My fellow teacher just came to my room and asked if she could speak to me privately for a moment. I felt like I was being called down the principal’s office but it turns out she had overhead some student talking about reading my blog. Luckily I love my job, think my kids are great and I am leaving for graduate school under great conditions so I hadn’t posted anything super exciting or embarrassing. If you’ve been following you might wonder why high school students would even want to read about a teacher’s reflections on her lessons. You’d think that sitting through the lessons once would be quite enough. They probably know my teaching better than I do in so many ways. In any case, if you are my student, I won’t be mad if you are reading this. Please feel free to come discuss! I’m curious about what you think-in fact I’ll be writing a dissertation about what students like you think about math so feel free to come get the process started.
Lots of things have happened this week that I’ve felt like I needed to write down. In Geometry we’ve been working on measuring the distance between two softball fields using a cross staff. Applying trig to the real world is a fascinating teaching experiment. At first I couldn’t believe how hard it was for some of my students to figure out how to use the ruler, pencil and rubberband contraption to measure angles. They had some pretty fascinating discussions surrounding what was going on. I loved that the endeavor forced them into thinking logically. They knew that I didn’t have an answer and that there was not an approved textbook way to solve the problem. I loved how creative some of their solutions were. I videotaped part of the class while we were running around the field trying to solve. It was so weird to talk about trig and triangles with it laid out in front of us. I love activities where you can check your answer in multiple ways by using reasoning. I think that the kids appreciated having something to solve where they were expected to use their reasoning and creativity. I was particularly excited today when we had to use properties of diagonals of rectangles to figure out how accurately we were measuring angles. We found a mistake in our records and were able to correct it using general properties of quadrilaterals.
I’ve videotaped some Calculus classes too. I’m sure that my observations about various perceptions of infinity are nothing earth-shattering but now every time a kid has a misconception or an interesting thought the math researcher in me wants to ask them “Why do you think that? What was your reasoning?” I hope the kids don’t think my desire to videotape them struggling to solve math problems is crazy. I always wish I had records of when students are trying to solve a real world problem and come up with some crazy illogical solution and say “the book made me think that was the only possibility.” This happened today when we were trying to write an infinite geometric series to model the distance a bouncing ball has traveled. The first bounce it only falls and then every other time it goes up and down the same distance. The first distance doesn’t fit the pattern so it has to be added separately. I realized that the student was right that every problem we’d done had all terms fitting the pattern so he thought we couldn’t separate the first term. The unintended consequences of our instruction are pretty interesting.
Anyways… bike time!