I believe that everyone "learns" better when they find the answer to their own question. Why is school not set up like that?
In other news, I have had two interesting things happen this week.
The first: 7th grade students have discovered, by patterns, what any number to the 0 power is.
I then asked, "what is zero to the zero power?" We spent a good 15 minutes discussing this and what our options might be. I went as far as to show why was cannot divide by zero and my students were still not agreeing on one answer. Therefore, that was their homework last night. Prove what zero to the zero power is.
Today, I let them work in groups that had the same answer to put their "proof" on the board.
I saw: 0^0 = 0 because 0^1= 0, 0^2 = 0, ... the pattern is that the answer will always be 0, therefore 0 ^0 = 0
0^0 = 1, because any number to the zero power is 1. 2^4= 16, 2 ^3 = 8, 2^2 = 4, 2 ^1 = 2, 2^0 = 1 (divide by 2 each time). Therefore 0^0 = 1
0^0 = undefined. Zero has no value, and you cannot divide nothing by nothing (paraphrasing my students' work).
I went through each proof and demonstrated why it was right or wrong. I was happy with all of their answers. I enjoyed seeing how my students are starting to notice patterns and are able to think more like mathematicians.
The other interesting thing was when a student said to me, "Why don't you teach us?"
What a great teachable moment and a loaded question. I am interested to hear how others would respond before I give my answer. Of course, this requires people to be reading my blog...is anyone out there?