Thursday, January 05, 2006

Is High School Science Turning Off Bright Kids?

A NY Times contributor explained how the study of evolution helped make the seemingly random facts of a high school biology class into a coherent whole. This was picked up by the blogosphere and discussed on some biology blogs. Then at Uncertain Principles the topic was turned towards physics, where Chad Orzel explained how a student who is successful at high school physics can be in for a rude shock when he starts college physics. The limitations of teaching physics without calculus mean that there is more memorization of formulas in high school physics. Since it is not possible to derive the right formula without the benefit of calculus one must memorize when each formula is appropriate. Once these students hit college the problems become more complex and not every applicable formula can be memorized. As Chad explains:
You can spot those students in the intro classes, because they struggle mightily with dynamics problems-- all those damn frictionless blocks sliding on frictionless planes connected by massles ropes over frictionless pulleys. Again and again I get asked "What equation do we use for this?," and the answer is always the same: "F = ma." Those aren't problems that can be solved by rote memorization-- each problem is slightly different, and there's no finite set of equations that can cover all of them. What they require is knowledge of the essential concepts that let you break a complicated problem down into a few simple equations.
Meanwhile the brightest kids who do not want to memorize things get frustrated that they cannot see the big patterns. Some get turned off by high school physics and don't give college physics a chance.

Just yesterday, I ran into a similar problem while helping my daughter with her math homework. She is working on the graphs of polynomial functions. She was given two concepts to work with. The sign of the coefficient of the highest power tells you whether the graph becomes infinitely positive or infinitely negative as x goes to positive infinity, and whether the highest power of x is a even or odd power tells you what will happen as x goes to negative infinity. She was trying to memorize the patterns and I told not to. I explained why the rules worked. If x gets very large the highest power term dominated the polynomial, and that is why it matters whether its coefficient is postive or negative. For the odd or even power part I said just think about the simplest cases. For f(x)=x the function goes in different directions at plus and minus infinity. For f(x)=x^2 the function goes in the same direction for both plus and minus infinity.

She was somewhat frustrated that I was telling her something differtent than she had been taught, but today she told me that it helped her on her quiz.

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At 6:22 PM, Anonymous Kristin said...

It's a really tough conceptual leap going from primary school math to algebra, and it's another tough leap to go from mastering calculus to learning how to apply it to physics. This is on my mind a lot right now because I'm working on my essay for that "She's Such a Geek" anthology, but I struggled with abstraction the first two or three months that I took algebra--and I was in an accelerated math class for gifted kids. I was a preselected talented math student, and it took some time and patience for me to understand how you balanced equations. With a lot of patience on my dad's part I did figure it out, though, and from then on high-school and applied college-level math was pretty logical. (Proof-oriented math is a different story.)

As for physics, that's a whole 'nother level of complexity. Even though I had calculus down cold my freshman year of college (I'd taken calculus three years before, and didn't bother taking AP physics in high school because nobody could teach it well), it was still a lot of work for me to grasp how to frame physics problems. I didn't come to it with this understanding of automatically lining everything up against some invisible set of axes. That required practice and discipline, too. It's not easy.

I think the challenge is that some teachers are enamored of formulas and aren't entirely comfortable with the conceptual thinking themselves. So they can't communicate the proper analytical mindset that a student needs to develop to become a physicist or engineer or mathematician.

At 9:19 PM, Blogger Mike said...

I have been wondering about what should a nonscientist learn about science. I do not see any reason for them to spend a lot of time learning to do boring calculations. The fact that physics relies on math is very important but I doubt that mastering constant acceleration problems is what we really want the nonscientist to take away from his or her only physics class.

I am beginning to feel that the same is true of the high school student who may be interested in science, but does not yet have the math or lab background to do it right.

At 3:32 PM, Anonymous Kristin said...

Not everyone needs to know calculus for their future work, it's true. But I think the way of analyzing a problem, such as what are the directions of all the forces on those infamous weights and pulleys, is useful. How you take a confusing situation and break it down into its basic components to start to figure out what to do with it.

Maybe physics could be introduced as more of a "Contemporary Topics in Physics" format. Learn a bit about the equations behind things like scanning tunnelling microscopy or how radio astronomy works, going a bit deeper than a science book aimed at a broad audience would aim. The bright kids would look deeper and maybe want to learn more of the underlying math, and the others would at least have a layman's appreciation of the capabilities of science today.

At 7:39 PM, Blogger Mike said...

When I was teaching, one of my colleagues developed a freshman course in electricity and magnetism that used modern physics as the organizing principle. He talked about what the atoms were doing. For example they actually talked about electrons moving through wires. He then pulled in most of the traditional topics as they were needed.

I never got a chance to observe the class though, so I don't know how well it worked.


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