making a good teacher

I don’t want everything that I write to be about how terribly math is taught. It is something that I think about quite frequently, but writing about only that gets boring, especially when I have other thoughts.

I’ve been doing my placement with a high school for about three weeks now. So far, I’ve really loved it. I’m exhausted at the end of each day and my feet are in a lot of pain, but I’m enjoying every minute of it. I started out just helping out when students were working and had questions, but last week I started to actually teach classes, and so far it’s been fun. I always underestimate how much time it will take me to prepare the class, which means I’m up late the night before, and I frequently overestimate how much material I’ll be able to cover in each class, but it’s a really good learning experience. I’m lucky to have teachers who let me do this, and don’t have me just sitting and watching the entire time. I’ve also gotten some really constructive feedback from a couple teachers. While it’s nice to be told that I’m doing a good job, actually hearing what it is that I’m doing well and what I might think about doing differently is a lot more useful.

So this leads me to wonder what makes a good teacher. I know that this is not a new question by any means, and I’ve certainly thought about it before, but I’m going to try to figure it out again.

I started out by wondering why some teachers seemed to get their classes to learn while others didn’t. I thought of it as a way of figuring out what not to do. I looked at the classes that didn’t seem to be learning too much, and tried to figure out what the teachers were doing that I should try to avoid. This didn’t work, though, because all teachers do different things and have different styles. So instead I thought about the good teachers I’m with now, and the good teachers I’ve had in the past, and tried to figure out what they all had in common (that maybe some of the not so good teachers were missing). This is what I came up with.

Good teachers have expectations of their students. They expect their students to work. They expect their students to think. They don’t lower their expectations when a student is being difficult or having trouble, but they consider a different approach. Good teachers assume that their students can learn the material, and want to learn the material. They listen to what their students say. They don’t assume they know what a student is going to say, but they listen and try to understand. They listen to questions, and let their students finish asking before they answer. They also pay attention to what their students aren’t saying. They look for problems that students are having. Good teachers let students know that they understand what it’s like to be a kid, and that they are sympathetic and supportive, but that they won’t lower their expectations. They explain that students aren’t expected to know everything right away, but that they will be expected to know something once it has been taught. They look closely at what students are doing so that they can tell the difference between someone who is struggling with the material and someone who didn’t listen all period. They recognize that students are people with more going on than just school, but they make sure their students understand that school is important too.

Those seem to be the basics. When a teachers don’t do one or two of these things, when they assume the worst of their students, they tend to be mostly right. When they assume the best of their students, they’re also usually right. This sounds sort of idealistic, but it seems to be true. From what I’ve seen, teachers who deal with problems by sending their students to the office end up with more students to send to the office. On the other hand, teachers who assume that, given a warning (or two), students will change their behaviour for the better generally end up with a relatively manageable class.

It’s probably really frustrating for a good teacher to listen to a cappy one complain about difficult classes. Maybe it’s time for the crappy teacher to make some changes.

what is the perimeter?

I sat in a math class a few days ago and watched them take up a homework sheet from a couple days earlier. Several students had found the work difficult (and a few had forgotten about it), so the teacher had decided to discuss it with them instead of just marking it.

The sheet said, “Find the perimeter of the triangle.”

“How do we find perimeter?” asked the teacher. The students looked at her, probably waiting for her to answer her own question, or at least hoping that they wouldn’t be expected to.

“What do we need to find?” she asked.

One student said she didn’t know. Another said (not very confidently), “Lenth times width.” A few others agreed that multiplying the length and the width (of a triangle?) would give the perimeter. Someone may have suggested multiplying the base and the height.

The teacher asked them for the English definition of perimeter from their books. Instead of turning to the page that had the definition on it, the students stared back at her, wondering what it could possibly be that she wanted.

The perimeter of any two-dimensional object is the distance around it. This is something that 14 and 15 year olds should know. I am almost positive that all of these students learned what perimeter was several years ago, and I know for a fact that they were told again earlier this academic year (and again earlier last week), but they all treated it like it was new information. Or maybe something that they had been told long ago but had never heard about since then.

To be honest, I’m not at all surprised by this. I’ve seen (and heard about) high school students who are surprised to learn that when adding fractions, they need to first find a common denominator. The simplest operations become complicated once students reach a certain age. Math is sometimes a little tricky, so some of them figure that everything is incredibly complicated. What’s going on here? What is it about math that causes amnesia in people who are actually quite bright?

Students lose confidence, so they don’t try. Class is boring, so they don’t pay attention. Eventually, they get so lost that they couldn’t catch up if they wanted to.

This is not novel by any means (or maybe it is and I’ve just been listening to the wrong people), but math is taught wrong. Educators and policy makers need to get over the idea that students need to learn the basics of math before they can do the interesting, creative, fun stuff. The basics actually become fun when seen in the context of what math really is. None of the students in that class knew what the perimeter of a triangle was, and why should they? What interest is it actually to them? (And don’t start telling me that it has practical applications. If they need to know how much fencing they need to go around their yard, they’ll measure.)

Some of these students will probably graduate from high school with no clue what a perimeter is. They will go through the rest of their lives not knowing, and they’ll probably be fine. But they’ll also go through the rest of their lives not knowing how beautiful and elegant and exciting math can be, and I think that’s a real shame.

scared of teaching

I have often thought that the thing that makes me most qualified to be a good teacher is the fact that I have been (am currently) a student. Of course, I share this property with most people my age, at least in this part of the world, so that should mean that most of my peers would be good teachers too. I know this isn’t the case, so I must have a different point.

I guess what I mean is that I would probably make a better teacher than someone who has never been a student. As a student, I am constantly thinking about what my teachers are doing well and how I might do things differently in their place. I don’t know if this is a common thought for students, but I would guess not.

Pretty soon I’ll be spending a lot less time sitting in a classroom and more time standing at the front of one (which, I am coming to realize, is not easy on the feet and legs), so I’ll have fewer opportunities to critique others and more to be the one on display. To be honest, the idea absolutely terrifies me. I know that, officially, teachers are the ones who do the evaluating in the classroom, but I’ve spent so much time judging my teachers that I’m paranoid my students are going to do the same thing to me. What if I’m boring? What if I try to explain something and end up confusing everyone instead? Worst of all, what if my students don’t actually learn anything? What if I come into the classroom with all these progressive ideas about teaching and learning and none of them works?

Anyway, my point was not supposed to be how scary teaching is. My point is that it would probably be a good idea to record some of my experiences as a student. I think the best teachers I’ve had remember what it’s like to be a student. Not only do they remember that students have more going on in their lives than school, and sometimes those other things take priority, but they also remember what it’s like to be confused, to have something make no sense whatsoever, and get frustrated when the explanation is just repeated.

So, today, as a student, I got a little frustrated when I had difficulty reading the board because the instructor was writing too small and there were white chalky fingerprints that blended in with the writing.

Chalk is inherently messy. It doesn’t make as fine a line as a pencil or pen. Also, students in a classroom are usually farther away from the chalkboard than the instructor, so writing big(ger than might seem necessary) is important.

I doubt my classrooms will be as big as the lecture hall I was in today, but I still learned a valuable lesson: keep your writing big and your chalkboard clean.

school is boring

I’m trying to figure our what the difference is between younger students (like the grade 4 class I was with a year ago) and slightly older students (like the grade 9 and grade 10 classes I’m with now). Obviously, I can’t generalize and say that the classes I’ve seen are representative of those age groups, and in terms of high school classes, I’m mostly talking about math, which is just one subject. However, I do know, from hearing people talk about it, from working in classrooms, and from my own experience as a child and teenager, that there is a big difference between elementary school students and high school students.

I think that, in general, kids want to learn. Children are ridiculously curious. If they see anything new, they want to know what it’s called, where it comes from, how it works. They want to play with it, experience it, touch it, climb it, taste it. As we grow older, we don’t behave like this as much. We don’t automatically try to play with every new anything we come across. Sometimes we want to, but we’re generally more reserved.

This seems to be a big difference between elementary school students and high school students. Elementary school students want to learn. They misbehave, they get distracted, they sometimes give up when their work is to hard, but from what I’ve seen, they mostly buy into the idea of getting an education. High school students, on the other hand, don’t always. They are more likely to see school as something they have to do. Sometimes they find the subjects interesting, but their main reason for doing the work is that they need (or want) the marks. There are, of course, exceptions. There are young children who feel that school just takes time away from what they’d rather be doing (climbing a tree, playing a video game, looking at cool bugs), and there are teenagers who get a real sense of satisfaction from producing a solid piece of work, but this does not seem to be the norm.

So is there just a point in our lives when we decide that we don’t want to learn anymore?

I’d say that’s unlikely. I don’t think it has very much at all to do with the students. Learning is generally fun. School, on the other hand, is often boring.

It’s an interesting coincidence that students become less enthusiastic to go to school and learn around the same time that school and learning stop being a time of moving around and talking and playing games and discovering ideas and concepts, and turn into a time of sitting at a desk and taking notes, and then trying to apply those notes to questions in classwork or a homework assignment. An interesting coincidence, but not at all surprising.

Why is it more fun to be an elementary school student than to be a high school student? It’s probably because elementary school is fun, and high school isn’t. If elementary school isn’t fun, the students won’t pay attention, so teachers do everything they can to make their classes interesting, engaging, and interactive. High school students, however, should be mature enough to participate even if they’re bored out of their skulls, so their teachers get angry or penalize them if they don’t pay attention.

To be fair, some students do find the actual learning part of high school interesting. Not even just the marks, but the actual learning. Coming up with original ideas and figuring things out. The problem, I think, is that there is very little of this in high school. This is especially true in math classes, but I would guess it’s true to varying degrees across all subjects. Thinking is not really cultivated. Students might be told to think if they are having trouble, but I would guess that they are really being told to think back, and try to remember what they were told. What they should really be doing (in a math class, when presented with a question they don’t know how to answer) is looking at what is being asked, seeing what information is given, and figuring out the answer from there. They should not be trying to remember what steps they took the last time they answered a similar question, or flipping through their notes to find an example that matches this question.

It would take quite a bit of effort to convince me that most high school students would not enjoy really learning something. However, it isn’t enough to, every once in a while, give students a real math problem to figure out. Learning is fun, but it is frustrating. It’s difficult and time consuming and a lot of hard work. Once all of that is done, it’s incredibly satisfying, but when students are only given the opportunity to try something like that every once in a while, especially when the rest of the time they’re mostly just following steps, they probably wouldn’t want to try it.

So I guess that’s the difference between younger students and slightly older students. Younger students are being entertained. They’re doing the playing and experiencing part of learning, which is fun, so they want to do more of it. As they become older high school students, they don’t get to play as often. In order to learn, they have to listen to instructions that they then need to follow perfectly. No wonder they aren’t excited about it.

first thought

I have a lot to say about the little teaching that I have done. I have several thoughts on how people learn. I have a ton of questions about students’ behaviour and (sometimes lack of) motivation. I talk about it a lot, so someone suggested keeping a sort of log (web log, perhaps).

However, right now, what sticks out the most in my brain is the that I should rest my legs and probably take a nap.