As the author of a widely used thermal physics textbook, I get a steady stream of email from students around the world who are using the book. By far the most common type of inquiry is requests for answers to the end-of-chapter problems. Some students ask for the answer to a particular problem; others want copies of the entire solution manual.
To most of these students, my standard response is “Ask your instructor.” However, not all of them are using the book in a traditional classroom setting. Some have moved on to advanced studies or workplace settings where for various reasons they need to go back and brush up on their undergraduate thermal physics.
Of course I’m delighted that people are using the book in such diverse ways. But I’m also dismayed that, even after earning an undergraduate degree, so many scientists and engineers still believe that answers come from textbook authors.
The whole point of science is that you can figure out answers for yourself, without relying on any authority. For physics textbook problems, that usually means you have to do some sort of calculation. And how do you know if the calculation is correct? Not by consulting a teacher or solution manual or some other authority! Mathematics has its own internal logic that tells you whether it’s correct, without reference to anything external.
But what about careless errors, which everyone makes from time to time? There are endless ways to catch them without any appeal to authority. Do the calculation a different way. Compare the answer to other known facts. Ask one of your peers to check your work.
Our educational system does a lousy job teaching these skills. In our fervent desire to “cover” as much material as possible in our courses, we don’t give students time to ponder their results and root out their own mistakes. Instead, we authoritatively mark their answers right or wrong, then hurry on to the next problem.
Nor is this situation unique to the mathematical sciences. Students of biology, economics, sociology, and history must all learn to distinguish truth from falsehood without an instructor’s help. Critically examining one’s methods, and thus developing confidence in one’s answers, is fundamental to every discipline that deals in hard facts.
It’s not enough to teach facts, or even to teach specific technical skills. We somehow need to help our graduates develop the intellectual toughness to know when they’re right, so they can become leaders in their chosen fields.
(I stole the phrase "intellectual toughness" from my former professor Leonard Susskind, who uses it in his book The Black Hole War to describe his ally in the "war", the great theoretical physicist Gerard 't Hooft.)
ReplyDeleteI’m also dismayed that, even after earning an undergraduate degree, so many scientists and engineers still believe that answers come from textbook authors.
ReplyDeleteThe whole point of science is that you can figure out answers for yourself, without relying on any authority. For physics textbook problems, that usually means you have to do some sort of calculation. And how do you know if the calculation is correct? Not by consulting a teacher or solution manual or some other authority! Mathematics has its own internal logic that tells you whether it’s correct, without reference to anything external.
But what about careless errors, which everyone makes from time to time? There are endless ways to catch them without any appeal to authority. Do the calculation a different way. Compare the answer to other known facts. Ask one of your peers to check your work.
Our educational system does a lousy job teaching these skills. In our fervent desire to “cover” as much material as possible in our courses, we don’t give students time to ponder their results and root out their own mistakes. Instead, we authoritatively mark their answers right or wrong, then hurry on to the next problem.
In American RadioWorks’s series Don't Lecture Me Harvard physicist Eric Mazur advocates abandoning lecturing in favor of a peer-to-peer problem-solving teaching method. But in comments following the broadcasts, Mazur acknowledged that both professors and administrators resist his teaching reforms – in part because they take longer than teaching. The goal of the educational institution is to SEND material to students; whether students absorb the material is someone else’s problem.
Thought of you today while watching NASA land an SUV on Mars. I discovered that a guy named Daniel J. Schroeder worked with NASA and thought “Ok -- could be….”
But when I saw the NASA gang celebrating Curiosity's landing, that synched it. Google "Proof that NASA has a time machine" to see a picture of you at the NASA controls.
Honestly, it’s amazing what you can accomplish while simultaneously pursuing the best weed Utah has to offer!
Eric the Cleric
Whoops. Make that "Mazur acknowledged that both professors and administrators resist his teaching reforms – in part because they take longer than lecturing." Professors need to be able to report that they covered a large amount of material during a class. Whether students understand or remember the material is a secondary concern.
ReplyDeleteEric the Cleric
I think you are partly missing the point here.
ReplyDelete1. People, like m,e studying physics on their own are sorely in need of feedback. Providing answers to selected questions helps provide some of that feedback. And feedback is just an essential part of learning. See eg "A Mind for Numbers" for a discussion of this.
2. The student can be convinced they are right but be on completely the wrong track. Several times working through the book I had a realization that an answer from earlier on was totally wrong and I had missed something important.
2. In a number of cases the questions are/seem ambiguous - at least to a beginning student, the sort of student who is studying an "Introduction". For example you several times say to see if the answer is consistent with the "expected result". As an example: the 2D Fermi gas questions where the expected result apparently comes from changing V (3d) to A (2d) in an earlier formula and nothing else. OK but in other cases things don't translate from 3d to 2d so obviously eg the uniform field approximation so how do we know this works in this case?
3. In other cases I had an answer but I was not sure it was good enough eg where we were asked to fit parameters a and b to an approximation for N2 gas. I did a rough guess at the numbers and then played around until it roughly fit visually. I still don't feel confident that there is not a better answer. How do I know to give up looking for a better answer?
People studying physics on their own have no shortage of character building experiences. I once spent 18 days working on one problem in special relativity before I worked out a subtle problem in my calculations. We have no resort to office hours or tutors, and it is basically impossible to find a peer group who are at the same point in their studies.
Students studying in a college have access to professors who have access to your solutions book.
Not providing *any* answers just makes life pointlessly difficult for people studying alone.
Thanks for reading my personal blog, and for using my book. Obviously the book isn't perfect for everyone, but fortunately there are many other resources out there. One advantage to studying physics on your own is that there's no professor telling you that you have to use a particular textbook.
DeleteRegarding that problem of fitting parameters to data for N2, I just did it by eye myself and you're correct that it could be done better. But you won't find a better method in the official solution manual! So this is a great example to illustrate the difference between consulting an authority and learning to think for yourself (which you have obviously done). It's also a good example to illustrate that the book does provide *some* answers: try looking up nitrogen in the index.