From Lower School to College

I taught this afternoon. No surprise--teaching is what I do, after all. But today's audience wasn't the usual run of five- to ten-year-olds. Instead, they were college students.

This is the third year now that I've had the opportunity to work with the students in the math methods class at Vassar College (taught this year by Professor Chris Bjork in the Old Observatory, pictured below). This semester, I'm presenting two workshops to the students, and they'll be coming to visit at least once during a math class at school. It's a nice way to bridge the gap between theory and practice for the students--and a nice way to connect the PDS and Vassar communities.

Today's workshop was on addition and subtraction. We looked at how and when to introduce these concepts, discussed a little bit of developmental theory, and talked about why it's wise to model operations and algorithms with manipulatives and real-life situations before moving into the realm of the abstract. We played a couple of computation games as well (field tested, of course, on genuine PDS children). The students were a pleasure--they were focused and interested and asked some thoughtful questions.

I'll write more about this visit later, but for now I have two observations about how college students are different from children in elementary school.

1. College students are much more skilled than elementary students at discussing a question with a partner. "Talk to the person next to you about what the answer to this problem might be," I tell the children at school, and the response all too often is "It's seven! It's seven, seven, seven, seven, seven, seven, it's SEVEN." It can take multiple prompts before they remember to explan why they think it's seven.

College students, on the other hand, at least these college students, discuss the question thoughtfully, carefully, and respectfully. They take turns talking (!). They don't shout, and they don't repeat themselves. Score one for the college students.

2. Elementary students, on the other hand, are much more comfortable than college students at sharing the results of their discussions (assuming they've actually had 'em). "Raise your hand if you'd like to summarize what you and your partner talked about," I'll say, and hands typically shoot up all through the room. The same question to college students is met with tentative glances, furrowed brows, and, after a long pause, a hand or two creeping up slowly until it's about even with the student's ear. They get there in the end--but it's slow.

Now if we could just combine the best of both worlds...