Learning as a teacher

I have learned a ton in these short four weeks as a math teacher. More than I could have thought I would, which has made coming to work every day constantly exciting. Since my time in the classroom is wrapping up soon (next week), I thought I’d share a few lessons that stuck out.

To be a good teacher, you have to be a good listener. It seems somewhat counter-intuitive…why would someone teaching a subject need to listen? You’re instructing, after all. What I’ve found is that planning is really only a small part of teaching. Of course, to be a good teacher, you need to know the material and be able to present it in a logical fashion. But it’s the improvisation of answering students questions that is what makes a really good teacher. 

It’s prodding students with endless “why?” questions to see if they really understand the material and are not simply regurgitating it. It’s walking around and seeing their work, finding not only specific struggles for students but also general trends. One other prospective teacher asked "what if they ask X?" and a veteran teacher said, "what if that happens? You can't prepare for everything now." Use what you know and what the students know to fill in the gaps.

For example, I taught a lesson today on graphing y = 1/x. From a class poll, the students had not seen it before. We went to a t-table and plotted (my carefully chosen) x-values with their tabulated y-values. But I noticed that many students wrote that 1 divided by 0 was either 0 or 1. Instead of just telling them “no, that’s wrong.” I wanted to get them to understand why it was undefined. To do that, I needed to come up with an on-the-spot analogy that would makes sense. So I asked, what’s 6 divided by 2? Everybody shouted out the answer. Why, though? I ask. Because 3 times 2 is 6! So the sky is blue because blue is the color of the sky? And so on. 

After considerable prodding, we got to the root of what division really means and why there is no combination of groups of zero that can give you six. A follow-up was why is division the same as multiplying by the reciprocal? At a certain point, we all take these facts to be just facts. Even I found myself starting out with some things thinking “well, that’s just how you do it.” But listening more acutely allowed me to fine tune my teaching and hopefully give students a deeper understanding of what they were doing.

Getting the answer, even in math, is not enough. Comprehensive understanding and a curious mind are what will help students succeed in subjects more than just math.

(Part II, with more lessons learned, will be soon.)