Support Materials

10. How We Organize Knowledge - The Structure of the Disciplines


Linda Darling-Hammond: Every teacher knows that there is always too much to teach. How do you decide, subject by subject, what's most important? How can you help your students to understand the big ideas of the disciplines they are studying? How can you get them to think and act like historians, mathematicians, or scientists?

I'm Linda Darling-Hammond, and that's our challenge for this session of The Learning Classroom.

Every discipline has a set of big ideas that are connected to each other and provide the glue that holds the subject area together. These include ideas like ratio and proportion, balance, and equilibrium in mathematics. In biology, we might think of major themes like evolution, adaptation, and the environment. Each discipline also uses particular methods of study that reflect how knowledge is built in that field; for example, scientists do experiments, and historians evaluate historical evidence from different perspectives. To really master a discipline, students need to understand what the big ideas are and how they are connected. If they learn to think like experts in that field, their learning will be much more efficient.

Lee S. Shulman, Ph.D., President, Carnegie Foundation for the Advancement of Teaching: If I'm a physician, and I'm doing an examination of you, I don't just randomly say, "Let me look at your nose, how's your toe?"  I have a structure; it's the structure of the human body and its organ systems, so I will systematically check the gastro-intestinal tract. I will check the respiratory system, the cardiovascular system, the neurological, right? Because, not only does that give me a structure for moving through the examination, it also structures my memory for any signs or symptoms that I encounter, that may be relevant to diagnosing what you have. So, every time we call something a subject matter, I would say, we call it that because it has some principle of organization that connects the ideas with one another that gives them some kind of order, some sort of meaningfulness, and it's like a code.

Linda Darling-Hammond: Julie Helber, a fourth grade teacher at Paddock Elementary School, helps her students to think and act like scientists and mathematicians as they learn about static electricity and fractions. She guides them through their inquiries by modeling the steps that experts follow in those fields. And then she gives them an opportunity to practice doing what scientists and mathematicians do.

(classroom scene)
Rub it on his hair too?
: It's moving!  It works! It's moving!
Do you see his hair moving back and forth?
It's a magnet.
You think it's a magnet?
And what happens when you rub the balloon on your hair? Your hair sticks out? Why do you think that happens?
Girl in yellow:
Since we can't like, come to the rod our hair does and it's the lightest thing on our body.
Ok, does anybody have another experience?
Girl in blue:
I think 'cause when I went on the slide out there you always get shocked and stuff.

Julie Helber: The students are experiencing a first hand investigation with electricity, so they're actually working with materials and figuring out which materials are static and which materials are not static in several trials and experiments.

Later we studied a second hand observation where the students looked at a notebook test, text from a particular student. And we read through the notebook text together to make some more meaning of what we were learning about static electricity, and we really tried to utilize the text and draw on what we already knew about static electricity to make some conclusions or some hypotheses about static electricity.

(classroom scene)
: And Michelle says she gets shocked. Are there any other cases where you've gotten shocked by something? Any other times? Josh?
Josh: We live on a farm, and when we had cows we had electrical wires, and, lik,e I would accidentally touch it, and I wouldn't really be able to let go. I would really have to force myself to let go.
Julie: You have a lot of knowledge right now about static electricity. What I'm going to be giving you are some materials that you will be working with a partner to use. Okay, you're going to be trying to create charges between the interactions of the materials that are in this bag. So how could I record your results for that? Jasper?
Um, just make two columns, one for if it had electricity and the other if it didn't, and you can just check one.

Julie Helber: The value in setting up the experiment this way, by allowing the students to investigate something that they might not have clear and concrete directions for – there's a lot of value in it. And what I see is the most valuable is that the students are constructing meaning by actually using these materials in a way that they have chosen, so I haven't determined how they are going to use the materials and told them exactly what to do. Because I want them to err in what they are doing. I want them to see that they've tested or tried something that doesn't work, because that's really when they learn.

If I tell them how to do it, it's not likely they're going to remember it later. But if they actually learned it while they were doing it, it is likely that they would remember it later.

When there are a variety of opinions regarding a particular topic really, I think that's the meat of teaching. The students interacting with each other, or I saying "Well, I disagree with another student," is probably the best thing that can happen in my classroom.

Lee Shulman: The notion of structure in mathematics is, is probably one of the most obvious ones. Mathematics is a field where most people who teach mathematics will readily understand the notion that there are certain kinds of structures. There's a notion of balance. There's a notion of equilibrium. There are notions of ratio and proportion that just keep on coming up again and again and again and whether you're doing primary arithmetic or you're doing algebra, those notions return, repeat themselves and you get a sense of how these organizations really make sense of the subject.

Julie Helber: I always offer lots of options for the students to demonstrate what they know. If they need to come up today – we were doing a math lesson, and somebody said, "Can I come up there and show you?"

(classroom scene)
Julie: Is this rectangle up here divided into thirds? And you need to be able to explain it to me…. Hmm. Okay, I need somebody to say, "No," to raise your hand and explain why you're saying "no." Melissa?
  First there's two rows of four, and then they have one extra and a half. It's a half extra part.
  Can you come up and show, because I'm not sure I get it.
They had added one extra part to it. Then we have that extra one.
Julie:  Okay, so how many, you're saying that it has an extra one. What do you mean by that?
  There's just this one extra triangle sitting there… Oh, wait.
What are you thinking about?… Melissa, can you tell me right now what you are doing to check that?
Um, I'm checking it by counting by these squares.
Yes, Brian you want to explain?
Here's, if you folded this they have too little. This one has too much, this one's right.
Yeah, this one's right, but these two are wrong.
Yes, this one has – they should take the half off of the eight… And put it on the seven and a half to make eight.
Okay, so if I did draw a line like this and gave that one, then would it all be divided in thirds?
Yeah, yes.
Take that line off, take that diagonal line off. So this line off and then we would have thirds.
: Yeah.
Okay, good!

Julie Helber: It's very helpful for students to hear another student explaining why they arrived at a particular answer, because it may not have been the way that they were thinking.

And so by hearing how somebody else is thinking, and it goes back to me modeling how I'm thinking about things, and to maybe change their of way of thinking or to expand the way that they think.

Linda Darling-Hammond: Did you notice how Julie tried to ensure that her students would understand not only the content they were studying, but also the process of experimentation that is central to science and the search for patterns that is at the heart of mathematics?

Tenth grade biology teacher Mary Edmunds helps her students understand cell biology by first connecting the issues of disease to the drama of the science fiction novel Andromeda Strain. She then engages them in the scientific method, so they can examine the features of cell membranes for themselves.

Mary Edmunds: Adolescents have to have hands-on investigations. They have to feel like they're a part of the learning process. They have to be able to take ownership of their own learning and they have to be able to feel that they're a part of the learning and that they can take it out into the world and utilize it. Especially urban youth. Urban youth need to understand that they can do it. They have the tools. They are scientists, and that they can go on, and they can become a big part of this world. And the way you do that is for them to see relevance. So how do, how do you get them to see relevance in cells? They have to know that they're made of cells. They have to know that the anthrax scare was not beyond their ability to cure. They have to know that bacteria can be grown, but that they have the scientific ability and the knowledge to destroy it. But they have to know the internal structure of a cell in order for them to take that knowledge out into the real world and solve any problems.

(classroom scene)
Mary: Did Andromeda strain like or dislike a high alkaline level?
Dis - Dislike.
You got it. So the optimal range for the Andromeda was not alkaline, correct? That's why it did so well in the human body. Do we like alkaline? No, that's why it did so well in the human body. So if we get away from our normal metabolism we do not stay at homeostatic conditions, do we? Alright, so diffusion would be best within the cell, moving around within the cell at body temperature. Let's look at it, okay. Let's say that this warm is body temperature. And this is cold. Who can give me a hypothesis for which of these containers will have the best diffusion, or the fastest diffusion?
I believe that um, the, the cold water will have the most diffusion because…

Mary Edmunds: Students love to be called scientists. I mean, I like to think of myself as a scientist. And if we, if I tell them that you are now a scientist, you're working on an investigation, they're really more interested in it. When they put a lab coat on, a whole new aura comes over them that this is really important, that this is really scientific.

(classroom scene)
So since we are scientists ourselves, right? We want to find out if it's true that the cellular membrane is permeable. Means that it lets things in and out, right? So we're gonna use an egg, okay, everyone? We're going to use an egg.

Mary Edmunds: You see in the classroom when I ask the students how would you get the membrane initially, that a lot of them thought, "Well, I'll boil the egg," – because they took their past experiences. They boil the egg, they peel it off, the membrane's right there. But I had to get them to understand that this is a living cell, and a living cell has cyto-cell…it has cytoplasm (she corrects herself) that surrounds the nucleus, so you can't do that, so what are you going to do?

(classroom scene)
Group 1
It'll start cracking, and it'll start peeling off. You ain't never boiled no egg have you?
Hard-boiled eggs, like what you do for Easter, like hard-boiled eggs.
Nichole: And after awhile it'll start to crack.
Group 2
It could be like, maybe lemon juice.
I say vinegar.

Mary Edmunds: They have to feel secure in making a mistake and not thinking that they're gonna be ridiculed by me or the other students in the classroom, and they have to be able to take chances. I, I don't know everything. And the kids can ask me something, and if I don't know it, and I tell them, you know, I'm gonna look it up, they feel more secure with me asking them questions and them not knowing the answers. But the best thing to do is to go around and catch it. Catch them while they're doing it and get, get them to think about it.

(classroom scene)
Mary: What do you think?
Nichole: We think to boil, to boil it.
Mary: Alright, why?
Nichole: Because when you okay, like when an egg, when you boil an egg, I don't know if everybody in here boiled an egg before, but if you keep on letting it boil the shell is going to begin to crack. And the shell is going to start, it's gonna start to peel off, the shell gonna start to peel off.
Alright now Nichole when you peel it off, what is the first thing that you see?
Nichole: The ah, skin of the ah…
Mary: That's right, and it would mimic the…
Class: Cell membrane.
Mary: So in theory they're absolutely correct, because I didn't give enough information. Now, I should have been very, very specific and said, "This was a liquid solution." Now, remember, we – it's only a substance that we use from the pH lab – your logic is excellent. That would be the easiest way to truly show the membrane, the easiest way to truly show the membrane. What did your group figure out?
It, the answer is vinegar because it'll, like, um, it'll like melt the shell and, like, turn the inside of the egg to, like, jelly.
Mary: Alright, she's absolutely right, absolutely right.

Mary Edmunds: And see, I had the students decide how to dissolve it. And then that made them interested. If I would've just said, "Okay, today you are going to dissolve the membrane of an, of an egg in vinegar," they would've said, "Okay," today. And if I would've asked them two days later, "What did you dissolve? What, what acid did you use?" They would say, "I don't know. Whatever you told us to." But see, now if I asked them, they would say, "vinegar." And I would say why? "Because the pH is low enough to dissolve the membrane, to dissolve the eggshell without effecting the membrane." That's why I did that.

A couple of the groups broke their egg, accidentally, and they thought, "Oh, the experiment is now a disaster." But that's, I wanted them to understand that that happens to scientists. That there's limitations in life, but the scientific word is a limitation.

(classroom scene)
Mary: What's the problem? What happened, what is this, you're a scientist?
It's a limitation.
Mary: Why is it a limitation?
Nichole: Because it was.
Girl: All the membrane of, the shell was gone for the…
Nichole: The membrane dissolved.
Mary: Okay, exactly, what is this?
Nichole: The membrane.
Mary: Okay, let's look at it. Can you describe the membrane?
It's rubbery, almost like a balloon.
Absolutely. So if it's rubbery, do you think it's, it's got pores in it?
Boy: Yes.
Mary: But we can't see them, how can we prove there are pores in this?
Nichole: With a microscope.
Without a microscope. How could you prove in your scientific investigation…
Because the vinegar got in…

Mary Edmunds: It was a perfect opportunity for them to see the consistency of the membrane and to see, they can't see the pores. They cannot see the pores, but they're microscopic.

Well, they, they read that, or they learned that in some past experience that we've done, because I didn't lecture to that. So that, that was a learning experience for them.

(classroom scene)
What happened?
Girl: It broke.
Nichole: It um, it weighed more.
Mary: It weighed more. There you go it weigh…
So it blew up like a balloon…oh!
Mary: You got it! Hey look it, the red blood cell. A red blood cell if it's put in a hypostatic environment…

Mary Edmunds: I think it's important for them to take the idea of cells to cellular membrane and then how the, the different solutions effect the passage across the membrane.

Problem solving is, is so essential in life. If, if students do not know how to problem solve, they're not gonna be able to make it in college.

But when I get them to problem solve, and I can get them to problem solve, that's where, that's where it all comes together.

Linda Darling-Hammond: Mary's students were able to solve both a fictional and a real life problem by working together using the scientific process. But what if Mary were teaching history instead, where the process of "finding the truth" is not so clear cut?   

Lee Shulman: Let's just take it for a given that experiment is a great idea in science. And now we start learning history. Well, how do you do an experiment in history? We then suddenly realize that that's not the way you do history. We don't have, we can't put one historical period in an experimental group and another one in a control group and see what the difference is. But we're still doing comparisons. We're still trying to create evidence. I mean there's certain ideas that do cut across – notions of description, of analysis, careful, careful observation, notions of what is the evidence for your claim, notions of theory. But the fundamental process of experimentation, which is at the heart of work in science, has no real analogy in history, if what you mean by experiment is that the scientist is controlling conditions and studying what happens under conditions that she herself has controlled. So what does a historian have to do? The historian in some sense has to look for comparisons where, if you will, nature has made experiments, not scientists.

Linda Darling-Hammmond: Avram Barlowe, a 12th grade history teacher at the Urban Academy, confronts this challenge every day. He has his students read the primary source materials for the period they are studying, so that they can explore the events and opinions of the time and understand the perspectives that shaped historical decisions. He focuses on central ideas like governance and human rights, and he raises essential questions like: Who should govern? And why?   

(classroom scene)
Avram: Let me try to give you just a little bit more context for a second, ah and refresh your memory. Johnson decides that he's going to implement a lot of Lincoln's reconstruction plan, which is pretty, pretty lenient on the South. What that allows to happen is it allows state governments to be created all across the South. They pass these Black Codes that we were about to look at. Okay, these Black Codes are laws passed by Southern State governments. Now what do these laws do?

Avram Barlowe: What I asked them to do was to look at that material and ah, to actually look at the text of these laws and decide for themselves what they thought the laws were designed to do, why they thought they were created, how they would have been defended by the people who wrote them. And you'll see, you saw in the classroom there were multiple interpretations of that. And the discussion hinges upon multiple interpretations and meaning of these codes through the looking at the evidence that the meaning presented.

(classroom scene)
Page three Section nine, go ahead.
Um, <reading> "If any person shall persuade or attempt to persuade, entice or cause any freed men, freeing or belonging to the servant employment…" you know, I don't have to read all of that. Basically what it says is, it's just like if a guy leaves his job, anyone else who tries to hire him, or tries to give him food or clothing, or anything else, they could be fined or put in jail. So it's beyond even, like, trying to keep them down. It's like, alright, if you want to help them we're not going to let you.
I think this gets to the part, you're saying that this is like slavery. Matt's saying it's not great, but it's not quite the same thing as slavery. Let's look at, try to figure out what this means and does this support Stephanie or does this support Matt.
When you look at them individually they don't seem that bad. You know, you're, like, okay that makes sense, it's job training. But when you look at them as a whole, it's just totally restricts what you're saying. If you want to hold, you know, freed slaves up to the same standards as white citizens, why are you going to make a completely different set of books for them?

Avram Barlowe: Um, when we respond to the arguments, we respond with them on the basis of the evidence, and when we present them, we present evidence to support them.

(classroom scene)
Matt: It says free, freed men and then freed Negroes, it's like, two separate categories.
And white people hang out with black people.
Yeah, so I-I- I think it's just like back in the 10 Commandments, which nobody's complaining about. Like "Thou shalt not commit adultery," it's just backing up what's moral.
Well, it says in it that if you associate with freed men, freed Negroes, or mulattos on terms of equality, then you're a vagrant. How is that moral and how is that anywhere in the 10 Commandments?
You really need to look at the text when she makes a kind of argument to you based on evidence. She's saying that all white persons assembling with freed men, freed Negroes or mulattos, or even associating with freed men, freed Negroes or mulattos on terms of equality. So a white person is hanging out with a black person and treating them as an equal, she's saying, and being a vagrant, and that's not morality to her.

Avram Barlowe: The evidence is always central. And what's your evidence and how do you, what, how do we analyze a piece of evidence? So there was an exchange there where that happened. Um, where a kid had not read the material beforehand, was sort of glancing through it as we spoke, and he was making some arguments, and then some other kids would say, wait a second go back to the text. You're making generalizations about this.

(classroom scene)
So I come back to this, what should be done with these guys who had passed these kind of laws? Should they be allowed to be in the government? Michelle's saying that they should be as long as they…

Avram Barlowe: I'm really trying to help frame a discussion for them so the inquiry can deepen, and we can get to deeper levels of evidence and argument. And that's basically what's going on, it's an exchange of ideas there. It's not a willy-nilly exchange of ideas; it's an exchange of ideas that's happening within the framework of an inquiry that's rooted in questions that I, that I, that I've designed.

(classroom scene)
Jose: Okay, how are you going to say you have all the rights of being an American, when like a month and a half ago I was ready to kill you, because I don't like America, you should not be able to reap the benefits of something you were trying to destroy a couple weeks ago, that's not right.
Michelle:  Part of the war was to keep the Union together, you know. You can't have a country together when you're pushing away half of it, you have to have the Congress and senators from, you know the other states, you had to have representatives and even if they did not agree with what you wanted or like what you want for the country or whatever, you still have to have it or else there would be no Union. What's the point of having a war over keeping them together if you're gonna push them out after when it's over?

Avram Barlowe: They're beginning to answer things like, they're, they're looking at the question of the freed men after the war in the context of, of the Emancipation Proclamation, Lincoln's role, the slaves self-emancipation. They're building on what they already know, so there's an intellectual growth I think that, that, that you can see.

Lee Shulman: What's really important as teachers teach different disciplines to students is for the students to appreciate that there are certain kinds of ideas like description, like analysis, like careful observation, like evidence, inference and theory, if you will, that are useful across disciplines. But there are other ways in which very important methods of work in one discipline just don't show up in another discipline. And I think history and science make a lovely contrast here.

History and literature also make a lovely contrast.

There are different canons that we use for determining whether it's a good novel, or a bad novel and they're not the same as the ones we use for determining whether something is good history or bad history…unless we're gonna use the novel for teaching people history. And so here again, understanding the differences in what counts as evidence and what counts as knowing a subject between subjects becomes terribly important for teachers to understand, and in turn, for students to understand.

Linda Darling-Hammond: Julie Helber, Mary Edmunds and Avram Barlowe teach the central ideas of their subject matters while they also teach their students the skills necessary to learn on their own. By helping their students to think and act like experts in each field, they're not just giving them fish, they're teaching them how to catch them – a skill that will keep their students nourished intellectually for the rest of their lives.

This is The Learning Classroom. Thanks for watching.  

Return to the Support Materials for Session 10

Contributors to this Session

Linda Darling-Hammond
Charles E. Ducommon Professor of Education, Stanford University

Lee S. Shulman
President, Carnegie Foundation for the Advancement of Teaching

Julie Helber
fourth grade teacher, Paddock Elementary School, Milan, Michigan

Mary Edmunds
tenth and twelfth grade biology teacher, Detroit High School for the Fine and Performing Arts, Detroit, Michigan

Avram Barlowe
tenth through twelfth grade American history teacher, Urban Academy High School, New York, New York.