Monday, June 28, 2010


I borrow the term ‘parsing’ from grammar:
To break (a sentence) down into its component parts of speech with an explanation of the form, function, and syntactical relationship of each part (The Free Online Dictionary, 2009).
In the sciences, the thing being parsed is not a sentence, but an experience or event. In class, I ask the students 'to draw what is going to happen next;' then I throw a piece of clay at the wall. It usually sticks. Representing this on paper is hard, very confusing, but very open and creative.

How would you do it?

Parsing would break such an experience into meaningful and analyzable 'components' or time intervals. Think about it a second: how would you draw everything that happened? Truth is, you can't. No one could. So, what do you do? You pick out the important parts, find where things change significantly, start making distinctions, make judgements about what to throw away. Bingo, the beginnings of scientific thinking.

However, most textbooks just jump right to the fictions: the ball instantly goes a constant velocity and then instantly stops. In truth—and students can easily see this—there is a period of acceleration while the ball is still in my hand, there is a period where it falls freely as it crosses the room, and there is some period of deformation. It might seem like this complicates the discussion, but I find that it clarifies it, makes it simpler to talk about, and the kids get quite engaged.

Passing along the tricks of the trade

The students can see where things change, but they grope for a way to capture it, to make it simpler. If they don't come to it themselves, I introduce the idea of ‘timestamps’ to parse the chronology of the event, and a standard tool of physics, ‘free-body-diagrams’, to help parse the relationships between objects. Math then becomes a great friend, a helpful language that really streamlines the conversation and enables thinking. We talk about who's pushing what, what direction, how hard, for how long. Student's typically find this kind of thinking fun, and excellence becomes breaking the world down into parts that are meaningful and can be analyzed with the math we know at that point.

The simplest things become fascinating

Another simple example of parsing for a class is analyzing the experience of pushing a toy cart a few inches with your hand and watching it slow down to a stop. I find this is very difficult for students, even the advanced AP Physics kids. Yet the exercise is very fruitful. They begin to bring up contradictions in their own thinking and begin to form real, workable questions. The 'granularity' of their experience becomes finer, and they realize they don't understand things as well as they would like to. Bingo: get curious, play, form a good question.


Pedagogy: the principles and methods of instruction. The main pedagogic difficulty is in keeping the teacher out of it while the students grapple with how to analyze the experience, and then, where to step in and give aid. Open-ended questions like “why did it slow down?” or “what made it move?” are baffling to students, but they tend to really enjoy the effort of figuring them out. They talk to one another. They get frustrated, confused.

'That's great.' I tell them. 'It's fine. That means you're really thinking.'

‘Formal skills’ vs. ‘formalizing skills’

This is completely muddled up in the science class, and I think it is disabling students… and beating them up.

What do I mean? Formal skills are what dominate learning and testing in school. The formalizing skills are where real inquiry begins. Formal skills are what Dewey called "dead knowledge, other people's knowledge." Formalizing skills are natural, born again in all children, and are the essence of engaging the world. Formal skills let us work within an idealized world. Formalizing skills let us build one and use it.

This diagram gives a schematic distinction between them:

The world of experience vs. an ideal world.

Why the two circles with the line between them? Scientists—all people to some degree—work in two worlds at once: an ideal world they represent with symbols, and the real world that they engage and experience.

The formalizing skills are parsing, modeling, and interpreting. These let people move between the two worlds. Parsing and modeling let a person create an ideal world, and interpreting lets a person use the ideal world to understand the real world.

Teaching people how to read the world as math

The hardest part in teaching science is getting a student to be able to look at nature and see mathematics. This is the bread-and-butter of any math-based science or engineering. In my opinion, it is not being taught in secondary science classes.

My position

I believe we can only teach this process, what I will call ‘formalizing experience,’ by presenting students with messy, fuzzy problems embedded in real, physical experience, and then by having them struggle through creating a mathematical formalism, a ‘model,’ to the problem. I believe teachers need to be careful in the language they use: they need to explicitly differentiate between the physical world we are describing and the mathematical models we use to describe and analyze it. Their choice of language can be disabling to their students, sending them back to scramble for the magic equation to fit the word problem.

What scientists do

How to answer this? I've found two ways, both useful.

Scientists describe, explain, and predict

Some science is just descriptive. Newton's famous mathematical model for the forces between particles of matter, his 'Universal law of gravitation,' is descriptive at heart. He tries to describe the forces between any two point masses. He was embarrassed and publicly ridiculed because it did not explain how two things could act on each other at a distance.

Scientists aren't embarrassed about that anymore. Supposedly, David Mermin, a Cornell physicist, explained the wild, mathematical excesses of quantum physics as 'shut up and calculate.' The theory described reality sufficiently to predict the outcome of experiments, to many decimal places.

Richard Feynman, the great theoretical physicist from Cal Tech, compared the big ideas of science to masturbation: OK as far as it gets you, but pretty empty. Put mathematics into it and it becomes like sex: now there is something to embrace and play with, reality.

Scientists play, pretend, and lie

I asked my high school students to make a cube out of clay and estimate how big it was, it's size. After getting over the fact that there was no 'right' answer, they came up with one, 'about an inch' or so.

Boom. Pretending. It wasn't a cube. It had twelve different lengths for the twelve different sides. No face was square. No face was even flat.

Somewhere in my wanderings through Nietzsche I ran across a quote something like this: "Truth, yes! But first we must lie." Nietzsche, in the 1840's, understood science. How can we describe the world without reducing it to a fiction, somehow.

Look up Indra's net. The Buddhists understood this. But they went in a different direction.

Scientific Method

A lot is written in the textbooks on science about scientific method. It's useless; worse. It's disabling. Gerald Holton has said, if you want to know how science works, don't listen to what scientists say they do, watch what they do do. Think of it as anthropology.

Here's what I think they do: 1) Get curious about something. 2) Play with it a while. 3) Ask a good question. 4) Design an experiment. 5) Do the experiment. 6) Answer the question.

This isn't something unique about scientists. Put something odd in a kids hand and they'll do this again and again, until they're satisfied. The institution of 'science' has honed this, concentrated it, funded it, and socialized it.

But school does not teach it. In fact, in my view, it kills it. Almost, perversely, on purpose. Why?