| 3. Never give a student a solution to a problem they don’t have. This reminds me of when I just started high school and realized, "school is just a bunch of answers to questions nobody asked." It's not that I didn't want to learn, nor even that I didn't want to learn those exact things -- just not have them fed to me at arbitrary intervals with total disregard for my actual state of mind. (The original Dalton school mine was inspired by did this right, over 100 years ago, but most of the methods -- ie. letting kids learn what they actually care about, when it interests them most -- are illegal in my country.) As for presenting the question first, at university this was often done, they would present us with some real world problem -- but then they would spoil the fun by instantly revealing the solution on the next slide! I like figuring things out, so in those moments I'd usually cover my ears and try to figure it out on my own. Somebody else's solution only becomes interesting to me once I've invested the effort to make my own, and then I can compare and contrast. |
I think one of my favorite professors, Gian-Carlo Rota summed it up best in a short essay, Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations, see [1]. It's hilarious and just like him.
I remember the first lecture of his I attended on probability. Wearing his trademark three piece brown suit and red tie at the front of the lecture hall and standing to one side of the stage, he said "I feel a draft, is a window open?". After a bit of looking around, we all reassured him that the windows were closed, he said "Well, I feel a breeze; yes definitely there is a breeze on my brow." Just then he looks up at the wall and does a double take as he notices he is standing under an air conditioning vent. He was whimsical, funny, and absolutely brilliant.
For anyone that has had to take the first semester of differential equations check out his essay.
[1] https://web.williams.edu/Mathematics/lg5/Rota.pdf