - but that would require you actually reading what I've written on the subject.

KDeRosa said...

Stephen, your views on learning are too inconsistent and non-specific and your site's search functionality too broken for most of us to have any idea what your views actually are and how (specifically) you think those goals are best accomplished in a k-12 classroom setting.

enlighten us

NMahoney said...

One way to prompt students to construct their own novel solution to this problem would be as follows.

An electrician has a spool with 52 yards of wire. He wires 4 identical homes. How much wire was used in each home?

Some students would divide 52 by 4 to get 13 yards of wire. Others might estimate and subtract equal amounts in succession. Others might have no idea.

From here you can lead into algebra. Define the variable h, as the amount of wire needed in each home. Write the equation, 4h=52. Now you discuss a more efficient method of solving for h which replicates their own procedures.

After modeling the method several times they can repeat the method.

That is a constructivist approach. It engages them and shows them that they know more than they think they know.

Your description of constructivism is a caricature. Get in the classroom sometime and try it.

KDeRosa said...

So what's the instructional benefit of the initial activity for the students who "might have no idea"?

RMD said...

Perhaps Stephen would like a "guest" blog entry to elaborate on his views of how K-6 education should work, with specifics?