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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