Day: May 18, 2008

When they’re wrong…, or, how the heck do I scaffold?

I started this post a long time ago (maybe two or three months ago), but scrapped it. But I’ve decided to finish it up and make a little plea for advice at the end.

What do you do when you ask a question and get a totally wrong answer? Okay, this question screams newbie, but it happens to me enough and I often get caught in an awkward situation. Let me explain.

A completely made-up but not unrealisitic example:

Me: So we now we have this: x^2-2x=-1. Where do you think we go from here? What are we trying to do again? StudentX?

[Context: We’ve learned how to graph quadratics, use the quadratic formula, complete the square, factor, and seen equations like this all year. It should be second nature to them. And for many it is, but for some it isn’t. The problem is this: we’re way beyond this. We’re working on some other concept, and these gaps force me to veer away from the current lesson and take a bunch of steps back to reteach these things to the few that don’t get it…]

StudentX:  Um… well, we could add 2x to both sides…
Me: [awkward silence while I think of what to say, because I don’t want to do that…]
Me: At every step, we want to ask ourselves: (1) why do we do that? and (2) what are we trying to find out? So why would we add 2x to both sides? What are we trying to do?

[Context: Even when they are on the right track, I will ask this question. I want them to think about every move they make.]

StudentX: I don’t know.

At this point, I’ll ask what type of equation we have, and what we know about it. StudentX will finally get it (“quadratic!”), and we’ll move on.

Sometimes I don’t make it a drawn out process. If I’m in a rush, I will ask if someone else has a different idea and call on someone who I know will have the right answer, and then move from there. And then I’ll return briefly to the original idea and explain why it won’t get us to where we want to be.

But this interaction takes 3-5 minutes, I know 80% of the students in the class are bored, some are trying to whisper the answer to the student, and we get held up.[1]

Of course, I’m all about meeting students where they’re at. And I’m happy to review. But these moments happen all too often, and using every one of them as a teachable moment takes too much time and would be bad practice. I have a curriculum to cover. Taking three steps back constantly is tough.  

That tension, between moving forward in the curriculum and making sure students are up to speed on the older stuff, is palpable. 

I often feel like I sacrifice the majority of the class when I do too many of these types of things. I don’t want to praise a wrong answer (“That’s a great idea, but I’m not sure it’ll help”), I don’t want to scare a student from speaking in class (“No”), I don’t want to spend a lot of time on a basic skill that the rest of the class knows, I don’t want to make the student feel dumb or ignored (“Anyone else have a different idea?”).

I’m afraid I’ve done all three.

To make this into a truly teachable moment would require me to add 2x to both sides, and then stick with the student and ask them what next. And just stick with them until they see that they’re stuck. But I tend to only go down really wrong paths in math when we’re learning something new and we have the time to have these dead end explorations.

Basically, when it comes down to it, I recognize that I still don’t know how to organize and manage a differentiated classroom well, how to scaffold lessons, how to keep everyone engaged and learning, while still moving forward in a fast-paced curriculum. It’s not that I don’t try. About 30% of my students have some learning difference or another, and I do think about that when I’m designing my lessons. I do. But what I’m doing isn’t working. At least not as well as I’d like.

I think that in addition to classroom management, this is one of those big topics that doesn’t often get explicitly addressed in teacher blogs. Maybe that’s because a good many teachers do it without thinking about it – it’s natural. But even though I do a lot of things naturally well, planning a scaffolded lesson for a pretty differentiated class isn’t one of my fortes. Yet.

So anyway, if you know of any blog posts or websites, or have any advice, holla out in the comments.[2]

Yeah, I know, I know. Everything about this screams “Newbie.”

[1] One of my fears is that I’m going too slow for a bunch of my kids, and I’m not sure where my focus should go. The middle of the road? Those that don’t get it? Those that do? For me, I think a complicating factor is that I was always one of those kids who did get it, and really quickly. I identify with them. I don’t want those kids to be bored. And I feel guilty because I am pretty sure they are bored.

[2] Five or so years ago, I read about differentiated classrooms in one of my teaching classes, but the readings were all academic mumbo jumbo with no connection to reality. I’m looking for something useful.

My Blogroll

I’ve been meaning to put a blogroll up for a while. But the problem is that my blogroll is constantly evolving, and I wanted something that updates as I update.

Well, my RSS reader netvibes — which I’ll tout as currently the Best. Thing. Ever. — allows you to see all the blogs I read, updated. So click on the netvibes icon on the right and check out some of the amazing blogs out there. Without further ado: my blogroll.

Bad Students Or Bad Teaching?

Okay, so here’s a story I somehow missed from a few months ago. A lecturer of writing at Dartmouth created quite a stir with a threat (then removed, then reinstated) of suing her students and some colleagues. Why? Discrimination. (Honestly, though, who knows of what kind. Even after reading everything, I’m at a loss.)

There have been a bunch of writings on the topic, most of which I’ve read, but you can get the overview with this initial article, and then chase it down with a much more interesting interview with the lecturer herself [1]. She alleges, when it comes down to it, that her students were bullies because they didn’t agree with or show sufficient respect to her and the ideas she was proffering.

The reason this controversy spoke to me is partly because the lecturer was teaching a class on Science, Technology, and Society. That’s my undergraduate major and an interest of mine in graduate school (and an amateur interest of mine today). And teaching STS to undergraduates is tough. Believe me — not only did I take a number of courses where the professors and their TAs had their hands full, but also because in graduate school, I TAed for a couple courses which were on STS or STS-themes.

It’s hard work. Here it is laid bare. Getting students to understand the concept that perhaps Science should be spelled with a lowercase ‘s’ and that it doesn’t necessarily always progress to Truth with a capital ‘T’ is mind-blowing for them. It takes a long time for them to even grasp onto that idea. That science is somehow intimately related to culture is contradicted by everything they’ve been taught. Many initially rail against these ideas because they think of science as this Objective thing which can’t have anything to do with culture. It deals, they think, with mathematical equations and physical laws of the universe, and has very little to do with the people who are writing the equations and deriving the laws of the universe

The lecturer notes in her interview:

So there was immediate friction, because basically the concepts that I was trying to bring to them were concepts I was not inventing on my own. They were concepts that were part of the field, and I was trying to bring it to the table. It offended their sensibilities, because the whole course of “Science, Technology, and Society” was about problematizing science and technology, and explaining the argument that science is not just a quest for truth, which is how we think about science normally, but being influenced by social and political values. Now I’m not telling you this to convince you of this. I’m just saying that this is the framework with which I approached the course—that I wanted to bring this view that science and technology; there’s an ethics behind it.

Once you can get them to cross over to the human side of things, you generally can then start talking about scientific innovation, paradigm shifts, and the cultural side of science. It’s hard work. And you can’t win over every student. But the best and most fruitful conversations that I had with my students as a TA, that I had as an undergraduate in my many STS classes, that I had in graduate school with other graduate students, was fighting over the framework. Disagreeing with it, playing around with it, falling in love with it. It’s controversial stuff, not the least of which is because some of it’s hard to read, some of it is hogwash, and some of it goes beyond being radical.

What reading the interview with the lecturer indicates to me, however, is that she probably just doesn’t know how to teach well. Who knows? I wasn’t there. But some choice-quote indicators:

I think that sometimes when you have some students and some instructors they mix like oil and water…

The whole integrity of the course, the whole academic integrity of the course was undermined because it never became about the students meeting my expectations, it became about me meeting their expectations. They abrogated that right. They abrogated, they turned the tables around. Bullying, aggressive, and disrespectful.

I talked about ideas that were strange, I came off as very eccentric. I can’t make things up, I can’t read their mind. So they would use any type of vulnerability. They would use this and write these horrible evaluations that hardly reflected my efforts and quality of my teaching.

I said what you did was unacceptable. They started arguing with me. I said fine. You think you know everything. You think you know everything without the knowledge base to boot, without the training, you think you have a command of all the knowledge in the world at this stage in your life, then I’m sorry, that is fascism and that is demagoguery.

That’s very arrogant because frankly, and I’m not trying to be an academic elitist, but frankly, they don’t even have a B.A. They’re freshmen.

I think a lot of professors are like, I’m the boss of the classroom and you listen to me, and that’s probably the norm. I’m a little more lenient, I’m a little more liberal, and I think this was kind of taken advantage of. I think also that many times when I was lecturing, many of the students would take over the class.

While they took over the class, the students that were questioning me would not question the student, but they would consistently question me.

She was probably the most abrasive, the most offensive, the most disruptive student. She ruined that class. She ruined it. She ruined it. That class actually had a lot of potential, there were some really bright kids there, but every time she would do a number of things that were very inappropriate… One of the things that she did, this is also really interesting, was that she would always ask me how to spell things. That was her thing. She would say how to do you spell this? How to you spell that? I mean—what am I supposed to do?—so I would tell her.

Yeah, I think professors are not immune from being questioned. I’m not saying that these scholars I’ve studied should not be questioned, but the comments I was getting on my papers were like “Oh, this thinker is like, the worst writer in the whole wide world,” or “This thinker thinks they know everything,” and I would be getting irrational things from them.

So yeah. I’m not sure she is knows how to teach. My sense is — and again, who am I to know? — she didn’t introduce the concepts slowly enough for the freshman. They’re hard concepts. She might not really have a (good) classroom management style, so the students ended up taking over the class. And the biggest thing that drives me nuts about this? She didn’t capitalize on their questioning, their dissent. That’s where the learning takes place, because it’s in the dissent that their confusion can be seen. Their assumptions teased out. And the truly academic dialogue can take place. She seemed to want her students to get it because she said so.

Academia isn’t about teaching. At least not at the big research universities, where research is privileged. That’s one of the huge reasons I had to leave grad school. The blame probably should be spread out a bit more. Still, a fascinating case study, tying together my interests in teaching and my interests in STS.

[1] A whole slew of links are here.