kitchen table math, the sequel: Barry on guided discovery

Wednesday, May 9, 2007

Barry on guided discovery

from Barry:

"Many of the instructions, and even basic discipline, seem to be a carried out like a full-scale Socratic dialogue with the goal being that the child discovers the all-mysterious point the teacher is trying to make."


Many teachers think that the above is an example of "guided discovery". It isn't. Guided discovery means providing direct information and then asking leading questions based on this information and providing scaffolding as necessary to get students to the next level. Information is given all along, but students are kept actively engaged through questions that 1)allow them to apply the information they have just been given, and 2) to make cognitive leaps to the next level, ala the "spark gap" analogy that Instructivist described some time back. Singapore does this in their textbooks.




I'm going to bug Barry until he writes up an explanation of scaffolding.

I've developed a sense of what scaffolding is in the abstract, but I need more!

7 comments:

Barry Garelick said...

Scaffolding is simply the process of providing guidance through information, hints. For example, when students are learning how to do simple one variable equations of the form 3x + 5 = 6, the teacher may prompt them on the first step, i.e., getting the variable on one side of the equation. "Do we have the variable all by itself? What do we need to do to isolate it?" The student is then reminded of that step, subtracts 5 from both sides, and then is left with 3x = 1. "Do we have "x" all by itself yet?" A reminder that x is multiplied by 3. "How do we 'undo' multiplication?" Student is reminded of this step, then divides both sides by 3. Student(s) may be walked through next problem with fewer prompts, then left on their own, thus removing the "scaffolding".

There are variations of this, but that's a simple example of how scaffolding works.

Barry Garelick said...

Just realized, that in the above example, the teacher would have already worked through an example on the board. (Or on the Smart Board depending on how tax dollars are wasted in the particular school district of concern). The teacher would explain, in the above example, that the object is to "get the variable" on one side, and explain each step.

That's the scaffold structure. The teacher then uses that structure as I indicated in my comment above to have the student work through an example. This "work by example" is done with less and less support until the student does it on its own. In another sense, textbooks that supply worked examples provide scaffolding through such illustrations. The "worked example" effect was discussed in the paper by Mayer (2004) (Why there should be a three strikes rule against discovery learning).

harriska2 said...

I wonder if one could think of guided discovery under the term and ideology of inquiry learning - seems Bruner was a little into this. I've yet to read an old book titled Interdisciplinary Inquiry in Teaching and learning by Martinello and Cook.

I'm also reviewing research in science by Klahr. He was actually researching direct instruction but used an initial discovery phase so kids could look at ramps to figure out confounding variables. It turns out giving direct instruction is more effective but all kids got that "discovery" portion first.

Seems everywhere I turn the actual definition of "discovery learning" is a little different.

Barry Garelick said...

There is a spectrum of "discovery learning" with direct instruction at one end and minimally guided discovery at the other. Reading Khlar and Mayer, they look at "guided discovery" as a combination of direct instruction with some discovery.

Seems everywhere I turn the actual definition of "discovery learning" is a little different.

That's the danger. I continually hear teachers say "Oh, we don't use minimal guidance; we use guided discovery". Or "We use direct instruction and discovery in a balanced approach." What this generally amounts to, however, is the Socratic approach alluded to earlier where students don't have a clue where the teacher is going with any of the questions. The so-called "guidance" is in the form of questions that are not situated in a well-defined context. The student has to discover the context. Well guess what? They don't.

harriska2 said...

Barry,

"The so-called "guidance" is in the form of questions that are not situated in a well-defined context. The student has to discover the context. Well guess what? They don't."

See, I think some people are ignorant of or misrepresent guided discovery as much as they do the same to direct instruction.

Sounds like guided discovery is mixed up with constructivist notions whereas they have several elements in common with direct instruction. ?

Barry Garelick said...

Sounds like guided discovery is mixed up with constructivist notions whereas they have several elements in common with direct instruction. ?

There's much confusion about this, because constructivism is a theory of learning which holds that people "construct" knowledge as part of learning. What escapes many people's attention is the notion that such construction occurs whether people process information from a lecture or from a hands-on activity. Mayer (2004) makes this clear and says that because children can't focus on a lecture, they have to be engaged in other ways. So questioning and activities is one way to do this. But feeding information directly while doing this is STILL considered constructivism by psychologists.

Direct instruction can indeed be a part of guided discovery. Take a look at Singapore's math books. And in general, math books that provided worked examples are in essence scaffolding the student through the steps. Subsequent problems in the exercise set start to get more complicated so there are cognitive leaps (i.e., discovery) that the student makes. But they make them in the context of instruction that they've been provided. As opposed to Connected Math's approach of showing a student a rectangle with an area of x^2 + 5x + 6, and asking the students to find the sides of the rectangle, without any prior instruction/practice with factoring.

Catherine Johnson said...

Or on the Smart Board depending on how tax dollars are wasted in the particular school district of concern.

I'm SERIOUSLY not getting off the SMART Board thing.