Agree with just about everyone else here. The main thing about the problem solving exercises is to try to solve them. That then gets you thinking so you can understand the solution when you see it.
Is nice if you can solve it yourself, then also the solution might show you a simpler or more elegant way of doing it. May be less important to actually solve them when learning though. Main thing is to try your best for at least a while, before you check the solution.
Same with maths. After all if you got everything right, what would be the point in attempting the problems?
Like: Here is how you solve these problems: ...
Here is a list of exercises...
tick tick tick tick - got them all right
- if that kept happening, then as teacher you'd think you must have made the problems a bit too easy for the students. They probably aren't learning as much as they would if you made them a bit harder. Though make them too hard and you will discourage them. Get a few wrong from time to time and it is probably about right.
As a research mathematician it is not unusual to spend years trying to solve just one problem, trying many different angles on it. And there are many problems in maths that are quite simple to state, which have never yet been solved by anyone.
If you were really mean you could turn one of these into a coding challenge (make the program equivalent to finding a proof or disproof of the conjecture). Then if anyone solves the challenge, then their program solves a centuries old unsolved maths problem.
Is nice if you can solve it yourself, then also the solution might show you a simpler or more elegant way of doing it. May be less important to actually solve them when learning though. Main thing is to try your best for at least a while, before you check the solution.
Same with maths. After all if you got everything right, what would be the point in attempting the problems?
Like: Here is how you solve these problems: ...
Here is a list of exercises...
tick tick tick tick - got them all right
- if that kept happening, then as teacher you'd think you must have made the problems a bit too easy for the students. They probably aren't learning as much as they would if you made them a bit harder. Though make them too hard and you will discourage them. Get a few wrong from time to time and it is probably about right.
As a research mathematician it is not unusual to spend years trying to solve just one problem, trying many different angles on it. And there are many problems in maths that are quite simple to state, which have never yet been solved by anyone.
If you were really mean you could turn one of these into a coding challenge (make the program equivalent to finding a proof or disproof of the conjecture). Then if anyone solves the challenge, then their program solves a centuries old unsolved maths problem.
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Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
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