"there is an inductive logic of discovery. And the way to make science intelligible and fascinating is to present the discovery process."
We gain knowledge by an inductive discovery process. Whether we consider the scientific genius who first made a discovery, or the student who is learning about it, the process is essentially the same. It begins with observations and low-level concepts, and moves by means of experiment and mathematics to higher-level concepts, generalizations and theories. Every logical step of the way, the discoverer must integrate the new evidence within the total context of his knowledge.
Perhaps this sounds obvious. Nevertheless, it took me a long time to understand it. And here is another obvious fact: today, nobody teaches science this way.
It is very challenging to teach science inductively. The curriculum developer must have in-depth knowledge of the historical discovery process, and thus of the factual basis of the relevant concepts and generalizations; he must think of ingenious ways to condense and simplify the enormous range of material; and he must present the material as an integrated whole, continually making connections between current and previous material. Nobody will go to all this trouble unless he is really convinced that it is both necessary and possible. And most people don’t believe either one—that it’s necessary or possible.
First, let’s consider the typical views about whether it is necessary. Today, the majority of educators believe that they can simply tell young students about the advanced conclusions of scientists, and if the students can repeat back what they have been told then they must understand it.
For example, first-graders are told about the correct theory of the solar system. They have a model in their classroom with the big fixed sun in the center and all the little planets—including Earth—revolving around at various distances from it. They learn the names and the order of the little balls that go around the big ball, and then they supposedly understand the solar system.
Now, imagine that I replace that correct model of the solar system with a different model depicting Ptolemy’s geocentric theory. The big Earth would be stationary in the center, and the moon, sun and planets would go around it. The model could be constructed so that each planet revolves in a smaller epicycle while orbiting the Earth in a bigger circle. The students would be able to memorize this model as well as they memorized the other one. Would they believe this geocentric model? Yes, of course; they would believe it for the same reason that they believe the heliocentric model—because the teacher told them so. Since they are never presented with the observational evidence and the reasoning, they have no choice but to passively accept the ideas on the basis of authority.
Here’s another example: If you pick up an elementary school textbook and turn to the chapter on matter, you are told on the first page that matter is made of atoms, and you see a drawing of a nucleus with electrons swirling around it. The students look at the drawing and then they supposedly understand the atomic theory of matter.
This approach to teaching science reminds me of an old movie called Time Bandits. There is a scene where the Devil is explaining how God did everything backwards and botched the whole creation process. God wasted his time creating things like worms and snails. The Devil says he would have done things very differently, and then he gives an example. He shouts out: “If I had been in charge of creation: Eight o’clock, Day 1—Lasers!” This is essentially how science is taught today. Maybe they don’t cover lasers until Day 2, but you get the idea.
And I hope you see that such an education is empty. It is just passive memorization of disconnected ideas, with no real understanding of content and no insight into method. As a result, most students are bored by science and they drop out as soon as the classes become optional in high school. We live in the wealthiest and most technologically advanced country, and we spend more money on education than any other country. Yet studies have shown that the United States rates below many third-world countries in science education. This is not just embarrassing; on the surface, it seems to be bizarre.
But there’s no mystery here. We are currently teaching science by a superficial, authority-based method, where the laws are just stated out of context as “thunderbolts from the blue.” It is interesting to note that the progressive educators, who give lip-service to method, are every bit as guilty in this regard as the old classical educators. To the extent that the progressives teach content, they present it as dogma that comes from nowhere and must simply be accepted on the basis of consensus. They are forced into this position because don’t understand or accept the logic of the inductive discovery process.
This raises the issue that I mentioned earlier: many educators have been influenced by the idea that it isn’t possible to teach science inductively, because there is no logic to the discovery process. Scientists just make guesses and sometimes they seem to get lucky. So what else can the teacher do other than simply present the guesses that have been accepted by the majority of scientists?
But there is an inductive logic of discovery. And the way to make science intelligible and fascinating is to present the discovery process—that is, to guide students on that logical path that leads from observation to theory. Then science becomes a detective story, and the students themselves raise the questions before they get the answers. By following the logic, sometimes the students are even able to anticipate the answers. When I teach science by this method, sometimes the students grasp the implications of the evidence they had already seen and beat me to the next major discovery. When I was explaining the experimental discoveries in chemistry that led to the atomic theory, one student anticipated Avogadro’s law by asking: “Don’t these results imply that equal volumes of gases have the same number of molecules?” And when I was teaching electricity and magnetism, one student anticipated Ampere’s next discovery by asking: “Don’t these results imply that two electric currents should exert a force on each other?” When a student grasps the law himself, and he has the full context to recognize why the law is important, then he doesn’t need to memorize it for a test. He understands it, and he has that understanding for the rest of his life.
For a teacher, this is the ultimate reward. This is what you work for—to see those “Eureka!” moments where the student makes the connection and grasps why it is so important. But such moments don’t happen unless the material is taught inductively. When the child is merely shown a model of the solar system or a drawing of atomic structure, he has no way to connect the model or the drawing to observations of the world. There is nothing he can do except shrug and say: “Well, okay, if you say so.” That is not a “Eureka!” moment.
Notice that the inductive approach offers one solution to all the problems that plague science education. Do you want the student to have a real understanding of the ideas, and not just floating abstractions? Teach the discover process—and the student will get all the essential facts that the abstractions are based on and refer to. Do you want the student to gain a deep understanding of method, and not just memorize the content? Teach the discovery process—that is the method. Do you want the student to be excited about the subject? Teach the discovery process—and the student will have the context that makes the material fascinating, and he will see science as a story in which brilliant minds such as Galileo, Newton, Lavoisier, and Darwin are the heroes.
The inductive approach also solves another problem in science education: The problem of selecting the content. There are countless facts about the world around us, but a random presentation of facts is not an education. So which of these facts should be taught?
The non-inductive approach leads to the view that anything and everything can be taught. If the curriculum developer has no appreciation of hierarchy, and he omits the discovery process, then there are no limits to what the student may be told. At 8 o’clock on Day 1, you can tell him about lasers, about superconductivity, about the molecular structure of DNA, about quarks, about black holes, about the big bang theory, about global warming, and about ten-dimensional space. Some of these ideas are proven and others are hypothetical at best. But without the evidence and reasoning, there is no way to make the distinction. Anything and everything can be covered very quickly. It’s MTV-style science: lots of colored pictures and rapid changes of topic.
The curriculum we are developing at Falling Apple Science Institute is very different. If we cover a topic, we cover it in the depth required for real understanding. So we must be selective about choosing the topics. They must serve the purpose of eventually leading to the proven theories that are essential to a basic science education. Our curriculum is theory-based, and the theories provide the standard for selecting the topics.
A proper education in science should provide the student with a thorough understanding of six theories: the heliocentric theory of the solar system, Newtonian mechanics, electromagnetism, the atomic theory of matter, plate tectonics, and the theory of evolution. In each case, the student needs to grasp the entire inductive process that goes from observations to proof of the final theory. If the proof of a theory requires integrating discoveries in different sciences, then that’s what we do. We don’t compartmentalize the sciences, separating astronomy from physics, and physics from chemistry, and geology from biology. Such compartmentalization rules out the possibility that the student will ever be presented with the proof of a fundamental theory. For instance, one can’t prove the atomic theory with chemistry alone or physics alone; it’s the integration of the two that leads to proof. When chemistry and physics are taught in separate classes, students never see the proof.
This approach provides the educator with an objective standard for selecting content, and it provides the student with scientific knowledge that is integrated, not separated into a bunch of different compartments.
There is one more key advantage to the inductive approach that is worth mentioning here—one more crucial integration that is almost entirely missing from typical K-12 science classes. And that is the intimate connection between physical science and mathematics.
At the early concept-formation stage of the physical sciences, not much math is required. There are many interesting facts about the world that elementary school students can grasp without mathematics. But as soon as one gets to the stage of discovering laws and theories, mathematics is absolutely essential. The point isn’t merely that the final laws are expressed mathematically—more than that, the reasoning that leads to the laws is mathematical. Teaching the scientific discovery process provides a great opportunity to teach math the way it should be taught—not as a Platonic realm of floating abstractions, but as the method that enables us to understand the world we see around us.
I’ll give you an example. When I was in high school, I took a trigonometry class. And here is what I got out of it: For some inexplicable reason, there are people who like to study three-sided figures, and these people have derived lots of theorems about such figures. And the tragic result of this strange activity is that students now have to memorize all these theorems.
Of course, the real tragedy is that I missed the whole point of the subject. Normal people don’t have any intrinsic interest in three-sided figures. But they are interested in the world around them. They want answers to questions such as: How big is the Earth, and the moon, and the sun? How far away from Earth are the moon, the sun, and planets? What is the height of that mountain? How big is France, and what is the distance from Paris to Berlin? Trigonometry is the method of answering these questions—it was developed in order to answer such questions. But that is not the impression that is conveyed to students today.
Mathematics is the science of relating quantities, and it enables us to measure some physical quantities and then calculate others. And because we show students how scientists arrived at their conclusions, rather than just stating the conclusions, we necessarily go into more depth about mathematics. The student develops a real understanding of math and its connection to the world. And as a result, math becomes much more interesting.
I’ll use Kepler to drive this point home. At the high school level, the usual way of teaching Kepler is just to state in words his three laws of planetary motion. The student isn’t even presented with the algebraic equations, much less the mathematical process of discovering the laws. But Kepler’s discovery process is a great way to teach trigonometry. He used trigonometry throughout the process, thinking of ingenious ways to calculate relative distances from measured angles. This is the way to learn math—by seeing how brilliant scientists discovered the nature of the universe.
Today, the way that science is taught indoctrinates children to passively accept floating abstractions and blindly submit to authority. They are not provided with the method and the knowledge that would enable them to become thinking individuals.
Imagine a high-school literature teacher who tells the students: “Our topic today is Cyrano de Bergerac, which is a great play that you don’t have to read. I’ll just summarize it for you. It’s about a man with a big nose who falls in love with a beautiful woman, but he doesn’t tell her and then he dies at the end. The theme is that even if you’re funny-looking, you shouldn’t worry about it too much. Remember that—there will be a test question about whether funny-looking people should feel bad.” With such an approach, the tremendous value of the play is completely omitted. Nobody would teach literature quite this badly—but nearly everybody teaches science this way. When they leave out the inductive discovery process, they eviscerate the subject—and students are left with empty dogma to be memorized for a test.
Our children deserve more than this, and our future depends on giving them more. If we want to create a better world, we must teach the next generation how to think. And that means teaching them how to reach generalizations from observational evidence, and thereby freeing them from dependence on authority.
That is what we are doing at Falling Apple Science Institute.