Yesterday my 5th period students were working on the Fort Hall Businesses activity from the IMP Meaningful Math Algebra books. Some of the groups in the class had #1 and some had #2. Each of the problems asked students to find the "starting point" for a situation. Anyway, I had "helped" the groups who had #2 first because it was a little more difficult. I had guided the students through how to take the two sets of data points and think through how to find the "starting point" which was the amount of money that a movie theater had started with in their cash register. We had "deduced" that they started with $10. What I didn't realize is that when I wrote down the two data points out of the problem I had written one of them incorrectly. Therefore although the students' reasoning in how they found the answer to be $10 was correct I had "led them astray" by writing down the wrong value.
So, my principal walks in and sits down for a minute. When he comes in I am working with the students who are doing #1 and writing on the back board. The problem that is still projecting on the front board is problem #2 so he finally asks me if we are doing different problems. He then goes and talks to a couple of the groups doing #2 and starts working on the problem. When I walk back to the front of the room he is telling the students that the starting amount of money in the cash register is $25. In my mind I am thinking, "O bless his heart! He is wrong and he is going to be embarrassed in front of all these students." Thankfully I didn't claim that he was wrong. I just asked him to explain his reasoning. He did a wonderful job explaining his reasoning and he was RIGHT - not bad for a former history teacher. My brain literally had a cramp in it because I was so confused why we had gotten $10 earlier. I KNEW we had used the right reasoning. After a couple of minutes looking back at the values I had written on the board we found the mistake. Needless to say my principal now thinks that he is a math expert!
I had a couple of students to throw their papers away because we had made a mistake. I tell them to never erase or throw away papers because I want to see their thinking on paper. I even had one student who graphed the 2 data points and extended the graph back to the y-axis in order to find the starting amount in the cash register. He had the correct points graphed and had $25 as the starting point until I went and "corrected" him because he hadn't graphed the points I had written down. I felt so bad! I told them to just write down "Owens was wrong" on that page in their notebooks instead of starting all over. I knew that they understood what was going on with the problem. I also used the situation as an "object lesson" about working in groups. I told them that this was an example of why you can't just accept everything that the "smart kid" in the group says. When you have different answers or ideas in the group you need to take time to explain and listen to each other's reasoning. Today they saw the mathematical practice standard #3 (construct viable arguments and critique the reasoning of others) acted out by me and my principal.
My principal and I are both former coaches and highly competitive individuals. I am sure he will never let me forget about the day he had to "set me straight" in my own algebra class.