Tuesday, June 10, 2008

A View of Pedagogy

[Bumped and dramatically restructured.]

Current pedagogy has been a disaster for schools. Dewey's epistemology leads to the pedagogy of hands-on experiments and denies that human minds can learn from anything other than doing and deciding. Rousseau's intrinsicism meant that he didn't really think teaching was necessary. Neither man captures how humans learn and what we need to do as teachers in order to effectively teach concepts.

Science in particular suffers from Dewey and Rousseau's beliefs. Dewey is why we have science experiments that don't actually teach anything. Rousseau is why people think kids will learn just from exploring outside. Children see science as baffling and boring using these techniques. I concentrate on science here, but each subject fails in this regard and benefits from the following approach.

Any learning done from books is set up to be as magazine-like as possible. Snippets of information here and there presented in a colorful way and always trying to appeal to the student through applications. These fail because there is no hope for the student to get a good grasp of the big ideas when they're broken up and removed from the work that supports them. The students know that, too. That is generally when they begin to feel lost and that science is just a game of trying to figure out what is on the test--if they even care enough to bother. No pretty colors or reference to pop culture is going to fix an out-of-context idea presented without a firm basis for understanding.

A different pedagogy is needed. There is a pedagogy that is much closer to how people learn. Lisa VanDamme (the founder of the renowned VanDamme Academy) does a wonderful job explaining the pedagogy here. The pedagogy relies on what is known as the hierarchy of knowledge.

The hierarchy of knowledge is how babies learn about the world around them and, historically, how scientists discovered the great truths we know now. They both begin by looking around and observing. Then they experiment. From those experiments they can draw conclusions about how the world works. That process starts with concretes and moves to abstract concepts. Babies don't usually have to go further than that until they start school. Montessori mathematics is an excellent example of using concretes and moving to further and further 'big ideas' (concepts or abstractions) after having a firm grasp on the perceptual level.

The hierarchy of knowledge can be applied to every study in school, moving from concretes (like nouns and verbs) to higher levels of abstraction (grammer and sentences) and once those are mastered, then even higher levels (like paragraphs and then essays). One would think, for science, I then advocate for starting with atoms and then moving to molecules and reactions. After all, that moves from smaller to larger like words to essays. Incorrect. The proper hierarchy is from concretes and the perceptual level to concepts and then more advanced concepts. Atoms are not directly perceived, they are, in fact, a very high level abstraction based on numerous observations--each one moving further from the directly perceivable and relying on each experiment that came before.

Students should be shown the path science took to understand the most abstract of principles, starting with the earliest investigation. Anything less would rely on telling students to believe it for no reason other than that the teacher said so. That would make for a poor scientist (and even worse, a poorly reasoning adult who accepts what others say without question). In science in particular, all truths should be evidentially supported. As Roger Bacon stated, only evidence can reveal the truth--not argument to an authority.

Let's talk about the typical learning experience. Have you ever heard in a class, or read from a book, some conclusion and thought to yourself "How could they know that? They could have just guessed that. Maybe they had a lucky guess that hasn't been proven wrong yet." I certainly felt that way a number of times in high school. For instance, when the teacher told us that everything really just consisted of tiny little particles with a lot of space between them even though the desk looks solid and hard.

That kind of information is called a 'floating abstraction.' It means you've been given the idea by someone else (you read it, or heard it) but because you don't know how anyone figured it out, you have very little actual knowledge of what it TRULY means. You just have that name with the definition taking up brain space but you don't have a deeper understanding. Even if you can solve your homework, you're working with a handicap.

What if, instead of just being told the final idea of atoms, you actually read or learned about the experiments done that prove their existence?

A philosopher, Zeno, introduces a puzzle. Zeno's Paradox questions how anyone can ever arrive anywhere if they always have to move half-way first. Wouldn't we then just have an infinite number of half-way steps? Democritus thought that had to be false and posited the idea an unbreakable bit of matter--it couldn't be halved--called the atom. Hero of Alexandria discovered that air is something, not the absence of things, by proving that water would not rush to fill up a glass lowered, inverted, into water. Hero thought that the atoms in solids and liquids touched each other and that's why those objects were hard and that the atoms of air had space between them. Hero thought that air could be compressed. Robert Boyle proved Hero's assertion.

In chemistry, evidence for atoms became more convincing. Antoine Lavoisier, a chemist in France, proved that reactions in a closed container do not lose or gain mass. Joseph Louis Proust, also a french chemist, showed that materials combined in chemical reactions in only specific ratios! John Dalton took both of those results and formed the Theory of Atoms. If chemical reactions maintained mass, then nothing is gained or lost, so atoms are not gained or lost--they are unbreakable. The proportions that Proust discovered also worked if atoms could combine with only a certain number of other atoms. Dalton put those ideas together--he was the first to support the atomic theory with enough evidence to convince other scientists and is rightly given the proper credit for it. More work is done to discover atomic weights and use the atomic model for determining how molecules are formed (which I will not go into here).

Still, very little was known about what an atom might be. We have an entirely different field to look at, the study of electricity, to help learn about the structure of the atom. Since learning of the strange property of matter that became known as electricity, scientists formed the theory of an electrical fluid moving from one substance to another (that's how we got the term 'current'). JJ Thomson was the first to prove, experimentally, that electricity is actually a kind of radiation, a part of matter leaving one substance and moving to another. He had electricity flow through a tube from which all air had been removed (a vacuum tube) and thus any flow of electricity could not have flowed through anything. He then showed that he could bend this flow with a magnet--showing that electricity and magnetism are part of the same effect and the amount of curvature allowed him to calculate the actuall weight of this small, charged particle (a great recreation of that experiment at this link).

Now there was some evidence that atoms had small, negatively charged particles that could easily be removed. Ernest Rutherford did another test. He bombarded a sheet of gold with the electrons--most make it through, but some are stopped by even larger particles in the gold. Rutherford realized that most of the electron couldn't make it through if the atoms were packed very tight--there must be some space between them. And also there must be a large center to explain the electrons that got bounced away. Thus the nucleus of the particle is discovered. After that there are a few other experiments with radiation to learn about protons and neutrons (which I, again, will not address here).

Now if you've read this far, I'm guessing you already understand more about atoms and why scientists know they exist. Imagine what a child in a science program structured in such a way could know--not just guess, not accept because the teacher said so, but really know. We didn't have to recreate every experiment, just the essential ones that the next step built upon. Each higher level abstraction, culminating with atoms, is fully supported with understanding how that conclusion could be drawn.

The knowledge then becomes certain and supported. With that evidence we gain a more in-depth understanding of the concept itself. It's not just a guess. It was proven. We can understand ourselves how the conclusions were drawn.

Not only do we, and the students, 'get' the final concept we SEE HOW it was discovered. This puts a stopper in the debate of 'thinking skills' versus 'information.' There needn't be one without the other. We can learn how to 'think' by learning how brilliant, dedicated people discovered the knowledge we need to know anyway! Presenting information in a hierarchical (one discovery building on another) fashion means passing on the info AND a great example of thinking all at once. It isn't about redoing every experiment (though recreating the experiments becomes meaningful in this context--not just 'dumb show' like it is today with no context and no hope of really understanding the essentials).

The hierarchy of knowlege as a pedagogy is about understanding HOW we know what we know--not just having the big final conclusions memorized.

Also see this post about a college professor who also uses a historical context (which is naturally hierarchical in science) for his college-level physics courses. He has a different, and compelling, take.

Updated to correct many mispellings and type-os. Thank you!


Deb said...

A great set of books that takes you through scientific discoveries is Joy Hakim's Story of Science set: Aristotle Leads the Way, Newton at the Center, and Einstein Adds a New Dimension.

They're written for middle-graders through adult. They're jam-packed with all kinds of terrific information about this history of scientific discoveries and an explanation from a contemporary perspective of just what they are about. The books can be read in small chunks.

They are not quite appropriate for my 7- and 8-and-a-half-year-old, but will be soon. Definitely appropriate for any adult who wants to become more math- and science-literate.

Kim said...

Thanks, Deb! I've found a few truly adult books (http://kimsplayplace.blogspot.com/2008/05/research-heirarchically-based-science.html and a few kids books (by far the best: http://kimsplayplace.blogspot.com/2008/04/science-book-recommendations.html and also nice http://kimsplayplace.blogspot.com/2008/05/how-and-why-wonder-books-science-book.html) but I need something more like what you're talking about. Good for older kids and a nice compendium for adults. I'll check those out.

LB said...

A ha! I was just going to comment on your most appropriate post and ask if you had ever heard of these books. I just started reading Aristotle Leads the Way and I really like it. I'm trying to figure out how best to work my next year's science co-op around them as a spine (I'm not done reading them yet - but they do seem pretty good).

Let me know what you think of them if you get a chance to review them. I'd be interested to hear your take.

Kim said...

I just got the book from the library. I've read the first three chapters. I dislike the magazine-style layout of the book. It's written in a conversationaly way. I like how the author stresses the proof of science. Chapter 3 is no where near enough reading to make any sort of judgment. I'll write something more formal when I finish the whole book. Uh, someday!

Kyle Haight said...

In your Objectivist Carnival summary, you wrote "So if you feel so inclined, take a look and let me know how much I got wrong!". One thing leaps to mind immediately: the word is spelled "hierarchy". I realize this is a nitpick, but (1) you did ask, and (2) this is a personal pet peeve of mine.

Kim said...

Yes--I asked for it! And in the title no less. Embarrassing! I think I'll fix it now. Thank you. I hope the content (though not optimally arranged) does not embarrass me as much.

Kim said...

Apparently that misspelling is pervasive. Every place I use hierarchy I wrote it incorrectly. Now that's going to take some work to fix.