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Making the Process Self-Sustaining

author: Dr. Daniel Rubenstein
published: 02/03/1999
posted to site: 02/03/1999

Reforming Science and Math Education:
Making the Process Self-Sustaining

by Dr. Daniel Rubenstein

page 2 of 4

And so what I'm going to talk about is the Asiatic wild ass tonight. Very briefly, the onager. And the onager represents an ideal that in Israel went extinct by the Ottoman Turks at the turn of this century. We're about to turn into the next century. But at the turn of this century, the last Syrian wild ass disappeared. And the Israelis want to, believe it or not, reintroduce every animal that's in the Bible back into Judaean Sumeria. That's their goal. Okay, so they breed them up. And they've taken the onager from Persia, which is the next closest race, and they're rearing them in the Hai-Bar, which is their breeding farm. And they release the onagers into the wild parts of Israel.

Now Israel can do this because most of Israel is wild, it's desert. That's where the onager lives. And what most people don't realize is most of it's a nature reserve. Well, now what's a nature reserve in Israel but a military training ground? And so that's why there's no people and there's no development to take away the resources. You just have to watch out for mines and bombs and unexploded rockets when you're (...inaudible microphone blip) around. And the only day you can get into half of those places, on Shabbat, on Saturday, and they have to tell you it's okay. That they've picked up all the garbage.

Okay. I'm interested in broad patterns of social behavior. The evolution of societies. But the Israeli government came to me and said, you know, we spent a lot of money releasing these onagers into the crater. They did this in this crater called the Makhtesh Ramon. Which runs 45 kilometers long and about 15 kilometers wide. It runs from the Arava Valley in Jordan almost to Egypt and the Sinai. Now you've (...inaudible microphone blip) heard of this place. And what's amazing is something that big was missed by the Israelites as they went through Exodus, okay? Can you imagine that? So something was going on there in biblical times as well.

But in any event, that's where they released the onagers. And between '83 and '87, they released nine males and 14 females. Now most of these onagers were lonely and they decided to head back the Hai-Bar. And most of them walked into the Arava Valley which separates Jordan and Israel. And at that time, it was mined and most of them blew themselves up. Okay, in the very early introduction. But that was mostly males. And males, when it comes to breeding biology, unfortunately guys are basically irrelevant. And so the Israelis are smart enough to realize that it's the number of females giving birth to offspring that's going to determine whether their reintroduction is going to take.

And they became very troubled by the fact that they released 14 females and, ten years later, they have 16 breeding females. That cost a lot of money. They want to know what is stopping the population from growing. So that's the question they asked us. Why such slow growth?

Well, slow growth can come in a variety of ways. One, there's something wrong with the birth rate. Something's too great about the death rate. Well, it's not the death rate. It's an uninhabited landscape, there's plenty of resources. So there's not dying if they don't blow themselves up. And that's stopped. And so we looked at the birth rate. And sure enough, the birth rate was low. Okay? Animals that were reared in the Hai-Bar, when they were released in the wild don't breed as well as those that are reared in the wild. And so there's a lag. But still, after ten years, that can't be the total explanation.

So they gave me the data. I looked at the data and noticed that the animals that were being born were all males.

Populations will give birth, the animals in populations will give birth to sons and daughters with equal frequency. We can prove that mathematically and you can do a thought experiment based on the frequency dependence of this phenomena. So that if you were having diripherous sex, if you were programmed to give birth to one sex over the other, that rarer sex becomes more valuable. Can you imagine the case where there's 99 females and one male and you're trying to spread genes into the next generation and each female can only have one offspring? Think about which sexed offspring you should make out of that one offspring. Obviously, a son.

Because the son can sire offspring from lots of females. Whereas your daughter's only going to give you one female. And you can do the experiment in reverse. If daughters are rare, most sons are going to shoot blanks and they're not going to have any offspring and that daughter's going to be very valuable. And so you can see that the only stable point is right in the middle at fifty/fifty.

But we also know from evolutionary theory that there should be exceptions to this rule. Four females that disproportionately controlled resources. So (...inaudible microphone blip) that are well endowed, that have resources and are fat, are those that can invest disproportionally in their son. And if their son is a son that can be the absolutely best, then that son will mate multiple times. Now females that can't invest in sons, because they're emaciated or they're feeble or whatever reason, they should have daughters because daughters will give them at least offspring.

Whereas the son, if he mates multiply, will do well. But if the son's out competed, what's the son going to give you in terms of grandchildren? Zero. So the high risk strategy only goes for those that are well endowed. And the tried and true conservative strategy goes for those that are less well endowed.

Now we know that from evolutionary theory and we know the species where these exceptions occur. And they occur (...inaudible microphone blip) can disproportionately control resources. Where resources are spatially distributed in clumps and females can elbow their way to get those clumps.

But onagers eat grass. And grass, even in a desert, is fairly homogeneously distributed, even if it's sparse. So this is a species that shouldn't be doing this. And yet the theory would give us a way to answer this question of the biased sex ratio. So we said, you know, maybe it's not competition per se. Maybe it has to do with age. Middle aged females, by their experience, by their accumulated wisdom, by small benefits in their recent past, might be better endowed than those that are very young and those that are very old.

And so we made the very strong prediction that maybe middle aged females should in fact be giving birth to sons and that new (...inaudible microphone blip) primiparous females and older females should be giving birth to daughters. And we said that's a prediction. So let's go and see what happens.

So we asked the Israelis for all the data. And what we found is, sure enough, the middle aged females were disproportionately giving birth to sons and young and old females were disproportionately giving birth to daughters. Now what was intriguing was the Israelis were being good managers. Good economists. When they were moving animals from the Hai-Bar to the crater, they didn't move youngsters who were inexperienced, who were going to die. And they didn't move oldsters who didn't have much life left. They used prime, middle aged females. And what did those middle aged females (...inaudible microphone blip)? Sons. The population stopped growing.

So we've answered the problem using our intuition, using our past experience. Drawing on a piece of evolutionary biology which normally doesn't go into management and conservation. Okay? And so the Israelis were doing exactly right. We've now told the Israelis to change their behavior. Told them to go and actually take old females, who are going to give birth to daughters, who became young females who are going to give birth to daughters. And so you'll get a double whammy. Immediate integration of females into the population.

And that's what they're doing for all their other reintroductions and their reintroductions are growing like crazy. So here's a case of using the scientific method in ways that really do illuminate how a scientist thinks. We became fascinated with this problem. We took apart the easy part, which was the birth rate due to the rearing experience, and then we drew upon things we remembered from our past, evolutionary rules. That made us fill in the gaps. We proposed a precise problem. We asked the what if question. We tested our prediction by looking at their data. And then we kept probing.

We then said, you know, this works on the Israeli population, but that could be a tautology. So we called up all the zoos and got their records around the world for onagers. And, sure enough, we'd get exactly the same pattern, even more extenuated, from all the zoo data. Where animals could be in their very best condition. So that become a confirmatory test. Okay?

So that's what a scientist does. And as you see, a scientist is using the traditional scientific method of discovery; hypothesis generation or hypothesis testing. But we're not doing it in linear fashion. We peel away problems, we look at many alternative simple problems, and then we reevaluate the completeness of our understanding based on the model we construct. Okay, nowhere is this more obvious than in the classic black box experiment. Where scientists and teachers do things very differently. How many of you have done the black box experiment at teachers' workshops? I assume most of you. Okay?

You know it. You get this little box and you'll have something in it or some wires and some hoses or whatever. And your job is to figure out something about how it works. And when you get done, you're going to stand up and share your reasoning process. Share the process by which you deduced this. As if that's science. And it is. But when I sit at the table with my science teachers, I reach under and I grab the answer and I tear it up and put it in my pocket. So my group never knows what was in the box. Because scientists can't open the box. They can't know what's in the box.

And so that process is short circuited right at the end. And if we bring that style of knowing the right answer into the classroom, we short circuit the process of science and make the science itself unsustainable. Because then there's an artificial end. The project ends when everyone knows whether or not they got the right answer. They don't keep going and ask, well, how do I know if I have the right answer because we gave it to them. And so ways to get around that in a workshop like this would be for no one to know what's in the box. And for everyone to stand up and share their reasoning about what they think is in the box. That's their model, their hypothesis.

And then everybody should get together and try to get generalizations. By comparing, you know, what's in your box sounds like what's in my box. Let's get together and talk about that and do a test to see if they are the same. That's more what science is about. That's what critical collaboration is about when you go to a meeting. So remember that. I'm going to come back to that point at the very end.

So the classic box experiment illustrates what's different between science as done by scientists and science as done by teachers generally. Not that it's wrong. The process is the same and it's right, it's just the end is artificial. We need to change that end. And so what I've done is I've tried to abstract the differences. If you look at the onager experiment I just talked about, scientists start with a result and effect and try to deduce causes by asking why questions and picking and probing with the what if scenarios, the hypothetical scenarios. And then, once we have a pattern explained, (...inaudible microphone blip) our answer, we keep asking is our answer right?

We'll never know if we're right. We're not God. We can't open the box. Wish we could, but we can't. We have to share it with our colleagues and skeptics that they are. What happens in the classroom between students and teachers? We tend - although it's changing with the emphasis on inquiry based science, but we're not there yet - to move from cause to effect. Whenever you lecture, it's about cause to effect. I give you the perceived wisdom. Textbooks give you the perceived wisdom. Teachers' guides, even in the kits, give you the perceived wisdom. And you're left with the tools that they provide to try to reverse the arrows between cause and effect.

And so we've got to move away from that. We're moving away from the canned explanations. But we still have to move away from this search for the right answer. And I want to explore some ways to do that in a moment.

Now how can we make the science the same between the science that scientists do and the science that students and teachers do in the classroom? We can take that scientific method and we can change it a little bit into what I call the four Ps. We start with perception. That pattern to be found in the problem that's compelling to us. Perceive the world. Then we work on problem posing. How do you ask a question, which is a guess, a hypothesis, which has a prediction to it? Not something that's generic.

A hypothesis shouldn't be of the form that doesn't have something that says if this, then that. It shouldn't just be an open ended, well, temperature's going to affect the process. And then a good scientist turns that into a no hypothesis. Temperature's not going to affect the process. Okay, and then I classify that and I do that statistically by rejecting the no hypothesis, I'm done. Wrong. Good science makes a prediction. So we pose a problem by generating hypothesis with a prediction and then we test whether that prediction is true. That's what we call problem solving.

And then lastly, we spend time persuading others that we're right. Now most times we're not going to be right. Someone with a completely different window on the world's going to say, you know, that's crazy. What about this? And you go, oh, I didn't think of that. Oh, God, my explanation completely missed that. Bang, done, you're over. Start over. The loop goes around. It's self-sustaining. It never ends.

Okay, so that's what we do. If we can do that, we're in great shape. The way I do it is to use two E's. I try to engage my students by providing them with compelling concerns. And then I try to empower them to act as scientists to solve it. Now I teach an introductory biology course to non-majors. So if you were at Princeton today and you were taking your required one science course or at Princeton it's two required courses, take my course. And you would go through this process.

And so what I'm going to do is to try to share with you some experiments that I use to engage students and empower students. To encourage fascination, that's the engagement, and then teach them how to answer the why questions. So if you'll bear with me, I'll share two experiments with you, okay? And both these experiments are mathematically tied. They're not the measurement kind of measuring bones and things like that. These are tied to mathematical concepts. They're about population dynamics and the students have learned the equations of change in numbers with respect to time in the classroom.

It means nothing to them. I can draw those graphs, I can talk about density dependence and its independence till I'm blue in the face and it means nothing. Unless they play with those concepts, they're never going to have the benchmark to move on for the rest of their lives. And so I debated typing these up so they'd be bigger and I said no. I'm going to take them and xerox them right out of the student manual. So this is what they read. See, rationale is misspelled.

So the debate concerning environmental problems too often becomes polarized. Rhetoric replaces reason as positions harden. Solution solving; little becomes adopted or imposed. So sound ecological considerations have been melded with human needs so that sustainable outcomes can become ensured. Incipient reintroduction of wolves into Yellowstone Park is just another recent issue pitting environmental groups against the economic interests of some local residents, i.e., the ranchers. Can a balanced ecological and economic analysis of avert an outcome where bitterness lingers? Hence the title, "The Wolves are Coming. My What Big Teeth They Might Have." Okay? Maybe they'll cause a problem, maybe they won't.

Now this lab worked for two years. We put a lot of effort into developing this lab. Why did we have to stop it after two years? We know the answer. It's not compelling anymore. I have to reinvent ways to use my pedagogy with students. Because if the problem isn't fascinating, they'll just do it because I tell them to do it. I can teach it, but they won't learn it. That's rule number one, take home message. If it's not compelling, it doesn't have a chance of being long lasting and to be that benchmark.

Now in that experiment, that's what they get. And they get just something like this that tells them about wolves in Yellowstone. You are going to be scientists. And what the purpose of this lab is to get them to build an ecosystem with all its complexity and see the impact of adding wolves. They don't know when they start whether they're going to be ecologists hired by the ranchers or the ecologists hired by the state. They both have to do the same process. And then they're told, you're going to be hired by the ranchers, you're going to be hired by the state. And you're going to have to come and debate to me on the environmental commission what I should do.

Okay? Should I allow the wolves to be introduced? If so, how many? If not, why not? That's the assessment. That's the project. In the end, some of them go for the jugular. They try to shout down the other group. Because the way I structure it, after they have a week to play with the models, is they come in and they present. And they get up on their soapbox with lots of rhetoric and they have a great time. And they each get 20 minutes to make their case. It sounds like what's going on in Washington today, except it last three days. 20 minutes to make their case. Then they get ten minutes to argue back and forth. That's coming next week, okay?

And then there's a pause. They get a half hour, and I leave the room, where they get to redo their models to try to adjust to the criticisms that they have perceived might condemn their case to the basket. When I come back, I ask them do they want to continue or do they want to drive for a consensus. And half the time they say we think our position's right, those guys are totally wrong, and they go for the jugular. The group that wins the debate gets an A and the group that loses the debate may or may not get an A, depending on the strength of their argument.

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