I told my geometry class today that I wouldn’t be back next week. Why? I’m retiring. It can’t get any better, and I should leave on a high note.
Today I returned chapter exams and students had some time to work together to talk through their errors. There was one proof which only two students had gotten full credit on.
Prove that the sum of the medians in a triangle is greater than half the perimeter.
Several had very nice demonstrations using actual numbers, but only two were able to carry out all steps of an algebraic proof. Yesterday, I asked one of these students to take her exam home, look over her work, and be ready to present her proof to the class today. Why have her review her work at home? I have found that on challenging proofs, students often are able to write the proof, but explaining it to confused classmates presents a challenge as they realize that their own understanding is a bit fragile.
So, she comes to the board, talks the class through step by step (to several audible “Oh WOWs” and “That’s SO cool!”). When she finishes the other student who got full credit asks to write-up her proof so that we can compare their strategies. Her proof is met with the same excitement.
Ok readers…you’re thinking, I know, this happens to me too. Why retire? Is that really as good as it gets?
No, there’s more.
Then, a student asks if she can take out her phone to take a photograph of the two proofs. “Sure,” I respond. Next thing I know, about 90% of the class is piled on top of one another, each trying to get the best view of the board for their photos.
Although her proof was quite elegant (ignore the black print as it’s part of the other proof):
the real photo was capturing the giddiness evoked by the photo session:
And the absolute highlight:
“Ms. Krasnow, can I open facebook and make this my profile photo and tag everyone from the class?”