I don't see anything wrong with thatthat kind of discovery either. Although, it's probably more along the lines of extending current knowledge to a new situation.

I would bet that this kind of teaching and merely teaching directly would compare favorably in a controlled test.

-- KDeRosa - 04 Aug 2006

"I'm not so sure such a question is even 'discovery'. the implication is that the students have been taught the rule already and are being asked to now evalutae the fact situtaion and determine which rule applies."

Sorry; I didn't make myself clear.

I was thinking of teaching parity rules, for instance, by showing the students a set of two-term sums and asking about the rules for getting an odd or even answer. Specifically, that is, asking students to infer a basic parity rule from samples. This would qualify under my definition as "discovery learning".

My take is that it's worth giving the students a chance to say, "If you add two even numbers the answer is even", or the like. If the students don't respond, you can teach directly. If the students respond with a partially correct answer (like that above), you can continue with something like, "That's correct, but not complete. What else can we say?" And if you get a correct and complete answer from a student, you can affirm it, which encourages at least a portion of the class to pay attention.

Especially in the last case, you're still explicitly teaching the answer to the rest of the class. (Even though you didn't state the correct answer first, you are still affirming the correctness.)

In all cases, once you have a rule, you should require practice to cement the concept, of course.

Note that I'm not suggesting that this take more than a few minutes, and I'm not suggesting that you look for "lots of different right answers". If I recall our discussion of Japanese teaching methods some months ago, this is very much like what they do, and to good effect.

And it's nothing like, "Form up in groups and spend fifteen minutes trying to figure out a rule."

-- DougSundseth - 04 Aug 2006

She definitely says that the lower the IQ the more explicit and incremental teaching should be.

It's probably more accurate to say that the higher the IQ the more implicit and non-incremental teaching is tolerated.

If the teaching were explicit and incremental, the higher iq kids would learn the material faster. I don't know of any serious research that any kid learned more or better using implicit and/or non-incremental teaching methods.

-- KDeRosa - 04 Aug 2006

Doug, I don't think we agree much either. Most likely it's a definitional thing.

"Can anybody tell me what rule works here?" seems to me a reasonable sort of thing to ask in even a grade-school class.

I'm not so sure such a question is even "discovery." the implication is that the students have been taught the rule already and are being asked to now evalutae the fact situtaion and determine which rule applies.

In discovery, the kids aren't given the rule first and are presented with an experiment or demonstartion from which they will hopefully discover the rule on their own. Guided discovery, just means the teacher helps the students discover, which seems to negate whatever effects were hoped to be gained by the discovery process, if anyone actually takes that rhetoric seriously.

If you give students a few seconds to come up with the answer and one student does, the class's efficiciency suffers little

If the answer is something the teacher wants the students to have learned, and only one student successfully answered the question, I think it's a good indication that the other students haven't learned the material they were supposed to yet. It is these first-tiem correct responses which are the best predictors of student learning. Once bright student answers the question, we've lost the ability to determine what the other students have learned until we test again after some delay.

Now the teacher has clear evidence that all but one kid learned the material. If the teacher were serious about student learning, the material would be retaught and retested until it is mastered by all the students.

In cumulative subjects like math, it's easy to see how many students quickly get lost if the teacher moves onto the next topic before they've mastered the material just presented.

-- KDeRosa - 04 Aug 2006

page 26 has the chart I was thinking of

Looking at it again, I wouldn't say she's necessarily arguing that discovery or inductive learning become more important as IQ goes up....

She definitely says that the lower the IQ the more explicit and incremental teaching should be.

-- CatherineJohnson - 04 Aug 2006

This is one of those "missing knowledge" things that bugs me.

If we'd spent the last hundred years trying to find out everything we possibly can about how people learn best, questions like these wouldn't be a mystery.

For what it's worth, Linda Gottfredson seems to think that the higher the IQ, the more discovery learning you want.

I'm basing that on an extremely cursory look at her paper, which I'll go rustle up now.

Back in a minute.

-- CatherineJohnson - 04 Aug 2006

well.....I'm not sure whether "guided discovery" means "inductive learning" - whether they're synonymous....

We've talked about Saxon's Investigations before....I love them.

No idea whether school kids love them, or whether they're the best possible use of time (seeing as how for me the Investigations are minor Eureka moments along Steve's lines - i.e. a eureka moment about material I've learned before).

I'm almost done with Algebra 1, and I'd say that Saxon purposely weaves in an inductive-learning, "discovery" strand throughout the entire text.

I like that very much, too.

He creates problem sets, structured across several different lessons, that point you to a discovery of a point he hasn't directly taught.

I think it's right to say that within a few lessons he'll then teach the point directly.

His books are incredibly complicated pedagogically speaking. To know what he's doing, you really need to work through the book once just to learn the material & a second time to analyze the structure.

Or else I could be taking notes.

-- CatherineJohnson - 04 Aug 2006

Hey Ken!

You're back!

-- CatherineJohnson - 04 Aug 2006

I doubt we disagree much on this. I thought that "...the graduate level" was a bit much though.

"Can anybody tell me what rule works here?" seems to me a reasonable sort of thing to ask in even a grade-school class. The problem arises when you spend the whole class stumbling about in the dark.

If you give students a few seconds to come up with the answer and one student does, the class's efficiciency suffers little (and if this keeps 10% of the class more involved, might increase overall teaching efficiency). And for the student that successfully solves the puzzle, the experience of discovery and validation of success can be a big boost.

(I don't think any of this is especially controversial around here, but I don't think this comes across in short comments sometimes.)

-- DougSundseth - 04 Aug 2006

I was actually talking about plain old direct instruct, not DI in particular, but I agree the eureka moment is the ultimate goal.

I also think the idea is to engage students, and by doing so make them think. The more they are forced to think, the more they are likely to learn. Eventually, it is hoped they will understand what they've learned. I'd call the eureka moment.

My personal experience is that the eureka moments only come after a lot of hard work and practice. I am reasonably good at setting up and solving math word problems today only because I've probably set up and solved thousands of them during high school and undergrad. The only thing that I've found that reliably aids in this process is having someone more knowledgable than me provide an explanation which clarified whatever confusion was holding me back.

Discovery learning may be fine for an expert. But the phony discovery used on novice learners is just too much and too early to really increase learning, IMO.

-- KDeRosa - 03 Aug 2006

I have had lots of "Eureka" moments while being directy taught.

The problem with (contrived) discovery tasks being used to foster the eureka moment is that they are usually done in child-centered groups. Perhaps one student discovers something (maybe not the correct thing) and then proceeds to DIRECTLY teach it to the other kids. There is lots of excitement and animation, but is this better than using guided direct teaching administered by a someone who knows the material very well? I don't think so.

Then there is the issue of discovery without basic knowledge and skills. I call this top-down discovery, a worthless exercise in modern educational vanity.

-- SteveH - 03 Aug 2006

The illusion of discovery, properly fostered and managed, increases the engagement of students. It's a worthy goal.

I say "illusion", because you aren't really trying to discover anything new, but are rather trying to get the student to make new connections. As you've described DI, Ken, some of this is done even in that curriculum.

None of this is to say that Discovery Learning, as the term is used here, is necessarily appropriate. I just think you are overstating the case against "Eureka!" on the part of the students.

-- DougSundseth - 03 Aug 2006

What is guided discover but the insertion of direct instruction by the teacher. In studies, scores go up as the amunt of direct teacher instruction incresases (unless it is porrly done, which is to say, a biased study). One wonders with these results why anyone bothers with any kind of discovery learning at all before the student has the proper educational foundation, i.e., the graduate level.

-- KDeRosa - 03 Aug 2006

3-strikes rule against pure discovery

I'm hoping Ed can pull the full text of this article on guided discovery versus pure discovery:

Should There Be a Three-Strikes Rule Against Pure Discovery Learning?

The author's thesis is that there is sufficient research evidence to make any reasonable person skeptical about the benefits of discovery learning--practiced under the guise of cognitive constructivism or social constructivism--as a preferred instructional method. The author reviews research on discovery of problem-solving rules culminating in the 1960s, discovery of conservation strategies culminating in the 1970s, and discovery of LOGO programming strategies culminating in the 1980s. In each case, guided discovery was more effective than pure discovery in helping students learn and transfer. Overall, the constructivist view of learning may be best supported by methods of instruction that involve cognitive activity rather than behavioral activity, instructional guidance rather than pure discovery, and curricular focus rather than unstructured exploration. (PsycINFO Database Record (c) 2006 APA, all rights reserved)

Mayer, Richard E.

Mayer, Richard E.: University of California, Santa Barbara, Department of Psychology, Santa Barbara, CA, US

American Psychologist. 59(1), Jan 2004, 14-19.