Writing into my Own

One month has passed quickly. I've only written a little bit, and not anything spectacular, but nevertheless it's refreshing to be able to write about a topic and see where I go with it. Furthermore, I like the idea that somewhere, someone might actually read this. There's the possibility that what I have to say matters to someone enough that he or she will finish the first sentence and decide to read the second. I have creative control over something, which I feel I often don't have in my mathematics courses.

Sure, you can be fairly creative with proofs, but there's still a right answer, a target. I appreciate that most of the time because I like having a specific goal, but sometimes I like to determine my target by how I decide to launch. That's how I feel it is with blogging. I start off with a general idea of what I want to say, and then fire and hope that where I end up is somewhat meaningful.

Finding a balance between structure and improvisation is not easy for me in general. It's kind of the same with being analytical and intuitive. I take sure steps when it comes to solving problems, and don't often go off in directions that I haven't tested before. Blogging has let me do a little more exploring than I tend to do, and I think in the process I've "found my voice," as they say.

As far as connecting this to the class material, I think it's pretty easy to see how this subject matter connects to my life. Jerome Bruner's The Process of Education is something I would have expected to have been assigned in one of my education classes. So much of what he writes, I have read in other contexts the past 2 years. The ability of children to learn abstract ideas increases as they get older. There is a step-by-step way we tend to learn, even if we don't realize it. All children can learn something if you teach it at the appropriate level. These things I believe true; they affect the way I teach.

Just yesterday, there were some guests at my house's worship night. One of our campus ministers invited Thad, one of his friends who works at Salt and Light Ministries in Champaign, to talk to us about volunteer opportunities. Thad in turn invited along the executive director of Salt and Light, Nathan, and Nathan's kids. After the night was over and everyone was milling around, I decided to talk with the director's son, Benjamin, just to be nice and make waiting around a bit less dull for him. As I talked with Benjamin, I learned that he "used to be good at math" but now is "horrible at it." "Oh no!" I thought. "Another child destined to hate math!" I immediately took it as my mission during the time we had left to change his opinion about math and his abilities as much as I could.

My strategy was to present a problem I think is pretty interesting and shape it to fit his 4th grade understanding of things. The problem starts out dividing a line segment with points to make more line segments. A fourth grader can surely define the pattern as (# of points) + 1 = (number of lines), and Benjamin did. Then, I took it a step further to dividing a disk with lines. The pattern here can be defined recursively or empirically, though the latter would be very difficult for a fourth grader because it involves linear algebra. With the right questioning on my part, Benjamin came up with a recursive definition, no problem. We started talking about different dimensions of objects and other related topics, and the conversation kept going until he had to leave. When he left, he took the notes we had written and told me he was going to show his friends and teacher. For the foreseeable future, I don't think math will leave as bad a taste in his mouth as it did before.

The point I tried to get across to Benjamin, and what I'll try to communicate to my students, is that math is well within their reach. It's my job to make it accessible. Through quality questioning, I think teachers can turn any student into a good math student. Maybe not good in the sense that they get all the right answers, but good in the sense that they have the right approach; that they understand the methods of mathematics and can apply them to problem solve. Anyone can learn math; I believe that.