We got up on Thursday morning, packed up, and headed south to Crater Lake for the day. It had been a week since we had been to a National Park, so I was definitely ready for some stunning beauty. As I’ve said before, my photography skills do not begin to do the scenery justice, but suffice it to say I was not disappointed.
As we toured the area, I was struck by how little I remember about volcanos. Even though I studied them in high school and college, all I really remember is that errurptions can spew lava, ash, or both. I don’t remember how they’re formed, how they behave, or anything else about them. But, I knew these things at one point, and I know how to find out more about them quickly if I want or need to. It was a little strange at the time to realize how much I didn’t know, and I wish I had addressed this in advance instead of on the fly in the visitors center, but it was still an amazing experience.
The parallels here are obvious. We talk a lot at school about focusing on what students need to learn/understand for the long term and what they can look up as needed. I clearly don’t need to know all this stuff about volcanos for my day-to-day life, so on one hand I think this falls into the “look up” category. On the other hand, I needed to have learned enough about volcanos at some point to know what I did not know. The question is, where do we draw the line between what we want our students to understand long term and what we just want them to know enough about to look up later?
Except I think that’s the wrong question to be asking. I’m not interested in my students’ long term understanding, I’m interested in their long term mindset. I want them to look at something 5, 10, 25 years from now and think about it logically, asking questions, looking for gaps in the information, and identifying possible assumptions. So the question really is, what do I want my students to know enough about to look up later, and what content and pedagogy is best-suited to developing this mindset? To me, that has to be the driving question for our integrated mathematics currriculum development.
So, what if I never had learned about volcanos at all? Would my experience at Crater Lake have been any different? I don’t think it would have been. I’m a curious person, one who likes to understand how things work and how they relate to other things I know about. I would have read the information at the visitors center and would now know exactly as much as I did before I got there. If it’s true for me with volcanos, why couldn’t it be true for my students with, well, any number of things?