November 16, 2006

Teaching Logic to Second Graders

Modern educators often deride direct instruction as the teaching of mere basic skills by rote memorization. It is said that this harms children by preventing them from constructing their own knowledge. They contrast this with what they claim they teach--higher order skills taught with understanding.

This is, of course, sheer nonsense. But, don't take my word for it. Let's take a look at an actual direct instruction lesson so you can judge for yourself. In fact, I'm going to present it to you like it is presented to students over the course of the next few days. See if you can construct the knowledge for yourself.

The lesson is about making written logical deductions based on a rule. This comes from Lesson 22 of Reading Mastery III. Normally, average students would get this lesson in the early fall of second grade. Advanced students might be presented with this lesson as early as early fall of first grade.

Pretend like you're a second grader just learning how to read. Follow my instructions and answer when directed to. Let's get to it.

Lesson one

Here's a rule about using rules: You must pretend that the only thing you know is what the rule tells you.

Here's a rule: Big men are heavy. Say the rule without looking.

The rule tells about big men. What does it tell you about? Answer: _____________ (The answer is (Highlight to see answer): Big men.)

You must pretend that you don't know about anything else. You must pretend that you don't know that whales are heavy. You must pretend that you don't know that elephants are heavy. The only thing you know about is big men.

Item 1: Follow along: Big men are heavy. An elephant is not a big man. So what else do you know about an elephant?

Nothing. This rule tells about big men, not elephants. The only thing we know is what the rule tells us.

Item 2: Big men are heavy. A whale is not a big man. So what else do you know about a whale?

Nothing.

Item 3: Big men are heavy. Jack is a big man. So what else do you know about Jack?

Answer: _____________ (The answer is (Highlight to see answer): He's heavy.)

If you didn't get it correct, read the following (Otherwise, skip to item 4): Jack is a big man. So what else do you know about Jack? Here's the answer: He's heavy.

Your turn. Big men are heavy. Jack is a big man. So what else do you know about Jack? Answer: _____________)

Item 4: Big men are heavy. Bob is not a big man. So what else do you know about Bob?

Answer: _____________

You don't know about Bob because the only thing you know about is big men.

(The answer is: Nothing. If you didn't get it correct, read the following: Here's the rule: Big men are heavy. Bob is not a big man. So what else do you know about Bob? Here's the answer: Nothing.

Your turn. Big men are heavy. Bob is
not a big man. So what else do you know about Bob? Answer: _____________)

Let's go over those items again.

1. Big men are heavy. An elephant is not a big man. So what else do you know about an elephant? Answer: _______________. (Answer: Nothing. If you got it wrong repeat the question until you can answer it reliably.)

2. Big men are heavy. A whale is not a big man. So what else do you know about a whale? Answer: _______________. (Answer: Nothing.)

3. Big men are heavy. Jack is a big man. So what else do you know about Jack? Answer:
_____________. (Answer: Jack is heavy.)

4. Big men are heavy. Bob is not a big man. So what else do you know about Bob? Answer: ____________. (Answer: Nothing.)


Here's a new rule. Dogs have hair. Say the rule without looking: Answer: ____________.

The rule tells about dogs. What does it tell about? Answer: ______________. (Answer: Dogs.)

You must pretend that you don't know about anything else.

Item 5. Follow along. Dogs have hair. A girl is not a dog. So what else do you know about a girl? Answer: ______________. (Answer: Nothing.)

Why don't you know anything else about a girl? Because the rule tells you only about dogs.

Item 6. Follow along. Dogs have hair. Jokey is a dog. So what else do you know about Jokey? Answer: ______________. (Answer: He has hair.)

Item 7. Follow along. Dogs have hair. A cat is not a dog. So what else do you know about a cat? Answer: ______________. (Answer: Nothing.)

Why don't you know anything else about a cat? Because the rule tells you only about dogs.

Here endeth your first logic lesson. We'll do lesson two tomorrow.
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This is the lower performers version of the lesson, so there is more instruction that you probably need to learn the rule. Plus you're an adult and know a lot. But I wanted to give you an idea of what a high quality Direct Instruction lesson looks like for teaching logical deductions.

When I did this lesson with my first grade son last night, we got to the third question and he figured he learned what he needed to learn and just finished the remaining questions independently. Elapsed teaching time: three minutes. This lesson might take 5-10 minutes with lower performers.

Bear in mind that almost all kids who've completed the previous lessons will be able to get through this lesson in a timely manner. This includes inner city kids, poor rural kids, kids whose parents don't love them, kids who didn't eat breakfast this morning, kids with toothaches, kids with low motivation, etc. Whatever wacky external factor you can dream of, with the exception of a legitimate cognitive disability, any kid will learn the skill taught in this lesson. A skill that most k-12 do not know, by the way.

I suppose this skill can be taught using constructivist techniques. (If anyone has any ideas leave them in the comments.) But, it is doubtful that this skill can be taught using such techniques in within the same 3-10 minutes interval that the skill can be taught using direct instruction techniques. That extra time is now available for practicing previously taught skills, which we'll do tomorrow.

Does someone still want to make the argument that this is rote learning? If so, then how do you explain the fact that students are able to generalize the skill by item 5, assuming they answer it correctly? Granted items 5-7 are very similar to items 1-4, and it is likely that students probably can't generalize the skill further by applying the skill to deductions that aren't as similar. That's OK, the students knowledge is still inflexible at this time, since the skill has just been learned. In time and with practice with increasingly difficult problems that knowledge will grow increasingly flexible and students will be able to generalize better.

Anyone have any ideas how the lesson could be improved? Teachers say they don't like following scripts. Fair enough. How would you improve the lesson?

Does anyone think that this scripted lesson relieves the teacher from thinking? In a typical lesson, the teacher would have to determine when students are firm with their answers. They have to know when to repeat questions, where to emphasize words, how to pace the lesson so kids will be engaged, when to apply the correction procedure when answers are wrong, and when to move on when it is clear that all the kids are firm on the material presented.

Is this a basic skill or higher order skill? If this is only a basic skill, what's a higher order skill?

I'll follow-up on this post later. You have a lot on your plate to digest.

Go to Lesson Two
.

5 comments:

SteveH said...

I like to have my son (5th grade) write out step-by-step procedures for doing (seemingly) simple tasks. Then I try to follow the steps exactly while he watches. It's pretty funny sometimes. Before we started doing this, I gave him an example of the steps (if-then-else) for getting something out of a candy machine.

His school has since done something like this too. However, they just told them to do it - write down instructions for making a peanut butter and jelly sandwich. There are a lot of assumptions to make and the kids didn't know how to do that.

The modern idea of education is that you don't give kids any clue before you have them do something. This can be quite frustrating and inefficient, especially if the kids get into groups to discuss their solutions. At the end, perhaps, the teacher will give his/her own version.

It's what I have always called bottom-up versus top-down teaching. Bottom-up starts with skills; top-down requires kids to figure out the skills. Explicit teaching versus implicit teaching.

KDeRosa said...

In the DI writing course (requires a 2nd grade reading level), they have the student write instructions to recreate a figure. The figure will show a large circle with a capital letter R on top of the circle and a horizontal line dran delow the circle. The students are instructed to provide instructions for recreating the figure, starting with the largest object (in this case the circle).

Bec said...

When I was in 5th grade, my teacher had us do the activity steveh described above - writing down the instructions for making a peanut butter and jelly sandwich.

It's one of the few class activities from back then that I remember (I'm in my second year of college now).

It was an incredibly frustrating assignment because we were given no explanation for it, nor were we told how literal our instructions were supposed to be.

Much more successful in teaching the same lesson were the simple computer programing lessons we were given starting in first grade using Logowriter.

The logic lesson here is interesting from my perspective as a college student interested in education, but I suspect that my second or first grade self would have found it senseless, repetitive, and frustrating if it were not accompanied by some kind of comprehensible explanation.

A better way of teaching this kind of thing, I think, would be to lay the foundations with Logowriter-type programing and then introduce logic lessons like the one in the post a little later along, when students are at point where they can understand what they're learning and why they're learning it.

SteveH said...

"It was an incredibly frustrating assignment because we were given no explanation for it, nor were we told how literal our instructions were supposed to be."

That's what my son thought, although he had some idea because we went through the candy machine example before. Even so, there are lots of assumptions that have to be made. You can't jump from assembly language level instructions to high-level 4th generation language function calls.

I think the real issue is between direct teaching versus constructive or implicit learning. The modern educational assumption is that it's always better to have kids try to learn things before they are taught anything. That's why you never see any individual desks lined up in rows facing a black (or white) board.

The amount and efficiency of learning is inversely proportional to the randomness of the desks.

MikeZ said...

I thought it was supposed to go:

All big men are heavy.
Jack is a big man.

Therefore Jack is Socrates.