From @JohnDenker: Let me emphasize again that overall, I really like the book.
It has a lot of good physics ... and it has class. I have
a long list of pitfalls that more-or-less everybody else
falls into, and you manage to avoid most of them.
There's not much I can contribute by commenting on the good
parts, so let me continue pointing out the goofs.
Concerning checkpoint 1.1 on page 3: Let me suggest an
alternative, and then explain why the alternative is better.
Suppose you (the student) are analyzing a sample containing
two unknown chemicals, trying to identify the chemicals.
The following figure shows a simplified view of some raw
data from the spectrometer:
You know that the data is the sum of two rectangles. Find
the center and the area of the smaller rectangle.
Discussion of this particular example: The problem is
ill-conditioned. There is no unique solution, but rather
a /solution set/ containing two elements. There are two
ways of dividing the data into rectangles:
versus
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXXooooo
XXXXXXXXXXXXXXooooo
Situations like this occur in the real world. Indeed, situations
far worse than this are very common.
This shows the importance of considering /all/ the plausible
hypotheses. To say the same thing another way, be careful
not to make any ill-founded assumptions. Be on the lookout
for hidden assumptions.
Discussion, comparing this to the existing checkpoint 1.1:
1a) The rectangle problem is based on a genuine real-world
problem.
1b) The 30-cent problem was artificial and hokey to begin
with.
In my course, we do not do hard problems. We do /important/
problems. Sometimes we do problems that /would have been hard/
if you (the student) didn't know the tricks, so let me show
you some good tricks.
2a) The teacher helped by simplifying the problem slightly.
2b) The teacher made things more difficult by adding a
sentence that was borderline ungrammatical, intentionally
hard to parse, intentionally misleading.
In the real world, when my boss and/or my customer come
to me with a question, I am alert to the possibility that
it may be ill-posed. It may be hard to understand, possibly
even misleading ... but usually not /intentionally/ so.
As the teacher, I am here to help you (the student). If
physics seems complicated, you're doing it wrong. The idea
is not to make your life more complicated; the idea is to
make your life simpler and better, by being able to solve
important problems.
3) I vehemently, passionately object to the pedagogical approach
advocated by Heller&Heller, where they start with an otherwise-
easy problem and then erect "barriers" (their word!) so as to
"compel" (their word!) students to solve the problem by a more
difficult method.
I say if you can solve the problem by some method that is
easier and/or better than the one I taught you, go for it!
I say the teacher is there to help, never to hinder.
As for equation-hunting in particular: Diametrically contrary
to what Heller&Heller say and do, I say that if the students
can answer the question by equation-hunting, there is nothing
wrong with the students, and nothing wrong with the equations
... but there is something gravely wrong with the question.
There's a lot more I could say about this, but I'll stop here.
You're smart; I'm sure you catch the drift. If you don't like
the rectangle example, I'm sure you can come up with something
better.
For something as prominent as checkpoint 1.1, it's worth getting
it exactly right, both as to style and substance.
From @JohnDenker: Let me emphasize again that overall, I really like the book. It has a lot of good physics ... and it has class. I have a long list of pitfalls that more-or-less everybody else falls into, and you manage to avoid most of them.
There's not much I can contribute by commenting on the good parts, so let me continue pointing out the goofs.
Concerning checkpoint 1.1 on page 3: Let me suggest an alternative, and then explain why the alternative is better.
Suppose you (the student) are analyzing a sample containing two unknown chemicals, trying to identify the chemicals. The following figure shows a simplified view of some raw data from the spectrometer:
----+----+----+----+----+----+----+----> (x axis)
You know that the data is the sum of two rectangles. Find the center and the area of the smaller rectangle.
Discussion of this particular example: The problem is ill-conditioned. There is no unique solution, but rather a /solution set/ containing two elements. There are two ways of dividing the data into rectangles:
versus XXXXXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXXXXXXXXooooo XXXXXXXXXXXXXXooooo
Situations like this occur in the real world. Indeed, situations far worse than this are very common.
This shows the importance of considering /all/ the plausible hypotheses. To say the same thing another way, be careful not to make any ill-founded assumptions. Be on the lookout for hidden assumptions.
Discussion, comparing this to the existing checkpoint 1.1:
1a) The rectangle problem is based on a genuine real-world problem.
In my course, we do not do hard problems. We do /important/ problems. Sometimes we do problems that /would have been hard/ if you (the student) didn't know the tricks, so let me show you some good tricks.
2a) The teacher helped by simplifying the problem slightly.
In the real world, when my boss and/or my customer come to me with a question, I am alert to the possibility that it may be ill-posed. It may be hard to understand, possibly even misleading ... but usually not /intentionally/ so.
As the teacher, I am here to help you (the student). If physics seems complicated, you're doing it wrong. The idea is not to make your life more complicated; the idea is to make your life simpler and better, by being able to solve important problems.
3) I vehemently, passionately object to the pedagogical approach advocated by Heller&Heller, where they start with an otherwise- easy problem and then erect "barriers" (their word!) so as to "compel" (their word!) students to solve the problem by a more difficult method.
I say if you can solve the problem by some method that is easier and/or better than the one I taught you, go for it!
I say the teacher is there to help, never to hinder.
As for equation-hunting in particular: Diametrically contrary to what Heller&Heller say and do, I say that if the students can answer the question by equation-hunting, there is nothing wrong with the students, and nothing wrong with the equations ... but there is something gravely wrong with the question.
There's a lot more I could say about this, but I'll stop here. You're smart; I'm sure you catch the drift. If you don't like the rectangle example, I'm sure you can come up with something better.
For something as prominent as checkpoint 1.1, it's worth getting it exactly right, both as to style and substance.