In particular, your section 1.8 "Solving Problems" would benefit
from a link to Pólya "for further reading". It would also benefit
from directly quoting Pólya's most famous dictum: Try something. If
that doesn't work, try something else.
@EricMazur: Good idea.
Students are so afraid of jumping in the dark, however. “Just tell me
what I need to do!"
@JohnDenker: Some quick comments:
1a) Of course you already know what I'm about to say.
You've said your ConcepTests are sufficiently challenging
that even the best students get stuck 30% of the time
or more. So learning to face a nontrivial challenge
is already part of the course.
1b) Yes, students /start out/ being afraid to jump into
the dark. That is fine as a starting point, but it is
unacceptable as an ending point. Therefore we need to
treat this as a moving target.
Teaching requires realism about the starting point,
but not fatalism or defeatism about the ending point.
1c) We agree students /want/ somebody to just tell them
what to do. However, as the famous philosophers Jagger
and Richards pointed out, you can't always get what you
want. The real world doesn't work that way, and the
course doesn't work that way ... nor should it.
2) My real point is: The book does not fully reflect the
ideas in item (1). All the worked examples make a plan
and then carry out the plan. In the book, plan A always
works. However, real life is rarely like that. Anybody
with any sense has a Plan B and knows when to use it.
It's unfair that the physics teacher gets stuck teaching
basic reasoning skills on top of all the domain-specific
physics skills, but that's the way it is.
Peer instruction covers a lot of sins, because students
get to see their peers make mistakes and get stuck, but
it would be nice to see the book to align more tightly
with this.
Also, much more importantly: In a maze, backtracking out
of a dead end does not mean you made a mistake. You
couldn't possibly have known it was a dead end before
you explored it. Students really need to learn this.
By the time they show up in your class, they've been
taught mostly the opposite for 12+ years.
Therefore, a serious suggestion: In the book it would
be nice to see some worked examples and some exercises
that involve more in the way of multi-step maze-like
reasoning, where students get to see Pólya's dictum up
close and personal: Try something. If that doesn't
work, try something else. Do not assume that Plan A
will always work.
I am emphatically not suggesting that the instructor
should introduce misconceptions just for the fun of
dispelling them. Exploring a maze is something else
entirely. Considering N hypotheses with the clear
expectation that N-1 of them won't work out is not
even remotely like buying into a misconception.
Specifically, one could start by assigning an out-and-out
non-metaphorical maze, so students know what the metaphor
is referring to. One could progress to logic puzzles
such as the notorious Cheryl's Birthday puzzle, or the
vastly more difficult Who Owns the Fish puzzle. In both
of those, if you choose a lousy representation, you will
get stuck, but that should teach you something about how
to design a better representation. And of course there
are plenty of real physics questions that demand complex,
multi-step reasoning.
The book should not tolerate, much less reinforce, the
idea that Plan A always works.
My real point is: The book does not fully reflect the
ideas in item (1). All the worked examples make a plan
and then carry out the plan. In the book, plan A always
works. However, real life is rarely like that. Anybody
with any sense has a Plan B and knows when to use it.
@EricMazur: Totally true. Believe it or not, but I toyed with the idea of better mimicking how real problem solving goes. I wrote a solution where I engaged on a dead-end and made a mistake. For some reason it doesn’t work and the solution becomes totally unwieldy. I abandoned the idea.
@JohnDenker: The book should not tolerate, much less reinforce, the
idea that Plan A always works.
@EricMazur: That’s definitely true. At least I should explain that somewhere — even if in print Plan A always works, because it really is Plan F and not Plan A and all the other plans have failed. Good point! Noted!
From @JohnDenker:
In particular, your section 1.8 "Solving Problems" would benefit from a link to Pólya "for further reading". It would also benefit from directly quoting Pólya's most famous dictum: Try something. If that doesn't work, try something else.
@EricMazur: Good idea.
Students are so afraid of jumping in the dark, however. “Just tell me what I need to do!"
@JohnDenker: Some quick comments:
1a) Of course you already know what I'm about to say. You've said your ConcepTests are sufficiently challenging that even the best students get stuck 30% of the time or more. So learning to face a nontrivial challenge is already part of the course.
1b) Yes, students /start out/ being afraid to jump into the dark. That is fine as a starting point, but it is unacceptable as an ending point. Therefore we need to treat this as a moving target.
Teaching requires realism about the starting point, but not fatalism or defeatism about the ending point.
1c) We agree students /want/ somebody to just tell them what to do. However, as the famous philosophers Jagger and Richards pointed out, you can't always get what you want. The real world doesn't work that way, and the course doesn't work that way ... nor should it.
2) My real point is: The book does not fully reflect the ideas in item (1). All the worked examples make a plan and then carry out the plan. In the book, plan A always works. However, real life is rarely like that. Anybody with any sense has a Plan B and knows when to use it.
It's unfair that the physics teacher gets stuck teaching basic reasoning skills on top of all the domain-specific physics skills, but that's the way it is.
Peer instruction covers a lot of sins, because students get to see their peers make mistakes and get stuck, but it would be nice to see the book to align more tightly with this.
Also, much more importantly: In a maze, backtracking out of a dead end does not mean you made a mistake. You couldn't possibly have known it was a dead end before you explored it. Students really need to learn this. By the time they show up in your class, they've been taught mostly the opposite for 12+ years.
Therefore, a serious suggestion: In the book it would be nice to see some worked examples and some exercises that involve more in the way of multi-step maze-like reasoning, where students get to see Pólya's dictum up close and personal: Try something. If that doesn't work, try something else. Do not assume that Plan A will always work.
I am emphatically not suggesting that the instructor should introduce misconceptions just for the fun of dispelling them. Exploring a maze is something else entirely. Considering N hypotheses with the clear expectation that N-1 of them won't work out is not even remotely like buying into a misconception.
Specifically, one could start by assigning an out-and-out non-metaphorical maze, so students know what the metaphor is referring to. One could progress to logic puzzles such as the notorious Cheryl's Birthday puzzle, or the vastly more difficult Who Owns the Fish puzzle. In both of those, if you choose a lousy representation, you will get stuck, but that should teach you something about how to design a better representation. And of course there are plenty of real physics questions that demand complex, multi-step reasoning.
The book should not tolerate, much less reinforce, the idea that Plan A always works.
My real point is: The book does not fully reflect the ideas in item (1). All the worked examples make a plan and then carry out the plan. In the book, plan A always works. However, real life is rarely like that. Anybody with any sense has a Plan B and knows when to use it.
@EricMazur: Totally true. Believe it or not, but I toyed with the idea of better mimicking how real problem solving goes. I wrote a solution where I engaged on a dead-end and made a mistake. For some reason it doesn’t work and the solution becomes totally unwieldy. I abandoned the idea.
@JohnDenker: The book should not tolerate, much less reinforce, the idea that Plan A always works.
@EricMazur: That’s definitely true. At least I should explain that somewhere — even if in print Plan A always works, because it really is Plan F and not Plan A and all the other plans have failed. Good point! Noted!