> What I'd like to see more of in physics texts is presenting a problem before offering the solution.
Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.
> As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution
My calculus instructor in college was one of those where they'd go through the problem and on step 7 (or whatever) go "Oh, where did we make the error?" where we'd all flail until they pointed us back to step 3 and then had to redo everything all over again. It was, for me, the most maddening way to teach. I was struggling just to get everything copied from the board to experience it by rote, completely unprepared to even process what was going on, much less have to go back and redo everything all over again.
I dropped that class. I always felt it was a mistake not taking calculus in High School. I had a very good relationship with the math teacher there, and we could have done it, to some level, casually between classes. I just didn't take him up on it.
I don't think it breaks trust, if you tell them what's going on. "Hey kids, I'm going to give you a problem that went unsolved until Newton. I don't expect you to find his answer, which I'll teach you later, but I want you to try to solve it your own way."
> If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
This does not destroy trust, but gives the student an important lesson: we only have the techniques to solve, say, 0.0000001% of the problems. So you have to learn brutally hard for the next many years (or rather decades) to have the minimal qualifications to be able to invent whole new techniques that no person has ever come up in history before to increase this ratio from, say,to 0.000000100000000001% (even this would trigger a whole new aera in the history of science).
Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.