I'm currently in Charleston, SC for a combinatorics conference and a joyously nerdy reunion with the Research for Undergrad (and In-service teachers) participants from summer. During the moments of downtime, while listening to presentations I didn't really understand, I started to wonder, "What gets people to love math rather than tolerate it?"
This year I've been teaching a colloquium class- intro to improv- for the first time. I REALLY love improv. I'm not a pro (by any means), but I see how improv is such a great thing for everyone to learn and enjoy. Students have a great time working together, improving, and laughing. Honestly, I don't really feel the same way about my math classroom, because the curriculum does not inherently compel students to work together, improve, and laugh. I'm currently teaching matrices right now, and I know that question will inevitably come: why are we learning this? I've heard a lot of answers to "Why are we learning this?" Most of them have to do with utility and vague fortune telling. "Well, in the future... you might be an engineer. The very specific type of engineer that requires you to apply matrices in a much more complex way that some type of computer will be necessary and the techniques you're using are outdated at best." I think these responses, though marginally honest, don't really address the heart of the question behind the problem. I think often "Why are we learning this?" is more of a statement "Let's not learn this." Let me tell you something: no one in my improv class ever asks: Why are we learning this? So I think back to my summer research program at Illinois State University. I've been through a lot of programs. A few summers back, I had the opportunity to go to Park City Mathematics Institute (PCMI) where we got to play with mathematics through a well developed problem set with 100 other teachers. I thought I understood what it was to do mathematics: great problems, depth in learning, learning with others. But the summer research program challenged my view more... It was like entering a new philosophical space. The biggest difference between PCMI and the summer research program was in creation. We are CREATING mathematics. Something I learned from our mentor and P.I (Dr. Saad El-Zanati): Great researchers are as much about the answer as they are about the next great question. It's hard to describe the impact of participating in mathematics research- I think that's partially because it's something that needs to be experienced rather than told. Which gets me back to my classroom. I don't know how great of a job the traditional curriculum does in getting students to wonder, create, ask, and eventually love mathematics. Er, I do know. and it's not great. I wonder if it's even POSSIBLE to do in the classroom given teachers' many constraints: curriculum, nationally normed tests, college requirements, etc. Maybe the best place to experience mathematics is outside the classroom- like summer camps, tutoring, after-school programs or fairs. Those kinds of things often incur additional cost and are inaccessible for students from low S.E.S. backgrounds. Seems unfair. Students who are most likely to be turned off by mathematics in the traditional classroom are also the least likely to have opportunities outside of the classroom. I've decided to propose a class next year for colloquium... something like Math Research in Graph Theory (or maybe something with more pizzazz). I'm determined to let at least some students get to experience mathematics in such a compelling way that "Why are we learning this" is never a question.
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I had just spent 30 minutes on an activity today touting the joys and benefits of working in groups and responding to each other think. So I set them on their book work in groups, hoping for the best.
Within 15 minutes, a student - Jori- says to me, "He's not helping me and I find him very rude! I can't work like this." I walked over to Jori's table and see she is pointing at Don, a generally mild mannered student. Jori: He's being rude! I can't stand when people are mean for no reason. Me: Let me hear your perspective. What happened in your eyes? Jori: I asked him for help on a problem and he wouldn't help me. He said, "I'm not going to give you the answer" and looked away. Me: Okay, I hear your perspective. I'd also like to hear Don's- it might not be the same. Don: I thought she was just asking for the answer. I would help her understand but not just give an answer. Me: Sounds like we have a miscom-- Jori: That's not what I was saying! I wasn't even asking for the answer! I just wanted help understanding it. Me: okay, so I hear you- Do you see Don's perspective? Jori: I wasn't asking for the answer! (Jori appears she will cry at any moment now) Me: Don, do you understand that Jori was not asking for just an answer. Don: (disgruntled) I'm sorry that I hurt your feelings. I didn't mean to sound like that. Me: It looks like Jori has a great contribution to the group by asking a question, and Don, it looks like you might have some progress. Let's talk this out. I watched them ask and explain the question before I walked away. I checked in with them 10 minutes later and they were conversing through the problem set as if nothing had happened. This is my SECOND piece of evidence (in my book) that has shown me that conflict resolution has better effects that splitting groups that don't work well together initially. *Names changed |
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