Setting the Stage

From Day 1 I have created an ethic of "

**we don't use things we can't prove**." I encourage them to use their intuition and estimation to make conjectures about new ideas, but I don't give them formulas to plug and chug on. I do my best to eliminate or limit lecture and instead give them guided explorations to work through.

In the last several weeks, they have proven: the power rule, the product rule, the quotient rule, and derivatives of sine and cosine.

Begging for Proofs (yes, really!)

What's so amazing this year is that students are begging to prove more things. When I mentioned that I might go through the proof on the board for the quotient rule one student said, "what, do you not trust us to figure it out ourselves?" is a gloriously sassy voice! Another student has been e-mailing me photos from home as she figures long proofs on her whiteboard in her bedroom. When she was home sick for a day she asked, "is there anything else I can prove, this is a fun game?"

Often some students will figure out how to prove something before others do. I've started to say "

**don't ruin the punchline**," as if we're talking about a joke. If someone finds out what to add and subtract to prove something, they may

**give small hints**if their classmates ask, but they must keep in mind the joy that they had with finding it on their own.

Hi Jasmine, I hope you'll consider this just the first in a series of posts on how to make the proof act tangible, necessary, and energizing for students. What you're showing here (to my eyes) are the fruits of a lot of work that you haven't detailed. I'm curious how you got your students to this point.

ReplyDeleteSo much confidence! I think that's what comes from seeing proof as a process rather than a collection of weird statements--people can feel energized about participating in the puzzle.

ReplyDelete