So I had a problem in my Honors classes where I wanted them to do application problems related to conic sections like:
Suppose you have a hot dog cooker made out of a parabolic mirror. If the parabola is 12 inches across and 6 inches deep, where should the wire be placed?
I had them working on them in groups to help things along, but I still knew what was going to happen: they were going to immediately ask me for help on each and every problem. How to encourage them to struggle?
I came up with hint tokens.
I gave each group several “tokens” (in my case, some chess pieces I found in a cabinet) and told them if they wanted help on a problem, they had to spend one of their tokens. Any tokens remaining by the end of the assignment would count as extra credit.
The result was astonishing. I saw students visibly straining, growling at the problems even, and when I came over to offer help they said “no, we must protect our precious tokens!”
Of course, some tokens were spent, but this was when the students were truly and completely stuck rather than just any point where they had to think a little.
It’s like in videogames where players tend to hoard health supplies, ammo, and so forth. Is there a word from psychology for this?
Filed under: Education, Mathematics, Psychology, Videogames |
The Number Warrior 
I don’t get the problem. Maybe because I am not sure what a hotdog cooker is, or what the wire is supposed to do?
King’s pawn to Number Warrior’s pocket, please. (e4 – self capture)
Jonathan
Great idea! I’ll have to remember this one.
I added a picture. Does that help?
The wire is located at the focus of the parabola, parallel to the mirror.
Good idea!
Do you give the same hint(s) to each group on each problem? How much would you tailor it to where they are? I think I would be tempted to standardize all hints… like come up with three per problem, in increasing order of helpfulness, and they have to take them in that order. If they already knew what was on Hint #1, well… too bad!
wow. makes me feel dumb for never figuring this out. i taught at alternative school where a lot of kids had the learned helplessness. this would of been huge to ween them off teacher dependency. darn.
What a simple but great idea Jason. I will try this during group puzzle solving tasks in the coming weeks and let you know how I get on.
Cheers,
Dan
You’re a genius. You’ve solved a problem that I’ve struggled with since day one in the classroom. I even have some “pieces of eight” sitting around gathering dust…
@Matt: These problems were the sort that one hint was enough to solve them. For instance, the key insight above is if the vertex it set at (0,0) the parabola passes through the point (6,6).
If the assignment was of the single-tough-problem type I might consider your method of fixed progressive hints (that is, like the game show Password).
This is a variation on a “token economy”; in token economies, the tokens are usually used as a positive reinforcer (awarding tokens when students show good behaviour, where the tokens can later be redeemed for something of value), but in your setup they act more as negative reinforcement (the behaviour of hoarding the tokens stops the punishment of losing the extra credit).
OMG, this is brilliant! There are several tabletop RPGs that do this – you get a certain number of ‘fate points’ that you can spend to counter the effects of a bad roll of the dice, and any that you don’t spend get converted to experience points (XP) at the end of the story, and you can spend them to give your character more skills or powers.
Ugh. I can’t BELIEVE I didn’t think of doing this with my students!!
@Clix: I am friends with one of the original designers of 7th Sea. (I don’t remember if they were the first to use fate points though.)
@Winawer: Sounds about right! I do think there’s something extra. Even without the bonus points I believe they would have been somewhat protective of their tokens because they were worried they’d need them later. The only descriptions I know of the phenomena come from the world of games, not psychology.
Winawer is correct. . .but the tokens need not be viewed as negative reinforcers. . .they can be viewed as pre-set positive reinforcers for insuring target behavior (struggling on their own).
That is interesting. I think I will pass it on to a couple of teachers I know.
Nice, Jason.
Maybe the word for this is from behavioral economics.
Try looking up “loss aversion”, or “endowment effect”, or “divestiture aversion.”
[…] in-class guide for the teacher, so that when giving hints either quite straightforwardly through hint tokens or more subtly through Socratic methods, the teacher knows what insights to […]
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