September 28, 2007

The root cause

One persistent problem in education is the ambiguous teacher presentation. A presentation is ambiguous when it can be interpreted in more than one way by a student. Since we know that children differ in their ability to learn, it should not be surprising that some of them will interpret an ambiguous presentation incorrectly. And, more often than not, it will be the less smart kids that will tend to make the most misinterpretations.

Here's an example of the typical ambiguous teacher presentation from Engelmann's book Your Child Can Succeed from 1969.

"Look at what I have," the teacher says, holding up a card that illustrates a red ball. The teacher then points to various cards on the floor in front of six four-year-olds. "who can find a card that is the same color as this card?"

The little boy next to Andy holds up a card with a yellow ball on it. A little girl picks up three cards and puts one of them into her mouth.

Andy looks at the teacher for a moment before returning his attention to his shoelaces.

"Listen, boys and girls. I want you to find a card that is the same color as the card that I have here."

Two of the children hold up the cards that they have selected. A girl shows two cards. None is identical to the teacher's.

Apparently unperturbed, the teacher picks up a card with a picture of a red apple. "This card is the same color as the other card that I have. Andy, look at the cards. Andy . . ."

Andy looks tentatively at the teacher. He doesn't look at the cards. Instead, he looks intently at her face, trying to figure out her game.

"Andy," she continues, "look at the two cards. They are the same color, aren't they?"

Without removing his stare from her face, Andy nods yes.

The teacher says, "And what color are the ball and the apple?"

"Re . . ." a little girl shouts.

"Re . . ."two other children mimic.

The teacher says, "They are red, aren't they, Andy?"

Andy nods yes.

"Can you find something else that is red?" the teacher asks.

Andy looks at his shoes. He then points cautiously in the direction of three or four cards.

"Is one of these red?" the teacher asks.

Andy nods and says, "Yeh," almost inaudibly.

The teacher picks up a card that displays another red apple.

"This is red, isn't it?" she says. "Were you pointing to this card?"

Andy glances quickly at the card and then back to the teacher's face. He nods yes.

"Leon," the teacher says, "what color is this?"

"Re . . . " Leon says loudly with his hands over his ears.

The teacher then holds up a card showing a green evergreen tree." And what color is this?"

"Re . . . " Leon says.

"Re . . . " one of the little girls says.

"Re . . . " Andy says.

Has the teacher actually taught anything through this activity? Was it possible for the teacher's presentation to teach all of the children? It seems that the teacher assumed that the children understood the concept of "color" when they did not. This might be an assumption in a middle-class school. But, it probably is not a safe assumption in a "poverty" school. But let's forget about the children's abilities for a moment and focus on the concept of color that the teacher was trying to teach and see if her presentation was capable of teaching it to a very intelligent being who didn't happen to know what red meant. Engelmann continues:

Since red is the same for all people, it is reasonable to begin with a simple analysis of the concept to see what it is that all people must learn about red. Red is a visual property. It is not dependent on the size of the object or on the object's position, shape, or texture. The first requirement of a demonstration designed to teach red, therefore, would be that the demonstration make it clear that red has only to do with that visual property of redness. Andy's teacher did not satisfy this requirement. All of the red objects were round, implying that red may have something to do with shape. Therefore, we could expect that a being with superior intelligence might come away from the teaching demonstration confused about the meaning of red. Specifically, this being might show us through his behavior that he thinks that red is another word for round object or that red is something that only applies to two-dimensional objects on a card.

Since the presentation would not be consistently capable of teaching a naive being with superior intelligence, maybe Andy, Leon, and some of the other children are not completely at fault for not learning from the demonstration. Maybe they would have responded well to a demonstration that carefully showed what red means. We can't make any clean assertions about the problems the children might have had, but it seems presumptuous to declare that the children ... should have been able to extract the appropriate interpretation from the teacher's presentation even if it was not logically possible to do so.

It is difficult to explain the difference between a demonstration that will teach and one that won't. So, Engelmann makes up an example that adults can better relate to since adults understand the concept of color.

Let's say that a teacher presented each of these objects:

The teacher says that each is a "glerm."

Next, the teacher presents this object and asks you if it is a glerm:

The response of virtually any child or adult would be "Yes."

Now the teacher presents this object and asks if it is glerm:

We cannot predict what your response will be. If we present the task to thirty different people, we can predict that over half of them will say, "Yes, it's a glerm." The others will say, "No, it is not a glerm."

In any case, some who respond will fail the task. The response of those that fail, however, is a reasonable response. Both responses are consistent with the presentation of the objects. One person might interpret the presentation this way: "The teacher showed a group of objects. All were rectangles and all were called glerms. Then the teacher presented another rectangle and asked if it was a glerm. I said, 'Yes.'"

Another person might interpret the presentation this way: "All of the initial objects were vertical. It seemed more than accidental that they were all vertical. The teacher then presented a rectangle that was not vertical and asked if it was a glerm. I said, 'No.'"

Now imagine that glerm did in fact mean vertical, but you thought, quite reasonably, that glerm meant rectangle. What happens when the teacher starts teaching more advanced material that relies on the concept of glerm and uses the word "glerm" in later presentations to describe the glerminess of objects? Do you think your ability to learn these advanced concepts might become more difficult because your understanding of glerm is wrong?

What is education but a series ambiguous teacher presentations designed to teach increasingly difficult concepts. Sooner or later someone is going to label an understanding of these advanced concepts "higher order thinking" and your inability to engage in this "higher order thinking" is eventually going to get you labelled a dummy or worse. Is it true that you're incapable of engaging in higher order thinking or is it simply that you lack the understanding of a bunch of prerequisite lower-order concepts, like "glerm," that prevents you from engaging in higher order thinking? We don't know, but that won't stop us from theorizing about your deficiencies.

Some people will notice that you and people like you tend to have lower IQs. People with low IQs tend to have a difficult time engaging in the kind of abstract problem solving that is needed to tease out and synthesize the correct concepts from the thousands of ambiguously presented concepts, both in and out of the classroom, one needs to understand in order to become "educated." Your low IQ will become a severe burden in becoming educated and will ultimately be a brutal predictor of your academic success under such less than ideal learning conditions.

Other people will notice that you and people like you tended not to have the kind of parents that made sure that you entered formal education knowing what the typical middle-class kid is expected to know. This is because teachers base their presentations on the typical middle-class child. That's why the hypothetical teacher's presentation of red in the beginning of the post would tend to convey the concept of redness to a typical middle-class kid who came into school with an understanding of the concept of color and probably already understood the concept of red. It's also why the presentation would almost certainly fail to teach the concept of red to a child who does not understand the concept of color in the first place. This is one reason why balanced literacy/ whole language finds some success with kids who come into school with a good understanding of the alphabetic principle, with good phoneme aware, and some rudimentary phonics skills. Same goes for fuzzy math.

Others will notice that having good parents correlates with academic success. Good parents make sure the child goes to school on a regular basis, well fed and ready to learn. Good parents also tend to monitor their child's academic progress and will ensure that the child understands imperfectly presented concepts and will help the child learn these concepts outside of school (reteaching or hiring a tutor if necessary). In short, good parents will maximize a student's likelihood of academic success and will make sure the student successfully navigates the shoals of choppy academic waters.

Others will notice that having a good teacher, say a hero teacher, also correlates highly with academic success. Maybe the hero teacher is able to present a better academic presentation that is less likely to induce wrong interpretations. Perhaps the hero teacher is better at monitoring student progress and ensuring that students are understanding the right concepts. Maybe the hero teacher is a good motivator of students and is able to keep the student motivated while he struggles to learn the concepts he is expected to learn. Maybe the hero teacher is able to act as a substitute for bad, uncaring, or incapable parents. Hero teachers tend to have some or all of these skills which correlate highly with academic success.

Lastly, others will focus on your motivation. More specifically, they will notice your lack of motivation to learn. It is the rare child that enters kindergarten unmotivated to learn and it is the rare child that leaves fifth grade motivated to learn unless that child has experienced academic success in the ensuing six years. Clearly, something inside the school environment went horribly wrong from a motivation standpoint during this time, yet for some reason motivational problems rarely get blamed on schools. Perhaps it's because elementary schools are quite adept at labelling students to excuse their inability to learn from the ambiguous teacher presentations. You didn't learn because you are learning disabled, brain damaged, not ready to learn, have a different learning style, and the like. Eventually, however, middle school and high school teachers will notice this lack of motivation to learn. They didn't see the six years of academic abuse that was experienced in elementary school. But, they do see that the students are unmotivated in their class. These students lack the gumption and drive needed to not only remedy all their past academic deficiencies but to also engage in the same punishing presentations that have failed them in the past. Should the student have the Sisyphean motivation to do the work now, the student's likely reward will be to graduate at the bottom of the class with real skills far below grade level. That's quite the plum. Some students may be dull, but you're not stupid.

Here are a few recent posts from some teacher blogs venting because their classrooms are full of unmotivated and/or disruptive students. (Make sure you read the comments.) I do sympathize with these teachers. They find themselves in an impossible situation, the direct result of bad school policies enacted to deal with students their schools have been unable to successfully teach. I'm not quite sure any tenth grade teacher is capable of teaching tenth grade material to a classroom full of students with skills ranging from 3rd to 12th grade, to give but one example.

But do notice the reasons these teachers are giving as to why some students aren't learning in their classrooms. It's usually one of the following: it's the students fault, the student's parents' fault, society's fault, or some other excuse external to the school environment. Sometimes, it'll be a school specific factor that is other than an instructional factor. More funding and smaller classrooms are the usual recommended cures despite the fact that both of these panaceas have a long history of not living up to the research base they supposedly have. At least not in the real world. Occasionally, a teacher will question his teaching ability and the ability of the string of teachers that have profoundly affected the students before they got to his classroom. But that questioning is usually fleeting and generally doesn't result in any teacher changing what they are doing instructionally. At least not in a way that improves instruction except in the most superficial of ways. Things have not really changed on an instructional level since Engelmann penned his passage on glerms nearly 40 years ago.

While the "glerm" example may seem far removed from the classroom situation, the "glerm" format is perfectly analogous to the one that the naive child encounters in the classroom. The teacher says a strange or unfamiliar word. She then gives an example that illustrates the word. She may say the word red and present an object that is an example for red, perhaps a picture of a red apple. "See? It's red," she says. And from this kind of demonstration the child is supposed to figure out what red means, just as you had to figure out what glerm means. The child must try to figure out whether the word red means an apple, something shiny, something the teacher is holding, the color of the object, or the position, or whether simply a word that the teacher uses arbitrarily.

Since any of these interpretations is consistent with the teacher's presentation, we shouldn't conclude that the child is "slow" for selecting a wrong interpretation. The labeling should be deferred until the teacher has provided a presentation that is far less ambiguous.

It does not follow from:

bad instruction + one or more external factors = academic failure


academic failure is caused by the one or more external factors.

especially since

good instruction + one or more external factors = academic success (at least in some cases)

As Engelmann suggests, let's save the excuse making until we clean up our instructional act.


Unknown said...

Excellent post. Just excellent.

KDeRosa said...

I was thinking of you and your volume of a cone posts as I wrote it. I knew you'd like it.

Anonymous said...

You could have just shortened it, though, to "most teachers suck".

I like your emphasis on the capacity for abstract thinking. Learning to avoid abstraction is a critical component of educating the lower half of the abilities spectrum. I am constantly finding ways of making my instruction more concrete.

KDeRosa said...

I could have, but that wouldn't be fair. It's not like they were taught how to teach properly in ed school or ever had a mentor that could model good teaching for them. And, it's not like teachers are taught curricula design.

What we have here is professional failure from top to bottom because the system lacks any incentive to improve on the knowledge base that ossified a century ago.

Unknown said...

I was thinking of you and your volume of a cone posts as I wrote it. . . .

One persistent problem in education is the ambiguous teacher presentation.

Oh, great! Make me cry . . . on a Friday!

I'm not sure how to begin to respond to Cal's comment. Must save for later.

KDeRosa said...

LOL, I meant that this clarity of instruction business is right up your alley.

Remember, there's no crying in education.

PaulaV said...

This is why I make it a point to read your blog every day. You are right on target!

You are the BEST!

CrypticLife said...

DI is a curriculum, but of course it's also a method of teaching. As opposed to methodless teaching, which is essentially what the teacher in the example uses.

There are good teachers, and I'm willing to bet most of them do specifically account for a lot of the potential ambiguities, just like I imagine a lot of them use positive reinforcement. However, I'm also willing to bet they don't do either in a systematic and consistent fashion.

Although I haven't observed very much, I suspect it's also one of the hardest parts of actually implementing DI. Teachers need to be trained to actually teach, in conjunction with being taught educational theory (which I guess is what they learn in ed school, though obviously not much in the way of behavioral educational theories).

Incidentally, I would have rejected the double-width "glerm". Obviously the point of presenting four glerms that are exactly the same is to show there's no deviation. I also would have completely flunked the "red" test and gotten really flustered and depressed in the process: I'm colorblind (and yes, I did have a lot of experiences like this in various classes growing up).

KDeRosa said...

All the rectangles were supposed to be the same size. I hate blogger.

silvermine said...

I don't think the problem is "that most teachers suck". I think the problem is that teaching is not the same thing as writing a lesson. They take different skills. If you have a pre-scripted lesson, many teachers could quite effectively use it and teach a wide variety of children successfully. But today, all teachers are also encouraged to try to make up lessons without a script (sometimes even on the spot!) and that isn't necessary the same set of skills.

On the other hand, I haven't been trained in teaching at all, and I'm homeschooling! ;)

Anonymous said...

"It's not like they were taught how to teach properly in ed school or ever had a mentor that could model good teaching for them."

That society expects any educational program to teach wannabe teachers how to teach is just another sign of how screwed up things are.

Career teachers are, as a group, the low folks on the college grad totem pole. They aren't terribly bright. At this time, the average teacher IQ is on par with that of a secretary or a plumber--nothing horrible, but certainly not an intelligence that would otherwise warrant a college education.

I agree that we have not moved beyond an educational system that only had to teach the already bright. But regardless of the method chosen, I'm not optimistic about improved results unless teachers get smarter--and that won't happen until the job is deprofessionalized.

But perhaps I'm thinking more of an interim step. I suppose that if teachers were all reading from a precise script and eliminating their own judgment and assessments, then teachers could drop even further down the IQ scale.

Anonymous said...

I agree. Excellent post.

Anonymous said...

It is the rare child that enters kindergarten unmotivated to learn and it is the rare child that leaves fifth grade motivated to learn unless that child has experienced academic success in the ensuing six years.

No doubt this is true. However, it is most emphatically not true that academic success will automatically mean the child is "motivated to learn" as he/she enters middle school. Well, okay, the child may well be curious and eager to know new things, just not the things we're teaching.

This disconnect between what we want to teach and what the child wants to learn becomes greater as middle school ends and high school begins. Some, who have done well or are "academically curious" or who have absorbed the message "do well in school or you'll be poor and unhappy" will put in the effort and get decent marks. Others will put more of their energy elsewhere.

Just what is responsible for this is an important question. I feel pretty sure the answer has many parts--and that both your post and the linked ones have correctly described parts of the elephant.

In any case, it doesn't much affect the frustration so many of us in high school feel.

I'm not quite sure any tenth grade teacher is capable of teaching tenth grade material to a classroom full of students with skills ranging from 3rd to 12th grade, to give but one example.

Heroes excepted, you can be sure.

KDeRosa said...

Roger, I agree that academic success does not automatically translate into motivation to learn. It is probably more accurate to say that those that are motivatable generally have experienced academic success. I do not believe there is such a thing as intrinsic motivation; motivation is extrinsic. And, I believe it is the school's job to provide that extrinsic motivation. Having said that though, some middle/high school kids just won't be motivated to learn regardless of their academic success in elementary school and regardless of the motivators provided by the school. However, I think that this number would be very low if the instruction and motivation techniques were better.

I would bet that the vast majority of the problem students in high and middle school fell off the academic bandwagon while they were still easily motivatable to learn and work. The remainder need behavioral remedies and some of the academic success stories might eventually need behavioral remedies as they grow older. And if there's anything that schools do worse than instruction it is dealing with behavioral problems preferably before they manifest themselves.

I'll have to write a post on this.

Anonymous said...

An insightful article.

Perhaps the most dangerous assumption one can make while attempting to teach others is the assumption that learning is actually taking place.

Anonymous said...

Anything accurate here? The "neurology-without-references" leaves me dubious.

KDeRosa said...

Looks like a bunch of junk science to me.

Anonymous said...

I second the 'excellent post' comments.

That lesson sounds like a typical English lesson at your local 'Eikaiwa' school here in Japan. That precise scenario is painfully familiar. Teachers get children to repeat back words and phrases, which mean nothing to the children, yet to the teacher's ear, make sense.

It takes a perceptive teacher to develop a lesson that not only conveys a clear idea, but verifies the student's comprehension.

Well, no. Make that a competent teacher. I'm still learning better ways to present basic concepts.

Regards, Peter Warner.
(Nagoya, Japan)