I recently woke up with a troubling thought. I took a year of Physics at an excellent private school and a year of Physics at an excellent college. But today I don’t know any Physics!!?

The only Physics I know now are things I learned in my general reading--bits about Einstein, the Big Bang, cosmogeny. But the stuff they taught me during those two years? I hardly know a bit of that! Similar story in Chemisty. Biology is almost as bad. Calculus is a zero. These realizations are both distressing and revealing. They prompted me to think again about how most schools teach most subjects shallowly and temporarily. It’s a cliche, isn’t it, that people look back at high school and shake their heads and say, “I don’t remember anything I learned.” So how do we create more efficient, more ergonmomic courses? I think the sciences, precisely because they are difficult and tend to vanish without a trace, are a great place to investigate these questions. Here’s another way to state the goal: how do we construct courses so they leave really large traces?

After this big build-up, here is the small gist I have to suggest: start slowly, explain the basics in e-l-a-b-o-r-a-t-e detail, build a much wider and deeper foundation than is normally done. Make sure the children, especially the not-so-academic children, are comfortable with (and master of) the fundamental concepts that the course will be built on. This approach -- starting slowly and picking up speed later -- will pay dividends. Is it not obvious when you think about it?

But go on the internet and look at some supposedly easy approaches in any subject. You’ll be amazed to find that many writers jump in the middle of a subject and never look back. They lose me on the first paragraph sometimes. The problem with a lot of textbook writers is that they’ve spent their entire life on one subject, and they often start off arrogantly, as if, hey, this is easy, come on, keep up. I’ve often thought that the very worst person to design a course in Physics or Chemistry is a guy who’s an expert at Physics or Chemistry. This person thinks the basics are too trivial to bother with. This person is impatient to get onto the good stuff. This person is very likely  to start in the middle of Chapter 3, because he will think of it as Chapter 1 because it’s so easy for him. In short, better to employ clever and theatrical amateurs to design courses. The brilliant experts can check facts and make sure there are no mistakes in the presentation.

PRE-START

Here is an example of something worth lingering over in General Science: the distinctions between animal, vegetable and mineral. You really can’t go wrong making kids think about this. Perhaps for a whole week. So that at the end they can walk around the classroom and look at every object and say which category it falls in and why. So they can walk outside and point at every object and say what it is. This is actually profound scientific thinking. A few thousand years ago nobody on the face of the planet could have pursued these distinctions very far. Similarly, the first few days of Physics, etc. might be spent entirely on the distinctions between Biology, Chemistry and Physics. Which objects, which processes and which questions tend to belong in each subject? Students should be able to explain why the hair on their arms is one or the other. Or does hair belong in two categories? And if the wind is moving it, does hair then belong in three categories? Let’s say there is a big pile of dirt in your yard. What would the Biologist see? What problems would the Chemist want to solve? What questions would a Physcisist ask first about that dirt? I hope you see my point here. It’s fairly easy to use and manipulate these categories and distinctions. It’s also fun. It’s also extremely instructive for the budding scientist. This manipulation is possible only with true scientific thinking. And scientific thinking is the whole point of taking science courses. At the end of this exercise, students can say: oh, now I know what I mean when I say I am going to study Physics, etc. I can assure you that nobody ever made me deal with these distinctions. It’s only now looking back that I find the divisions between Biology, Chemistry, and Physics to be profound and as well delightful. Wow, it’s almost poetry.

THE FIRST RULE

Now, to state the general principle, I think the goal is to find the quintessential events, the MOST elemental situations, that each given field deals with. Let’s say, for example, we want to teach electricity (as part of whatever course). The simplest thing I can think of is the flashlight: you have power, you have a primitive circuit, you have a resistance (i.e. the bulb), and you have an on-off switch. My point would be that you could spend DAYS on the flashlight. Learn the symbols and how to draw the circuit. Build different versions. Add a new feature each day. A second bulb--series and then parallel. A rheostat. Over and over, going over the same ground in different ways, so that when these kids are in nursing homes, they’ll still be able to build circuits in their minds.

CHEMISTRY

So what, for example, is the quintessential situation in Chemistry? Here’s what I came up with: a glass container filled with distilled water. There is nothing more elemental than this. The chemist must be able to prove that in fact it is or isn’t water. You can then put things in the water--salt, sugar, pepper--making mixtures and solutions. Then you try to take these things out of the water--filtering, boiling, paper chromatography. You start with pure water, you come back to pure water, you prove it is or it isn’t. How does a chemist really know? Over and over, you ask Chemistry’s basic question: say you’re looking at a clear liquid, how would you prove that the liquid is water? You start talking about smell, taste, viscosity, flammability and all kinds of things because Chemistry is very much an empirical science. Thousands of people worked millions of hours accumulating databases of information about elements and compounds. Some substances are granular; some have a distinctive color; some dissolve in water, some don’t. So students see that each Chemistry problem is a kind of puzzle or mystery: evidence points one way or another. (Also, I think Chemistry is a lot like learning to cook meals. You have recipes, so to speak. You do certain steps, and you do each one in a certain way, and that’s because many people have worked at finding the best way to prepare each “dish.”) My sense is that you could stay with water in a glass container for a week at least. Adding complexities, taking them out, solving them, introducing a new term, then a new procedure, then a new piece of equipment, looping outward but coming back again and again to the wonderful purity of the first question: how do we know this is water? The pretty part is that all of this is real Chemistry. Then, the class might spend a day on what it means to speak of H2O. How you put H and O together, how you take them apart. Then a few days on salt--and what it means to speak of NaCl. And what it means to speak of NaCl “dissolving” in H2O. When does someone really know what they’ve been taught? When they can teach it. Ideally, in the first few weeks, Chemisty would be reduced to its beautiful atoms, and these would seem to be so simple, so easy, that all the students would feel they could explain everything to their friends.

PHYSICS

Now, to return to Physics, I think the fundamental need is to focus for a week or several weeks on the fundamental things which Physics deals with, for example, mass, volume, weight, and speed. How do we measure anything?  Where do these units come from? How do we figure out the volume of something? And speed? Sure, we are sitting in a car, we can look at the speedometer and know how fast we are going. But suppose you are watching the car from outside. How do you figure out how fast it’s going? My point is that adults are at least familiar with these concepts, but I’m not sure they actually understand any of them. But when we’re talking about children, we have to deal with the fact that the words are almost empty sounds. Volume? That’s how loud music is, right?   So what are the central problems of Physics? Consider a pool table with only two pool balls. One moving ball strikes a stationary ball. What happens? Why? Just creating a vocabulary to discuss this problem is a big step. Then you figure out different ways to ask the question. Or if you are talking to teenagers, it might be helpful to focus for a day on this crucial moment: a car is going north at 60 miles an hour, another is going south 30 miles an hour, and they hit each other head on. What happens? Why? These are not rhetorical questions; I don’t know the answers. As I admitted I can’t do any Physics. But what I do know is that these are the fundamental issues that Physics deals with. And the teacher should pull students more and more deeply into this sort of problem.  Another basic problem, e.g., is a refrigerator that is on the street. You want to move it to the second floor. What are the easiest ways to do this? Humans have been struggling with precisely this problem for 50,000 years, ever since they had a floor higher than ground floor. I vaguely suspect that half the Physics that most people know can be taught in this dilemma. Which is simplest to make--an inclined plane? Or something using a fulcrum or a pulley? In any case, teachers would extract like juice from an orange every last drop of knowledge or teaching that could be found in each of the proposed answers to this problem. Why not stay with this problem for days or even weeks? Eventually, you would reach every possible way to move that refrigerator upstairs. What about hot-air balloons? I think the worst thing that happens in some courses is that they jump ahead and become a blur. It’s as if you’re driving through some beautiful countryside, but the car is going 70 and you’re not having any fun and you’re not seeing very much. What you remember years later is your terror that the fool at the wheel would crash the car. Sometimes when writers try to be more ingratiating, they end up insulting the audience by making everything sound airy and  empty. For example, I encountered this: “We are surrounded every day by events that Physics can help us understand.” Please, no empty generalizations. What events? Name three that are interesting and representative. Then we want to zoom in on the essence of those “events.”

BIOLOGY

Biology is the study of life (bio being Greek for life; and logos being Greek for truth). So give me 20 examples of “life.” Good. Now here is a list of 40 things. Mark which are “life” and which are not. See how basic this is, but also how reassuring. Suppose we are going on a journey. Isn’t it comforting to know which cities we will see, how we will travel, why are we traveling at all, and do we have enough money to pay for it? Point is, first things first. Get oriented. I’d say that every course must to some degree be a seduction: the students are drawn into it, they are made to feel comfortable, they are sold on the idea of bothering with this course. If the teacher is really good, the students start to think that the course might be easy. It might actually be fun. At this point they scream “Geronimo” and leap from a plane. Airborne all the way. Note: the Army accomplishes this miracle all the time. You’d think a lot more schools would figure it out. I would propose that biology’s central event is the cell. Aside from being very small, typically microscopic, the cell has three epic traits: it’s alive; it’s working very hard to stay that way; and it’s blindingly complicated.    Cells are fascinating. Every course in biology should spend a week on the cell; maybe a month is better. Life on planet Earth didn’t really start cooking until the cell evolved. This story itself is totally fascinating. That the cell can reproduce itself is fascinating. That this invisible thing contains trillions of molecules, all ingeniously arranged to accomplish hundreds of task, is endlessly fascinating. Then you have the story of cells forming larger colonies and eventually multi-cellular plants and animals, where the organs might themselves be viewed as multi-cellular organisms. People like to talk about which is the most amazing organ in the human body--the eye, for example. But my money is on the fertilized egg cell, where we all begin. Because this thing, although microscopic and close to being a mere speck of jelly, somehow has instructions in it on how to build an eye! No story is more amazing than that. Then when the course moves from cells to large animals, it might be good to pick an organ and focus on it as a way of studying all the others. For example, the brain is a popular choice, a subject you can never exhaust. But I’ve been thinking a lot about skin recently. It is, as Trivial Pursuit players know, the largest organ in the body. It is also plainly visible and you can touch it and play with it. You can grip that fold next to the thumb and know exactly how thick skin is. Perhaps the equivalent of 8 or 10 sheets of paper. It would be good to find the exact equivalent, because when you study the details of what is going on inside skin, right before your eyes, you have to be continually amazed at the complexity built into this stuff. For example, there are oil glands, sweat glands, and hair follicles. Skin has heat sensors, cold sensors and pressure sensors. Skin can, of course, rejuvenate itself, as everybody knows from personal experience. But the most startling thing I’ve read in years is that every hair has its own muscle, and its own nerve, and that’s how fear and cold can make hairs stand up! We’re talking about tens of thousands of tiny muscles, just waiting around for those special occasions. Point is, the typical course will give an equal amount of time to each organ; but I suspect the best way is to cover most organs in a day and then go crazy with details and depth about the eye, the brain, or the skin.

CALCULUS AND SUCH

To start the study of something like geometry or calculus, first lay out the terrain for the students. Show them the kinds of problems that early humans were faced with. Why did somebody need to invent geometry? Or calculus? Or trigonometry? You try to take the students as far verbally as they can go. For example, as a rocket travels, it’s using up fuel. It’s getting lighter. Will that affect its speed? Yes, and that’s exactly the moment you want the students to focus on, and think about, and talk about. Yeah, that thing weighed 10 tons, but it’s slipping towards 9 tons. Hmmm. It’s going to go faster or it’s going to get better mileage. Something’s got to change. What you would be doing here is letting students travel down the same road that Newton traveled down. Getting them to struggle with these questions just as Newton did. Then you reveal bits and pieces of his solution. You ease them into some of the terminology. Keeping students focused on what might be called the central problems of calculus is the pretty part. Here is a funny aside. Years after I was gone from college and had forgotten any little bit of calculus I ever knew, I read somewhere that calculus was all about finding the area under a curve. And I immediately thought: of course. Exactly. I get that. You just divide that area up into lots of little slivers, and add them up, and you’ve got the area. I even had the fantasy that were I in prison for a year, I would be able to invent calculus for myself. In fact, I still don’t know how to find that area. I don’t know what a differential is or an integer or any of the rest of it. But I know that I, not that good at math, can grasp the essential problem and take a certain amount of pleasure in trying to figure out how to solve the mystery. There was a point, way back there, when Newton and Leibnitz were just like me: they couldn’t figure that area either! I looked on the Internet for supposedly easy approaches. One starts this way: “Objectives: The basic object of study in calculus is a function. DEFINITION: A function is a rule or correspondence which associates to each number x in a set A a unique number f(x) in a set B.” Isn’t that just peachy? The writer has no sense of humor or he’s actually a sadist. He’s also the poster boy, by my nomination, for everything silly and slow in education. He thinks he’s being so precise and scientific. What he is actually doing is making sure that only the smartest students can follow his tune.   I had a distinct epiphany when studying geometry in the 10th grade. They were making us study a new theorem each week. I knew even then that I would never be able to recall these things after the course was over. And I had this sort of longing for the proof that I thought was most beautiful: the Pythagorean theorem. I remember thinking that the teacher should come back to this theorem several times and force us to memorize it, so that everyone could write it years later. In other words, instead of 20 proofs once over easy, better 18 with a real devotion to one or two. So that this most perfect of theorems, the one about the hypotneuse of a triangle, would be a permanent treasure, like a piece of poetry that you don’t want to have to memorize, but you are so glad you did.

IN GENERAL...

Courses should focus on what might be called the high points, the beautiful moments, the exquisite truths within each subject. And not try to cover everything quickly, evenly and superficially, but really move inside those premier moments, so the students will own at least a few of them forever. Here’s a completely different way of solving the organization of a course. Let’s divide the course into 100 bits. Then we arrange those bits in a strict sequence from EASIEST to HARDEST. Then we start with the easiest. Isn’t that pretty? It’s amazing how many courses and books will toss aside a wheel barrow full of simple stuff and somehow jump right into something difficult. Please don’t do that. If I’m reading that book, I’m going to be screaming, hey, what about all that easy stuff, why don’t you start with that? You are making me feel dumb and I hate that feeling. I think most people hate that feeling. Another way would be to arrange those 100 bits in a sequence from MOST INTERESTING to LEAST INTERESTING. That would work. Now suppose we merge these two decks, and then we could  start with the items that are both Easiest & Most Interesting. This would be the ideal, I believe, and I would like to dub this approach PPP1 (Price’s Pedagogical Principle #1). And what is the purpose of all these thoughts? That students should not only understand material, but own it, take possession of it for life. Another word for all this is mastery. A lovely word, and a lovely goal.   Astonishingly, the Education Establishment actually has the nerve (in Reform Math et al) to dismiss mastery in favor of something called spiraling. As they practice it, spiraling out of control is the basic idea. Spiraling is everything I’ve been mocking in this article. Spiraling is careening around a room looking for a few minutes at each object in the room. Whereas I suspect the best way is to stand in one spot and wallow -- yes, wallow-- in intense appreciation of the most interesting object in the room, then the next most interesting, etc. On the other hand, if you learn something well, and then come back to it next month or next year, that's good. But the "spiraling" promoted by the geniuses in Reform Math recommends moving quickly from A to B to C, without having mastered A or B.     Nor should anything in this article be confused with Constructivism, where students are encouraged to find their own truths. Teachers are supposed to stand in the back of the room and murmur occasionally. No, the teachers I have in mind are experts in their subjects. And they deserve to be hailed as the sages they are. Naturally, they should hold forth on stages. Such teachers are not encouraging students to find their own tadpole truths, but cunningly leading students to a full appreciation of the best truths that the teachers know after many years of study.

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