When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

## Sunday, March 4, 2012

One thing I noticed while talking with some freshmen physics majors is how few of them actually know how to use a physics book. I think it's due to how different high school physics textbooks are from university physics texts-- the high school texts are usually readable on a per chapter basis, as opposed to a text like Young and Freedman's or Resnick's.

It's also due to how low high school physics expectations are here. I recall surviving high school physics without actually learning anything, and doing a cursory reading of my high school physics book when there was a looming exam. So it comes as a surprise to many students how different university physics textbooks are from what they've encountered in high school.

The common reading strategy seems to be memorizing equations or the end of the chapter summary, and so whenever students encounter textbooks without end-of-chapter summaries, they complain how hard it is to read the book. That's one of the most common complaints I encounter whenever I assign  reading from Spacetime Physics.

A similar strategy is looking for boxed equations and then memorizing all of them. When such a student encounters a physics problem, the problem-solving strategy becomes "Try all the equations with the same variables!". What students forget is the boxed equation is actually something that should be understood in context. The surrounding text is there to explain what assumptions underlie a derived result, and once the underlying assumptions are understood, one can also understand the limitations.

One of my favorite ways of teaching students to be sensitive to underlying assumptions is the De Broglie frequency relation $E=hf$. The problem I assign is to find the De Broglie frequency of a free electron in terms of the wavelength. (The mass of the electron is not given within the problem statement but listed on a table of physical constants.) One common mistake is to write, for free particles with nonzero mass, $E=\frac{hc}{\lambda}$; the wrong assumption here is the wavelength frequency relation $\lambda f=c$ which only works for particles with zero mass. To ensure that my students make an effort to understand underlying assumptions, I make multiple choice items with distracters that reproduce their most common mistakes.

So a student who memorizes equations and is not sensitive to underlying assumptions will find the correct answer (which is derivable from invariance of mass) and the wrong one. One student, who merely memorized formulae and then used a trial and error approach, was unpleasantly surprised to find that his trial and error approach generated all the choices in many test items.

Having talked about the wrong way of reading an introductory physics text, what is the correct way? The right way is to read introductory physics texts on a per-section basis. After reading the section, go to the end of the chapter and then try solving all the odd-numbered problems for that section only.

Probem-solving is a sanity check. The only way to find out if you've actually understood what you've read is  to try to use it, and that is what the problems are for. If you can't solve the problems, reread the section (assuming you actually understood the prerequisite knowledge!) and then try to solve the problems again. If it still doesn't help, try talking it over with classmates, a tutor, or with your professor. Bring your problem solving attempts, and then try to find out why you get the wrong answers-- finding out why you're making mistakes is also part of the learning process.

Obviously, this is not something you can cram, and it means doing the reading and problem-solving on a regular basis. But if you do it right, your understanding will last a lot longer than the formula-memorizers. As a bonus, when faced with a new technical situation, you can build on what you know, and eventually become the expert in your field.

#### 1 comment:

Steve Solun said...

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Let me share with you the post about physics: