Being Dissapointed and the Fractal Nature of School

We’re getting toward midterms and spring break at my college, which means that I’m wrestling with disappointment. This week, I’m disappointed that so many students are missing class. And I’m disappointed in the energy they are putting behind their work. Being disappointed really sucks. I immediately personalize it (“They hate me”) and then get incredulous (“Don’t they realize how hard I’m working for them? Don’t they realize that when they do lackluster work and don’t even show up that it hurts all of us?”) and then I get mad and mean (“I’ll get them back when their grades reflect their poor effort!”). I’m not proud of going from hurt to bewildered to hostile, but I’m only human and I can’t separate my feelings so easily from my job as an educator (as I wrote about a few weeks ago). Midterm time always feels like the end of the honeymoon to me. I realize that they aren’t the perfect enthusiastic students that I wanted, and they realize that I’m not the teacher that will make math easy or effortless. I have to remind myself that there are problems that I can’t solve for students, and that many of them have nothing whatsoever to do with me. I think back to what I was like as a college student and remember that I skipped classes like I was allergic to them and once wrote out the lyrics to a Beastie Boys song because I had no idea how to start answering any of the questions on a calculus exam. I turned out OK (although I did fail calculus) and they will too.

What I was really wanting to write about today is how as teachers our struggles are the same as our students’ struggles. You know what I want as a teacher? I want to know how to be successful. I want to know what tricks I have to do and what buttons I need to press in order to have students that are creative, competent, and successful. I want to know the best way to teach every topic and the right way to respond to student difficulties. I want to know an easy way of telling if I’m doing the right thing in the classroom. I get really frustrated when I look for those answers and they aren’t out there, and I also get frustrated when the answers are out there, but the methods proposed don’t work for me. I get easily overwhelmed by the enormity of the problem of how to be a good teacher.

You know what my students want? They want to know the tricks and methods that will make them competent and successful. They want to know the right way to do every problem. They want an easy way to tell if they are “doing it right.” They get frustrated when they can’t find that kind of structure, and they get frustrated when the methods they find don’t have any meaning or don’t work for them. They want sample solutions for every possible problem. They get overwhelmed by the enormity of the subjects I am teaching them and the difficulty of finding a path through those subjects.

And you know what my administration wants? They want to know the tricks to making a school that produces bright and capable alumni that go on to graduate school or successful careers. They want to know the right way to structure majors and general education to meet those goals in a cost-effective manner. They want an easy method to assess students and faculty so they know if the school is “doing it right.” They get frustrated when faculty screw up their plans  — they’re looking for simple solutions that are quick to implement everyone gets overwhelmed by the enormity of the task of providing students with a quality post-secondary education.

So we’re all doing the same thing, just at different scales. Kind of fractal, really, which is nice since I’m teaching students about fractals right now in Math, Art, and Design.


Great Find on Empathy in the Classroom

I wish that I had more time to read blog posts about teaching. I stumbled across this piece by Michael Wesch today, who is an anthropologist, but had some quality wisdom for every classroom. He wrote about how teaching “techniques” are hollow without what he calls empathy. I’d name it “connection,” but I loved how he framed the problems that occur when people use great techniques without bringing their heart to the classroom.

Ever have one of those days?

Today I had one of those days as a teacher, the one where everything goes wrong. The kind where I got to class one minute late, forgot something I needed to hand back to a student, had four students absent out of nine, and planned to show several video clips as part of the class, none of which actually worked. And of course, after a day like this I’m heading back to my office and I get to thinking about how I really should have done the first two units in Math, Art, and Design differently this semester. I should have combined the topics of infinity and fractals which would have allowed me to alternate classes that were more abstract and cerebral with classes in which the fractal visuals provided both grounding and motivation. Why didn’t I think of that?

That’s when I got back down to my office and realized that I left my keys upstairs. On the way back up I started thinking about how I should have just abandoned my script once I realized that technology was not going to be my friend today, and done something hands-on. Moments later I’m back to the classroom, but the door is shut and I have now left the ID that I need to get into the classroom downstairs by my office. So I turn around in something of a huff and that’s when I realize that I’m not really all that good at going off script, especially not in this class, and in my current frame of mind that just says that I’m kind of a crappy teacher. Then I’m downstairs getting the ID, back up again getting the keys, and back down to the office, and my main focus is berating myself for my lack of student participation and the fact that this class isn’t inquiry-based and student led.

Yes, I know I’m not really a shitty teacher, but teaching is a job that we are going to screw up repeatedly. Wait, maybe all jobs are like that. I think maybe teaching is like being a stand-up comedian. In either case you are going to fall on your face repeatedly, and when you do there will be an audience, magnifying your failure. But tomorrow is another day…

What does it mean when students don’t do the assignment?

For today’s calculus class, I had the students read about average rates of change in the textbook and answer some questions on the reading. Most students did the reading. A few students did not. I expected this, but it is still difficult. One of the difficulties is around how to proceed with a lesson which some students are prepared for and others are not, but I want to leave that difficulty aside for the moment. The difficulty that is interesting to me right now is my interpretation of the students’ actions (or lack thereof).

This summer I read a great article — “The Emotional Practice of Teaching” by Andy Hargreaves. One of the things Hargreaves talks about in the article is emotional misunderstandings (p. 839):

Teachers frequently misconstrue their students’ exuberance for hostility, bored compliance for studious commitment, embarrassment for stubbornness and silent respect for sullen resistance. This misunderstandings seriously interefere with teachers’ ability to help their students learn.

When I have students that don’t do assignments, I leap to any of a number of conclusions. I go to that old standby of teachers everywhere — the students are lazy and want to be spoon-fed the material. Or this one — the students just don’t want to think for themselves. I go to the favorite of math teachers — the students just aren’t interested in learning math (so I guess I’m going to have to do all of the work around here).

After I had lots of these feelings in class today, I realized that I was feeling crappy about my students and about myself. So I decided I needed to write something about my feelings down here — after all, that’s why I’m blogging this semester — to give myself a way to process the emotions of teaching and a way to reflect on the relationships I am forming with students. And what I realize through this reflection is that I’m making a lot of assumptions that may be wrong — I don’t know why some students didn’t do the reading. I didn’t ask. What if I tried to find out rather than making assumptions? Digging down to the real reasons students fail to do assignments isn’t likely to be an easy task, because we all love to give nice excuses for things rather than being honest, but perhaps its a task worth attempting.

It is at least worth noting that my assumptions about why students don’t complete assignments paint them in a bad light and don’t point toward my own culpability. Maybe the reading assignment I gave was harder than the students were prepared for. Maybe it was too easy and thus boring. Maybe I didn’t give them any real reason to do the assignment aside from the fact that I’m grading it. Maybe the assignment was a complete waste of their time. Those reasons are potentially just as valid as the conclusions I came to, but they are less appealing to me as they point to my own flaws rather than the flaws of my students. I’m not proud of it, but there it is.

I’m not sure where to go with this next, but I think that I at least need to be communicating the purpose of assignments to the students, and I also need to solicit their feedback about assignments (are they at the right level of difficulty? do they seem designed to increase understanding?).

Some success!

Today’s Math, Art, and Design felt better to me than the last one. I had the students sit at one large table again, and that helped since it is a very small class. It’s a bit awkward since I’m always getting up and writing things on the computer and coming back to sit down, but the arrangement is going well. I also read last week’s feedback before class and their writing assignments, including the one in which they came up with goals for the class so that made me feel more connected right from the start. I started class with an activity done in pairs, a game they had to play and figure out strategy, so there were connecting with each other, and then we discussed the strategy as a class. Then when we got to the challenging part of the work (we were doing Cantor’s diagonal argument), I made them tell me their objections. When I had a couple out, we went over the argument again, but this time everyone was warned to watch out for how we handled the objections. It wasn’t totally smooth, but I was still talking math with one student while the class was ending and everyone was headed out the door, and another student stopped to tell me about an artist showing at the AIB library that might interest me, so I’m calling it a victory!

Energy draining, again

My second section of Math, Art, and Design still feels very difficult to get through. I feel like the student are on the other side of a brick wall that has just one tiny window. Every once in a while I can see someone, but most of the time there’s too much in the way. The feedback from this class seems to be fine (as of the last feedback I collected from them last Thursday), but it’s hard to get them to talk to each other or to me. I had them sit around a larger table today in the hopes that would help, but it didn’t seem to. I find it draining to lead a class when I don’t feel connected with the students, and I’m stuck on ways to really connect with these particular students.

Next week we may start on a different unit, and perhaps that will help. And perhaps at the beginning of class on Thursday I’ll talk to them about why this is a problem for me and ask them to address the issue in their feedback. I’m also going to try as much as I possibly can to have them engaged in activities rather than having classroom conversations (those go fine in my other class, but it’s a very different group). I’ll find a way through.



Arguing About Math

In my Math, Art, and Design class today, an awesome thing happened — students were arguing with me about math! In this class right now, we’re looking at the concept of infinity. We’ve talked about hotel infinity, and understanding the size of  a set through one-to-one correspondence, and defining an infinite set as one that is the same size as some part of itself. Today we talked through Zeno’s dichotomy paradox, and then we looped back to answer a question we asked last week. Suppose you have an infinite number of piles, each with one peanut. And suppose a friend also has an infinite number of piles, but she has one peanut in the first pile, two in the second, three in the third, and so on. Who has more peanuts all together?

I left this hanging as an open question last time, and we talked today about the answer. I showed them a method for making a one-to-one correspondence between the two sets (thus showing that they are the same size), and that’s when they started arguing with me and with each other. The thing that felt so wonderful to me is that so many of them felt they had the right to claim space in the discourse as their own. They saw themselves as arbiters of truth, rather than allowing me to dictate mathematical reality.  In the end I think that some of them were convinced that the two sets were the same size and others weren’t, but I loved the quality of everyone’s ideas and the fact that we had a space in which multiple views were being heard and debated.

That feels hard to do in math class, with math’s emphasis on “right answers.” I struggle with allowing this kind of discourse to remain open, without forcing it to close with a final decree on my part that I force them to accept. As a mathematician, I’m uncomfortable with ambiguity and uncertainty. I know that I get frustrated at my students when they insist on narrowing everything down to one “right answer,” and not allowing for the complexity of real problems, but I realize that I also crave that certainty because it helps me know where I stand as a teacher.

One other great thing happened in class today. After we discussed a worksheet the students had done on Zeno’s dichotomy paradox (finding the sum of the infinite series 1/2+1/4+1/8+…), students spontaneously opened up a discussion on problem solving process and how they felt as they were solving the problems on the worksheet. It was a brief discussion, but it made me really happy.