The classroom I now inhabit is equipped with four fairly large mobile lab tables and a single, oval-shaped wooden conference table that was probably designed to seat about 14 adults, but manages to fit closer to 20 students when necessary. The table is usually referred to as “Harkness-style”, and I just want to take a moment here to link a blog post from a Chemistry teacher who toured Phillips Exeter Academy in New Hampshire, where the “Harkness Method” of teaching was first developed. As Hans (the blogger I linked) notes, the Harkness Method was developed at Phillips Exeter Academy in the 1930s and has been used in the humanities ever since… but they did not use that method in the science classrooms until the 1990s.
Rhett Alain is an Associate Professor of Physics at Southeastern Louisiana University. He is one of many physics educators who has impressed me by being insightful and funny on Twitter (@rjallain), and at Wired.com Science Blogs.
Recently, Rhett wrote about a brain teaser. Then people on Twitter and in the comments section of his blog told Rhett that he was wrong, and he responded in the way we all should – he admitted he was wrong. I suspect that most people think they would be honest and forthright when their errors are pointed out, but I don’t know that most people actually do that. I always appreciate it when somebody does it correctly.
But that’s not exactly what prompted me to reflect here. The puzzler Rhett wrote about reminds me a bit of another that I heard a long time ago (I have no idea the source):
A man starts at the bottom of a mountain at sunrise and takes all day to hike to the top, arriving at the summit exactly at sunset. He camps at the peak overnight. The next day he starts down the exact same path from the peak, beginning at sunrise and arriving at the bottom exactly at sunset.
Keeping in mind that he’s on the same trail, does it have to be true that at some point, he will be at the exact same place and time on the second day as he was on the first day?
Years ago when I first heard this, I figured the answer would have to be “no”. I’m not sure why – it was just a gut response. Probably the reason I remember the question years later is that my gut response was wrong, and the reason it is wrong was explained very clearly. If I change the way the question is asked, it should become very clear.
One day, a man walks up a trail from the bottom of a mountain to the top. During the same day, a woman walks down from the top of the mountain to the bottom, using the same trail. Does it have to be true that at some point, they will be at the exact same place and time?
Clearly the answer is yes.
One of the most important things teachers ask students to do is to step back and gain some perspective on what they have been learning. Obviously, teachers must allow themselves the time and space to do the same thing. And as with students, we must seek feedback from others – peers and mentors in the field. I hope I am able to elicit some dialogue on various topics in education and physics. Without reflection and feedback, our ability to grow is compromised – and I would like to avoid that at all costs.