Reforming Science and Math Education:
Making the Process Self-Sustaining
by Dr. Daniel Rubenstein
page 1 of 4
Spresser: I get to do the fun part. Remember the question, where do you stop? That is one of the most important questions that you as teachers have to deal with. The second one is where do you start your investigation? Scientists intuitively know how to do this. I'm not convinced that teachers do and I certainly know that students don't. Only when both you and your students master the skill will you be able to do science. With these words, professor Dan Rubenstein begins to engage his 1989 audience at the Bredlove(sp?) Conference on Teacher Education and the Liberal Arts Colleges.
He's been in the business of talking and writing about critical thinking and the teaching of science for a long time. As a faculty member at Princeton University who teaches and researches in ecology, evolution, and behavior, he's thought deeply about matters such as the structure and values that are intrinsic to the disciplines of science. About how the scientist goes from unbridled discovery to channeled discovery. And about how this contrasts with the way students actually learn and practice science. So please join me in welcoming Dr. Dan Rubenstein.
Thank you very much. I'm delighted to be here and I thank Susan and Carlo for inviting me. Because it gives me the privilege and the opportunity to do some of the things I like best. I love doing my science, I love teaching, and I love working with teachers who want to talk about teaching science. And so here we are in this room. And my goal tonight is to try to examine ways in which we can reform science and mathematics education so that the process of doing science and mathematics, as well as the process of systemic change, can be self-sustaining.
So my talk is going to be divided into two parts. Talking about the science and mathematics as well as alluding to the processes of assessment and the structure in which education goes on in our society today. And in that way, I'll be foreshadowing some of the topics you'll be addressing in more detail for the next few days.
Now this cartoon was in yesterday morning's Trenton Times. And as I reading the paper and I was making the talk, I said, "I have to start with this." Because it typifies the response that happens when the President of the United States in the State of the Union says we're going to invest more money in improving science and mathematics education in the United States. So what's the cartoon say? It says, well, we start out with a cloudy future for public education. We're not there yet. And standards are falling, the schools go underwater. Heat arises from the public and reform ideas bubble to the surface. And then they evaporate and they get lost.
And one of the things I want to explore tonight is why that happens and how to stop that from happening. So that this cycle can be made self-sustaining. Because this one isn't. This is a cycle that collapses and then you get push from outside and you start all over again. We want to make it self-sustaining so it can support itself by the operation of everybody that's inside this diagram. And so that's going to be the theme that I want to address. At the end of the talk, we're going to come back and we're going to change this cycle to see how it can be made self-sustaining.
As I alluded to earlier, my goal is simple. I want to explore ways of making teaching of science self-sustaining. And I'll do that in two ways. One, I'll talk about how we align science and math to the disciplines that scientists and mathematicians formulate. And to do that, I'm going to share with you the understanding, as I see it, of the nature of science and mathematics in both the classroom and in the real world where practicing scientists and mathematicians operate.
And then I'll talk briefly by connecting these ideas to the processes in the community. How we have to adjust the structure and the culture of schools and their communities to make the whole systemic effort itself self-sustaining. And I will talk very briefly, not about reforming curriculum, you'll hear about that tomorrow morning, but I'll talk a little bit about student assessments and the links to parents and taxpayers that can help buoy the system and give it it's own self-sustaining energy. So let's begin.
Okay, I will put these transparencies on the Web. Not tonight, but I will be sending the material and it will be there when? Next week? Okay, next week. So don't write down copious notes. Just put down points that you want to talk with me about later. I hope I can provoke some of you to ask questions publicly. But if not, we can meet for drinks afterwards, we can meet for breakfast tomorrow morning to share ideas. Because I must say that Carlo and Susan have put together an absolutely wonderful book.
In the hour before dinner, I was reading your project summaries and your projects in the deserts, in Alaska, the math and science in Baltimore. They're compelling, they're exciting. I want to hear more about them. I want to hear about how you are making the transformation work in your areas. I'm privileged to be part of the executive committee of one of the projects, "E=MC2". Which is on page 38. And some of those people are here tonight. Okay.
So let's start by asking what is science. And I've culled a long list of properties and processes that most people will think of as science. First off, science is really about the process of producing knowledge. And what does that mean? It means we create explanations from making sense of how things happen in the world. It's creative. You come up with ideas. Explanations to account for the unknown. That's what a scientist does. We're fascinated by problems that we don't know the answers to. And we put our minds and our discipline to work to try to solve that.
We design tests that improves and discards explanations. So we're continually picking and probing at the explanations we come up with to see if they're doing their job. Are they accounting for all of the patterns that we try to explain, that we see in the world? We then try to convince others that our explanations are accurate. That's the hard part. We think we've got it right. We've got to publish the papers. We've got to get through reviewers. We've got to convince the skeptics. Because scientists are skeptics that what we're proposing as an explanation in fact is the explanation. And of course it depends on making careful observation.
Science is also built upon evidence. It's built upon observations, comparison, it's based on perturbations. We push systems. And it's based upon experiments where we do fair tests. Most of our ideas, the evidence that we use, are used to test models. Hypothetical constructs about how we think the world is organized. And to build a model, most scientists build that model mathematically. Mathematics is the language of science as a scientist would define it.
And why do we use mathematics? Because it's precise. It's a sentence. It's a sentence with no ambiguity. It is bare. It puts the relationships that we think are important in structuring our thoughts about the world precisely in front of us. It makes our assumptions naked so that our (...inaudible microphone blip) can say, "Well, maybe your explanation is true, but that assumption is too general. It's not realistic." If you relax that or change that, how good is your explanation? How good is your model?
With words, we can fudge. English is a hazy language. Mathematics is not a hazy language. And so mathematics and science go hand in hand. And it's delightful to see in the booklet the number of projects that are blending science and mathematics. When speaking of blending, science is about blending imagination and logic. There is creativity. We play with ideas. It's not very rigid. We use everything we know about the world to give us insight and then we use disciplined processes of reasoning. Either from common sense or based on more rigid rules of inference. And again, quantitative reasoning enters into play.
So this is what we mostly think of science as. But any list that's this long is something you're all going to forget. So I've reduced it to something simpler. Science is a way of knowing. Knowing about how the world works. How do we use this way of knowing? We construct statements that are very simple. We use if then statements. That's ultimately what science is about. What do we mean by an if then statement? It's as follows.
If this hypothesis I've just formulated is true or this model, this caricature of reality that I believe explains the pattern that fascinates me is true, then this should happen if I were to change x and perturb it to y. Then I'd expect the response of my system to go from A to B. So it's a series of if then relationships. That's what science is all about. You build a model. Once you have that model, you then ask, well, if something is slightly different, what would the consequences be expected to be and then go out and examine whether or not they're there. So it's about prediction.
It grows from the childhood processes that we all use everyday, but different. Every day, when we don't know something, and especially children in the schools, ask the question slightly differently. They don't say if I do this, then such and such should happen. They go if I do this, what will happen? That's a subtle, but real difference.
It's what separates the curious child (...inaudible microphone blip) from the disciplinary approach to doing science. The moving from, well, anything could happen it, what is it? I'm amazed, fascinated, I want to see it. To if this happens and I understand how the world works, then I can predict such and such should happen. That's the difference. And the trick is for us, as teachers, to be able to go from this curiosity to the discipline of doing science. Okay.
So children themselves are budding scientists, but they're not scientists. They're curious and they do all the things that discipline scientists do. They marvel at the world around them. In fact, they probably marvel at it more than we do because, as you get older, you get jaded and you put blinders on and you find certain things more interesting than other things. To children, everything's equally interesting. So they marvel at everything. And they probe. They're hard to stop probing. The parents say not to do something, they'll do it anyway. They'll test anything, they'll eat anything, they'll taste anything. They use their senses. They divine information about the world, okay? Because they're trying to make sense of the unknown.
It's not magic to them because they're picking and probing. They're learning. But they are not doing it in the predictive fashion that I just illustrated. So I'd say they have the right stuff. They have all the potential to become scientists, but they're not scientists yet. So if we're going to make them scientists, let's examine exactly what a scientist does every moment every day when they're thinking about the unknowns in the world.
Well, the first thing a scientist does is they become interested and fascinated with a phenomenon or a problem they don't understand. Now that can be something they read in a book. It can be something thrown at them as a question. It can be something that follows on from a previous investigation that they've solved, but opened up a Pandora's box of other interesting phenomena. So whatever captivates a scientist, they work on.
Now a lot of people call me up and (...inaudible microphone blip) work on this project. And there's money there. You'll get a salary. And many times I say no, it's not interesting to me. I'll only work on things that I find compelling. And part of what I find compelling are problems that are also important to society at large. So we, as scientists, find what we become fascinated with. And that's why there's so much diversities of scientists and the type of problems we attack.
The first thing we do when we become fascinated with a phenomenon, is we start to organize it. We search for a pattern. What do we really know? What do we not know about that phenomenon? Now this is again where mathematics comes into the process. Because how else do you see patterns but by organizing data? Often by taking measurements, by categorizing, by pigeon-holing. Asking is the green group different from the red group? Are cold days different from hot days in their response? We use numbers as indices. We plot data as graphs. We reason quantitatively. And that's how we find our pattern.
So right at the beginning of the investigation comes a distillation of a myriad of strange relationships and you crystallize them down into patterns that give you some hope of finding some organization. Okay? So that's the first thing that you do. And then you try to find the parts that you don't understand at all. What I call the missing pieces. And so you use intuition, which is your cumulative past experience, knowledge about the world. Book learning, deductions from the past. Things that you might have heard, that you don't know if they're true, but you heard them in passing.
That wealth of knowledge is your past experience. And it often is what you use intuitively to help pick and probe through the first layers of the problem. It allows you to make the initial associations. How do you know to ask are the red group different from the blue group? Or that hot days should be different from cold days? You do it from the facts that you've seen, phenomena that are shaped by temperature, that are shaped [by color?]. You use these patterns from other parts of the (...inaudible microphone blip) that you've had and you start to organize the data.
As patterns emerge and you can understand some of them, you set them aside as solved. Now do this at your own peril. This is where the art of science comes in. You may think you understand something by relying on first principles and previous relationships. You think you've solved it and you put it aside. That part of the problem is done. Now let's get on with the hard work, the stuff I don't understand. It may turn out that that part of the problem you set aside is going to lead you down a garden path for five or ten years because that was wrong. And that becomes an assumption for the caricature or model that you're building.
So scientists do this all the time and they do it at their own peril. So you start to focus on the remaining part of the problem. It's what I call the mental gymnastics of being a scientist. This back and forth. This starting and stopping. Putting problems aside, bringing them back when, eh, they don't seem quite right, (...inaudible microphone blip) understand it. A new piece of data suggests to you that your old insights were wrong. Your old intuition was biased. That you misjudged a relationship. And so that's the back (...inaudible microphone blip).
Once you start to do that, you're peeling away the problem. The simple parts fly away. It's like peeling an onion to the core. You're getting down to the nub of the problem that you do not understand. And this is where the fun and the hard work start to come in. Now you're at the point where you propose a precise problem and you start to ask these magical what if questions. And that's what scientists, as they pick and probe and try to ask why something is what it is, we essentially transform the problem into, okay-- [Interrupt to fix microphone]
Okay, so science, when you try to answer why something is the way it is, you try then to say what if I do this? What should happen? And so that's where the what if questions come in. And that's where you start to generate your model creation. Because from the model, comes the ability to make predictions.
Then once you have your predictions, you test the predictions with experiments or comparisons. The irony is that's what we do in the classroom. That's what we do best. We teach scientists, little children as scientists, how to do experiments. We teach them what controls are, we teach them how to make comparisons, we teach them how to actually do an investigation. Do we teach them number one, two, and number three? We spend most of our time on number four.
And then what a scientist does once they have their answer, we go and we keep probing. We ask ourselves, am I right? Because we never know if we're right. There's no way to know if you've got the right answer. But you keep testing and trying to falsify the answer you had. And so you use either confirmatory or discomfirmatory tests. You make further predictions on systems that are very different. Where you change assumptions. So it can be as different as possible. Because that's when you're going to have the power, if those predictions are borne out, to believe that you actually might have the right model, the right explanation that organizes the unknown into the known.
So that's what a scientist does. Now that's very abstract. So what I'm going
to do is share with you one problem that illustrates all those points, okay? And
that's from my own work. I study the behavior of horses, zebras, and wild asses.
And I do this in lovely parts of the world. The horses on a barrier island off
of North Carolina. The zebras, as you can imagine, are in Kenya and Tanzania.
And the wild asses, well, they're in Israel. And there's a lot of asses there.
Both of the four legged kind and the two legged kind. But there's plenty to go