We spent Monday in Reno, NV, where we did some hiking, went to the planetarium, and explored a little. Everything we did was on the recommendation of a friend of ours who had grown up in Reno, so as she said, we were effectively reliving her childhood. This was a very different experience than the ones we’d had in Portland and Seattle. A lot of our activities there were also based on recommendations of friends, but in that case it was friends who had recently moved to the area and had only recently discovered these things themselves. The differences in the recommendations between Portland and Reno were subtle, and we had great experiences in both cities, but if you looked closely there clearly were differences.
It occurred to me later that this very much mirrors my experiences as a teacher. I teach math, but my degree is in engineering. In my experience, this makes me an “outsider.” I don’t have the same training, mindset, or background as many of my colleagues who have undergraduate, and in many cases graduate, degrees in mathematics, which makes them “insiders.” Put another way, insiders are people who grew up in the field while outsiders are people who moved into it. Because I’m an outsider, I’ve had to work a lot harder to master the subtleties of concepts, see my way through proofs, and communicate what it is to look at things like a mathematician.
As teachers, we make the same insider/outsider distinctions of our students. Within any given class, we have students for whom the ideas come easily and we have students who have to work hard to master the concepts.