The theme for Blogsplosion this week is “We All Fall Down”. The times in your classroom where you make mistakes, accidentally teach a mathematical inconsistency, try to do a really cool activity and it’s a disaster…we all know those days.
One particular day immediately came to my mind when I read the theme. Algebra 2 was working on systems of linear equations earlier this year, and Ms. Kormann from next door was filming the class for my model teacher application. Of course filming leads to miniature disasters – why would something go well when you’re recording it?
The day before, we had been working on an assignment and one of the students called me over, saying, “Miss Mastalio, the solution I got doesn’t work in the equations but I can’t figure out where I made a mistake.” I looked at her work for several minutes and also couldn’t find a mistake in her work. The whole class thought it was pretty funny that I couldn’t figure it out. When the bell was about to ring, I told her to just turn it in and I’d find the mistake later, and I would let her fix her solution then.
So we started this class with me coming in and saying, “Hey, so the mistake that we couldn’t find in [student]’s work yesterday? It turns out that 6+8 isn’t 13, guys. Just in case you didn’t know.” ARITHMETIC, MAN.
We all had a good laugh at our collective student/teacher brain meltdown, and I began the day’s activity.
We were completing a Question Stack (one of my favorite forms of practice) to help them choose a solution method (graphing, substitution, or elimination) and get practice solving systems before their assessment. The nature of Question Stacks means that students don’t begin with the same problem, and they also have an answer bank of all the possible solutions to work from.
So I was circulating, answering questions and clarifying things, when one of my students hit a problem where she kept getting a solution that wasn’t in the answer bank. I came over, quickly glanced over her work, and couldn’t find the mistake. Because of the mistake I had made on the student’s work the day before, I checked all of my arithmetic with a calculator. A few other students noticed me doing this and laughed, then continued working.
When I still couldn’t find the mistake, the student suggested, “what if I tried to solve it with a different method and see what happens?” I agreed that sounded like a great idea, and began circulating again. Soon, another student hit that same system. She picked a different method than the original student was using, because they were sitting next to each other and she realized that there was some issue. So we now had all three possible solution methods going on this problem.
They kept getting the same solution. Other students in the class realized that something weird was happening in our corner – some of them were reaching that system in their work, and some of them decided to skip to it and try it. I called Ms. Kormann over from behind the camera to come check the work as well.
No one could find a mistake. We kept getting the same solution with every solution method. The whole class started a heated discussion of each solution method and the process behind it. Instead of getting mad and giving up, they started getting mad and analyzing their mathematics.
Meanwhile, I was panicking because I could not figure out where I had gone wrong. I grabbed the textbook I had pulled the problems from to double check their solution. In my classroom, I had students checking each other’s work, trying multiple solution methods, and discussing algebra. (To be fair, they were also yelling “WHY” a lot and declaring themselves failures, so that wasn’t good).
Anyone want to know what the mistake was?
Because it was awful.
I transposed the x and y in one of the equations from what the textbook problem said.
Just. Switched them.
Of course they weren’t getting the solution in the answer bank.
That day was the best possible kind of disaster – the disaster where your students stay with you the whole time and persevere in their attempts to solve. Not all of my disasters go that way, believe me. This one was super memorable though. I was so proud of my students. We bonded over brain melts and those days where you just can’t even add.
They still tease me about it, and I’m totally okay with it.