Part 1 - Sun, Moon & Planets

Part 2 - The Stars

Part 3 - Seasons & the Celestial Sphere

Part 4 - Conclusion - Teaching Science Inductively

The Inductive Way to Understand the Sky

"This course is an unusual combination of elementary science and advanced epistemology."


Part 4 - Conclusion - Teaching Science Inductively

After we cover basic observational astronomy in a qualitative way, what comes next? History is a great guide. Look at the early astronomers who first learned this subject; what did they have to discover next in order to make progress? The answer is: They had to start making measurements and begin to transform the subject into a quantitative science. So our next unit is on early measurements in astronomy. How did people first figure out the size of the Earth? How did they first estimate the distance to the moon and sun, and the sizes of the moon and sun? How did they measure the angular positions of the planets and the stars? How did they determine the times of the equinoxes and solstices, and therefore know the exact lengths of the seasons? This unit is fascinating, and it leaves you with tremendous admiration for Greek astronomy.

Now I want to make a side-point about repetition. If an educator needs to merely repeat lessons, that’s bad. It means that the students didn’t understand the lesson the first time, which probably means you’re teaching it wrong. But there’s a good kind of repetition, and that’s when you revisit a topic to add a significant new point and integrate the new knowledge with the student’s existing knowledge. This reinforces the previous material and builds on it.

As an example, consider our treatment of the stars. We first introduce them in a simplified, two-dimensional presentation. When we revisit them a second time, we present them on the celestial sphere and discuss how their positions in the sky change as we move north or south. Then, when we revisit them a third time, we discuss how their angular positions can be measured accurately. Every time we go back, we add something that is a major step forward. It’s the opposite of the old Springsteen song; with us, it’s one step back and two steps up.

Okay, after we have measurements, what’s next? At this point, it is finally time for a theory to integrate the measurements. Here is where we present Ptolemy’s geocentric theory of the universe. Now, since this theory is wrong, why do we bother with it?

Well, certainly Ptolemy’s theory is wrong as a physical, causal theory of the universe. But, for the most part, it is successful as a mathematical theory for describing and predicting the observed motions of celestial bodies. And because it is a geocentric theory, it describes those positions and motions from our point of view—in other words, it describes what we actually see, not what we would see if we observed from the sun. In this sense, it is closer to observation. By studying Ptolemy, the student really learns the observations, and learns to appreciate the challenge of developing a theory that accounts for the observations. He also sees the weaknesses in Ptolemy’s theory, so he is perfectly set up to understand the Copernican Revolution. The last two units of our astronomy course deal with the advances made by Copernicus, Kepler, and Galileo, culminating in the proof of the correct theory of the solar system.

So, at the end of our course, we arrive at the place where most elementary schools begin: Kepler’s theory. But our students really know the theory. And, along the way, they learned an enormous amount about scientific method—and, more broadly, about how to arrive at generalizations from observed facts. In other words, they learned how to be good inductive thinkers—in other words, they learned how to think.

Now, we’re getting toward the end of this very short course, and I want to make some general comments about the state of science education today. And rather than just saying it’s bad—which it is—I’ll start by identifying a few points that educators at least partially understand.

First, they understand the need for motivation. I don’t think they understand how to achieve it, but they do understand the need for it. Now, there are many factors that can contribute to the student’s motivation, including a likeable and entertaining teacher. But there is one factor that is the essence of motivation: the student must have the context for understanding the material and its importance. Without that, all the clever jokes, the games, the visual aids, and so on, are just diversions to alleviate the boredom. At best, it’s the dessert without the meal—which is not very healthy.

Let me give an example of how educators desperately seek to provide motivation and yet fail. On the internet, I saw a lesson about Galileo’s law of motion down inclined planes. Whoever wrote this lesson must have thought that the topic was pretty dry and boring, and therefore it needed to be “jazzed up.” So, instead of using a metal ball like Galileo did, the curriculum developer used a dinosaur in a go-cart. And the dinosaur roars as the cart rolls down the inclined plane.

Now, to put it generously, this doesn’t quite work. First, students are not ready to study Galileo’s theory of motion until at least 7th grade, and any child of that age who is still excited about cartoon dinosaurs is retarded. So this is the opposite of motivation, because the students who aren’t retarded will be insulted. But here is the main point: Ask yourself—why was the educator driven to this level of desperation? Why did he think that the dinosaur was necessary? The answer is: Because the students hadn’t been given any of the background that would enable them to grasp the importance of this crucial experiment. When they are given the background and the material is presented properly, the students get excited about Galileo’s discoveries.

This dinosaur example is typical; science lessons are littered with gimmicks that are supposed to make the material more palatable, like putting sugar on bad-tasting medicine. But rather than burying the medicine in sugar, why don’t we just figure out why it tastes so bad? In the case of science education, it’s not in the nature of the material to taste bad. In fact, children start out very curious about the fascinating world around them; young children love learning about animals and plants, playing with magnets and colors, seeing pretty rocks and shells, etc. Their enthusiasm wanes only after years of getting it beat out of them by bad science classes. Eventually, they draw the conclusion that science is just memorizing floating abstractions and disintegrated concretes. The material seems unintelligible and boring, and they drift away.

So, in regard to motivation, my main point is this: When science is taught inductively, the solution to the motivation problem is built right into the presentation. It isn’t some mysterious ingredient or candy-coating that is added to the material—it’s in the material.

Now, I said that educators today understand the need for motivation, but not how to achieve it. There’s another issue where they understand a need but not how to satisfy it, and that is: The need for “hands-on” activities. I definitely believe there is such a need—but they have to be the right sort of activities, designed to learn material that has been selected and ordered in the right way.

Perhaps it sounds like I’m making a concession to pragmatism here. The progressive educators, influenced by John Dewey, are major advocates of “hands-on activities.” This is the way to teach, they say, because people learn by doing, not by thinking. The pragmatists even define truth as “an idea that works in practice.” In this non-intellectual approach, all of the emphasis is on activity and to heck with thought.

This is nonsense—yet the progressives are not wrong about the value of student activities. Put it this way: They’re wrong epistemologically, but not pedagogically. The fact is that activities are an indispensable way of permanently implanting the knowledge in the student’s mind, rather than simply having it wash over him in a torrent of words and figures.

At the end of a week, when I ask my 9 year-old daughter to give me the highlights of what she learned in school that week, she almost always mentions some lesson where she not only learned something interesting, but also got to do something, either during the learning process or using the new knowledge. Learning is an active process, not a passive one. A well-designed activity makes the material memorable, meaningful, and fun.

Now, what is a well-designed activity? First, the time required by the activity needs to be consistent with the importance of the material; in other words, we don’t design a time-consuming activity for a minor point. The payoff should be worth the time investment, and we aren’t just trying to kill class time here. Second, try to maximize the fun; if possible, add an element of competition, make it a game, whatever. Of course, fun is an end-in-itself, but it also provides a long-term, practical value: A fun experience is memorable experience.

But, as always, the most important point is: Teach the right material, in the right order and in an integrated way. Then the activities will focus on essential points, they will connect to each other, and they will contribute to deep knowledge of a science. For the most part, the activities designed by progressive educators don’t achieve this goal because the curriculum itself is a disintegrated mess.

I’ll mention one more point where educators have some partial understanding but still manage to miss the essential. And this is the big issue pertaining to the relationship between observation and theory.

Educators know that they can’t just talk about scientific theories; the student also needs the relevant observations and experiments. In fact, many science classes seem to put a lot of emphasis on observation and experiment. So, you ask, why do I still insist that their presentation of theory is rationalistic and based on authority?

The answer is: Because they don’t arrive at the theory from the observations and experiments. The observations and experiments are shown to be compatible with the theory, they concretize it, they illustrate a few of its applications, but they certainly don’t provide an inductive proof of the theory. Remember, I can cite hundreds of observations that are consistent with Ptolemy’s theory, even though many aspects of the theory are wrong. Without the inductive approach, the student can never be in a position to say: “I know from my own first-hand knowledge that this theory is true.” And the student never learns the method that leads to such knowledge. This is the proper goal of science classes, and the inductive method is the only way to achieve it.

Finally, one more point before we wrap up. There are several elements that contribute to a good science course. Obviously, it helps if a school has the money for good facilities, equipment, and an occasional field trip. More importantly, it makes a big difference to have a good teacher—a teacher who is knowledgeable about the subject matter and enthusiastic about teaching it, and who is good at interacting with the students. We all have memories of our favorite teachers, and we know how much they contributed to the learning experience.

Nevertheless, my point is this: A teacher cannot make up for flaws in the curriculum. Give a bad curriculum to the best teacher in the world, and what you get is a bad course. The students come away with floating abstractions and disconnected items of knowledge, rather than coming away with a proven, integrated theory and deep insight into method. There is no way around this. You can call it the primacy of curriculum principle (although the PCP acronym is unfortunate).

I’ll give an example from my own experience. At my high school—many, many years ago—the best science teacher taught chemistry. He was very good; he knew a lot of chemistry, he loved teaching, and he was very likable. But, like all other chemistry courses, the structure of his course followed the standard, deductive way of presenting chemistry. It started with the periodic table of elements and lessons on atomic structure; in other words, it started with the fundamental theory, and then the experiments illustrated aspects of the theory. I didn’t have a clue where the theory came from, so the ideas were floating and disconnected.

A good teacher can find ways to improve the presentation, but it isn’t the teacher’s job to start from first principles and figure out what to present, in what order, integrated by what means, etc. That is the job of the curriculum developer. It’s a different job that requires a different set of knowledge and skills. The teacher is dependent on the curriculum developer. The basic problem with science education today is the curriculum, and the only solution is to develop a brand new, inductive curriculum. A school can buy the best equipment and hire the best teachers and still have a lousy science program. Think of it this way: It’s like a baseball team with lousy pitchers and lousy hitters; you can’t solve the problem by building a new ballpark and hiring a great announcer.

I’ll end this course with a comment on the big picture. Over the past decade or so, based on what I’ve learned about induction and its application to science education, my perspective on how to bring about a radical improvement in the culture has changed.

The key to improving the world is people using their capacity for logical thought. But what is logical thinking? It consists of two processes: induction and deduction. But people don’t have any major problem with deduction. In fact, some very bad ideas have come from people who were very good deductive thinkers. Deduction isn’t the problem. When we say that we want people to think better, what we really mean is: We want them to properly induce their generalizations from the observed facts. And, in essence, that is really all we mean.

But herein lies the catch. High-level induction—the process that leads to abstract generalizations in philosophy, business, politics, and science—is complicated. Keeping one’s abstract thought integrated and connected to reality every step of the way is difficult, and most people know little about how to do it. This is the root of the problems we face today. There are many other problems one can point to, but this is the problem that leads to all the others.

And let’s be clear what the problem is. I’m not talking about people accepting bad ideas because they evade thinking about the issues. Evasion is a real and destructive phenomenon, but the world would be in better shape if that were the main problem. Most people honestly try to arrive at correct conclusions based on the facts; they just aren’t very good at it. Why not? What stops them? The problem is that their automatized method of thinking is flawed.

As adults, we do not have direct control over our basic method of approaching issues. We have a certain style of thinking that we automatized during our formative years. To some extent, adults can change their method, but only by years of effort, and few adults have that kind of time and motivation.

This is why we have to reach people during their intellectually formative years. And by “reach” them, I don’t mean give them lectures on epistemology. That is much too abstract and it doesn’t have a deep, lasting impact. We have to reach young, developing minds by showing them examples of proper inductive thinking day after day, year after year. They have to become masters of certain topics where they have grasped the entire chain of reasoning that leads from observations to broad, abstract conclusions. Then they know what a logical argument is and what real knowledge is. Once they understand that, and their own minds function in that way, they will be invulnerable to the nonsense that sometimes passes for argument today.

That’s why Tom and I created Falling Apple Science Institute.