Friday, June 26, 2009

We Make the Road By Walking

“Even when teachers develop new conceptions of what it means to learn mathematics, they are, in general, working within a culture in which good teaching is assumed to mean ensuring that students get right answers.”

Somehow, this way of teaching (math) has become the dominant paradigm for most, if not all disciplines. How do we change course?

Budding Conversations

NEW PARADIGM: Walks up to Old Paradigm. Hey, I’ve got some new information for you. I think we can work together. I know that you like precision and finding answers. I think we can get there, but with a little bit of a different route.

OLD PARADIGM: What do you mean we can get there using a different route? I’ve been taking the same path to and from the problem to the solution, and I’m just fine. This is the best way.

NEW: Well, have you ever tried another way?

OLD: Sure. I tried the road that goes over the little hill over there. It was rocky, there were other travelers, signs, and lots of distractions. It was too difficult, so I turned around and came back. This good old path does me just fine.

NEW: I see, I see. Well, what if we tried again? If we know that the road is rocky and that there are hills, many signs, and lots of distractions, we can come prepared. I’ll go with you. We’ll wear the right shoes, plan our route, and bring the appropriate supplies. I bet that we can even ask questions of other travelers along the way.

OLD: Eh, I’m pretty sure that the arrangement I’ve got here on the Old Road is pretty good. Anyways, it doesn’t matter how I get we get to the solution, it just matters that I get there. To the right place. Every time.

NEW: But Old, honestly, that must get a little boring.

OLD: Boring? Yes, a bit. But safe. Definitely safe.

NEW: Okay old, let’s try another path, just once. If it doesn’t work, you are free to turn around.

OLD: Okay, fine, fine, fine.

Old and New begin down an alternate path. Things look very different. They run into other travelers along the way, some walking, some skipping, some hopping, some dancing at different speeds down the path. Occasionally, they skip, hop, and dance together---sometimes in a funky combination. Sometimes there are barriers in the road—a fallen tree, a rocky path—but the travelers help one another along. At first, Old seems a bit uncomfortable and anxious. He keeps glancing back towards the Old Path, but it continues to get smaller and smaller in the distance.

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