Teaching Science Inductively- Part 2
By David Harriman, historian and philosopher of physics
“The curriculum should not artificially separate 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. ””
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.
If a topic is covered, it should be covered in the depth required for real understanding. So the curriculum developer 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. These theories provide an objective 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 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 should be done. The curriculum should not artificially separate 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.
There is one more key advantage to the inductive approach that is worth mentioning here—one more crucial integration that is 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.
