February 23, 2012, 6:48 am
Someone asked me recently what was the one thing that’s changed the most about my teaching over the last 10 years. My response was that I’m a lot more likely now than I was in 2002 to organize my classes around asking and answering questions rather than covering material. Here’s one reason why.
The weekly Mathematica labs that we have in my Calculus 3 class are set up so that some background material (usually a combination of math concepts and new Mathematica commands) is presented in the lab handout followed by some situations centered around questions, the answers to which are likely to involve Calculus 3 and Mathematica. I said likely, not inevitably. There is no rule that says students must use Calculus 3 to answer the question. The only rules are: (1) the entire solution has to be done in a Mathematica notebook, and (2) the solutions have to be clear, convincing, and…
February 13, 2012, 9:33 pm
A lot of my posts here are about alternatives to the traditional lecture-oriented classroom. Based on that, and on somewhat testy comments like these that I leave lying around the internet, you might get the idea that I am firmly anti-lecture. But that’s not entirely true. There are times and places where lecture works quite well, even better than the alternatives. Here are a few purposes for which I think lecture is well-suited:
- Modeling thought processes. The benefit of hearing an expert learner lecture on a subject is that, if the lecture is clearly given, the audience can gain some insights into what makes the expert an expert. A good lecture does more than convey facts or put problems on the board — it lays bare the cognitive processes that an expert uses to assimilate those facts or think his or her way through those problems.
- Sharing cognitive structures. Lectures provide…
January 30, 2012, 7:55 am
Since moving to west Michigan in July, my family and I have been living in an apartment while our house in Indiana
sells sits on the market. This is the first time since 2001 that we’ve spent longer than six months in a rental property. Sunday morning, as we woke up to find that we’d been buried in snow overnight (as per usual in west Michigan), I realized that the home ownership habit runs pretty deep with me.
When I looked out the door and saw the image you see in the photo, I naturally grabbed the snow shovel, walked out the door, and started clearing off the walkway and the van. I got some curious looks from my neighbors, as if to say: What are you doing? We are paying rent not to have to do stuff like this. And it’s true: The apartment manager usually comes through shortly after a snowfall and clears off the walkways. Usually. But who knows? Maybe he won’t come today. And anyhow,…
January 18, 2012, 7:12 am
Here’s a previous article in an ongoing series of What I Learned in 2011.
While it was still on TV, the show LOST was a favorite of mine. No, that’s not strong enough — it was an obsession. I discovered the show about halfway through its fourth season when I downloaded the series pilot from iTunes on a whim. I was hooked. I proceeded to watch the episodes online at a rate of about one per day — sometimes two or even three — until I caught up. I read the blogs, edited the wiki, listened to the podcasts. I was completely and totally absorbed. And this is coming from a person who otherwise watches TV maybe about an hour a week (modulo football and kids’ shows).
What was it about that show that I found so engaging? For me, the main thing was the deep humanity of the characters. In the first few episodes, it was very easy to pigeonhole them all. Sawyer was the criminal you had to…
January 3, 2012, 1:59 pm
One of the main reasons I’m at the AMS/MAA Joint Meetings this week is to take an MAA short course on discrete and computational geometry. That course is wrapping up this afternoon, and it’s been a good experience. I came into the course with zero knowledge of computational geometry, a within-\(\epsilon\)-of-zero knowledge of algorithms, and an extremely rusty skill set in topology. But I’m coming out with an appreciation for this subject and, hopefully, a basis for pushing farther into the field and eventually contributing something new.
Teachers ought to take courses more often. Apart from being intellectually satisfying, it’s useful to be on the receiving end of academic teaching in one’s own discipline every now and then because it helps you remember what it’s like to be in the shoes of your own students. Here are some things I’ve re-learned about being a student in a math…
November 29, 2011, 7:45 am
This year, I did something new on Thanksgiving: I ran one of those 5K “turkey trot” races on Thanksgiving morning. It was actually the second such race I had done in the space of a week. There’s something invigorating about getting up early and joining a crowd of a few hundred people to buck the temptation to lie in bed or on the couch all day.
Running has been a hobby of mine since my 40th birthday (July 2010). Turning 40, I was overweight and constantly tired, and I decided to do something about it. So I declared I would start training for a 5K, to commence as soon as the birthday party was over. As for how that beginning actually went, I’ll get to that later. For the moment, it’s enough to say that running has always accompanied a reflective mood for me. As I was doing the race on Thursday, I got to thinking about the connections between running and teaching. I think I’ve learned a…
November 15, 2011, 8:59 pm
Blogging’s been light this week due to a
stupid instructional decision to give exams in all three classes on the same day a couple weeks ago and then dealing with the grading fallout, plus having to get an actual print article finished by deadline. Let me ease back into it by sharing this quote by Seymour Papert that I just found, which really sums up my thoughts about teaching and technology:
The best teacher is someone who brings personal knowledge, warmth and empathy to a relationship with a learner. The effect of the new technologies is to provide better conditions for such teachers to work directly with their students. Of course tele-teaching has a role, but I hope it will never be the primary form.
That was from 1997, but it rings true today as well. It’s easy to forget these days that education is a fundamentally human thing, and at bottom it’s about relationships (and trust). …
October 25, 2011, 7:30 am
I just gave midterm evaluations in my classes, and for the item about “What could we be doing differently to make the class better?”, many students put down: Do more examples at the board. I think I’ve seen that request more often than any other in my classes at midterm. This is a legitimate request (it’s not like they’re asking for free points or an extra day in the weekend), but honestly, I’m hesitant to give in to it. Why? Two reasons.
First, doing more examples at the board means more lecturing, therefore less active learning, and therefore more passivity and dependence by students on authority. That’s bad. Second, we can’t add more time to the meetings, so doing more examples means either going through them in less detail or else using examples that are overly simple. In the first case, we have less time for questions and deep thought, and therefore more passivity and dependence….
October 14, 2011, 7:30 am
When we moved to Michigan from Indiana over the summer, my wife moved to a sort of “standby” status with her employer, a conglomerate of medical labs based in South Bend. They are considering opening up a new lab nearby, and if they do, my wife would not only work in the area in which she was trained — cytotechnology — but she would also be the general do-it-all lab worker for clients. To prepare my wife for her possible new duties, her employer is paying for her to take a class in phlebotomy this semester at a local college. That means she’s learning how to draw blood.
I joke with my students that if they think Calculus 2 is bad, then they should try taking a class that consists of sticking each other (and being stuck) with needles — literally, bloodletting — for 4 hours every week. But all jokes aside, there happens to be some pretty interesting pedagogy that takes place in my…
October 11, 2011, 7:30 am
I came across this Seymour Papert quote over the weekend, the best part of which is below. In context, Papert is speaking about effecting real change in the content of school mathematics, and he focuses particularly on the teaching of fractions:
One theory [among educators about why we should teach fractions in school] was that manipulating fractions was actually closer to what people needed back before there were calculators. So a lot of school math was useful once upon a time, but we now have calculators and so we don’t need it. But people say that surely we don’t want to be dependent on the calculator. To which I say, Look at this thing, these eyeglasses, that make a dramatic difference to my life and the life of everybody who reads or looks at any tiny detail. Once upon a time we would have been crippled, severely handicapped. Now we’ve got these and we don’t need to go …