Friday, September 30, 2011

Sitting in the Back

In the last week or so, I've tried a new technique when I pose a question to the class, or want the class to solve a problem together: I sit in the back.

Typically, when I pose a question or a problem to the class, there are a few things that impede learning. First, the focus is still on me, so most of the students are just waiting for me to give the answer. Second, whenever a student does contribute an idea or question, it is directed at me. Not what I'm going for.

So, this week I wanted the class to work though a proof together. I drew the diagram on the board, asked the question, and then sat in the back row. This helped in two significant ways. For one, the focus was no longer on me; it was on the problem on the board. There was also a clear implication that with me sitting in the back - that this was their problem, and I'm giving them the time to do it (instead of the usual wait-long-enough-and-Mr.-Krenz-will-do-it-for-us game).

Additionally, the discussion of how to do the proof changed significantly. Questions and ideas were now being addressed to peers and the rest of the class rather than me. It wasn't me piecing together different students' correct responses to put a proof on the board with the false impression that the students did it. The students were offering ideas, critiquing, and collaboratively deciding on the next step.

When they completed a solidly challenging proof with almost no assistance, which they have been struggling with, I was still sitting in the back row. And I could not have been more proud of them.

It isn't perfect. I still give some guiding hints from the back, which I'm going to try to cut back on. The discussion can be confusing and solutions offered may not be correct. The path that is taken is not necessarily the most direct. But these are good things. Students start to understand that the perfectly linear proofs and thinking in the book isn't the way you need to think. I'm not sure it's the way that anyone thinks.

I'm sure other teachers have tried this. If so, I'd love to hear your experiences. If not, try it. Sit in the back and let me know what you think.

Thursday, September 22, 2011

What Do We Change?

This is long, and I'm unapologetically not going to bother proofreading much. This post is more or less a free write reflecting on the most intense day of my teaching yet. A day in which I didn't teach any math. I wrote this for myself, but I'd love to get some feedback.

This is my first year teaching, and my first experience teaching geometry. I have three standard, blocked geometry classes, and it is hard. The pace is quick, most of my students are freshmen, and we're having trouble "covering" what we need to at a pace necessary to finish.

I introduced proofs for the first time about a week ago, and we had a test yesterday. Scores were, well, less than what I was hoping for. I expected trouble with the proofs, which I found, but I was more concerned with the basic lack of understanding that I was seeing. The core pieces of the test - conditionals, converses, inverses, contrapositives, biconditionals, and the properties of congruence and equality - were simply not there. It's not that the students could properly interpret them and use them to judge and create. They failed to demonstrate a basic recall and application.

As a new teacher, this is difficult to deal with. It's frustrating and depressing. Without a doubt, part of this reflects my (in)ability to effectively teach the material and skills. I think this is more devastating to me than it is to my students.

However, I also know that this isn't all me. For one, I know that my students need to take responsibility for part of this. The choices that they're making in class aren't often the ones that will help them learn, and I think I need to teach that. Learning does not just happen; it is a choice that you make. I will do everything I can to make that a positive and helpful experience if you do choose to learn, but I can only do so much. I need to help my students understand that they are more of the class than me.

So, the response. Even though our schedule is a breakneck pace, I decided to take a full block - 90 minutes - to talk about how we do class. Preparation, learning, studying, review, interaction, behavior, everything. I wanted to do something to help them realize why we are in class, what the goals are, and what drives my decision making process.

So, rough lesson plan:

I asked six very basic questions that only require remembering the information absolutely necessary to doing well on the test. This is basically the lowest bar. I then read off the answers, had students mark their own answers, and then asked them to think about how they did. We talked about Bloom's taxonomoy and the different levels of thinking.

Passed back tests
I gave student a few minutes to go through their tests, thinking about what we had done so far. I explained that most scores were 5's and 6's. I use an 8-point standards-based grading system. A 5 means you demonstrated only a slight understanding of the concept, and a 6 means you're on the right track, but there is still a significant gap in your knowledge. So we have a ways to go yet.

Free write
I gave students about 4-5 minutes to write whatever they were thinking and feeling. Frustration, anger, reflection, ideas for improvement, whatever. I said that I wouldn't collect, so they could write anything. During the third block, I gave the option to turn it in, with or without a name, and I was surprised at how many students wanted to turn it in. They felt a need to be heard.
Next, students got in their groups and had a brief discussion about what they felt comfortable sharing. The discussion was reserved. While some students were happy to talk, I think many were feeling quite vulnerable and weren't entirely comfortable.

Word wall
On the whiteboard, I put a heading of "Thoughts/feelings", and encouraged students to write anything they wished relevant to this class. This was mildly terrifying. At first, only one or two students would slowly walk up. Then a few more, and then more. The atmosphere became markedly more relaxed. Students were seeing that they were not alone - others shared the same ideas, thoughts, and feelings, and I think it was comforting.

Then we spent a few minutes discussing what was up there. I summarized what I could, and students added a few more thoughts. Discussion was starting to roll.

Next, I had students brainstorm ideas for improving things. Class structure, assessments, practice, homework, behavior, teaching - anything and everything was fair game. Groups recorded their ideas, and then as a group, we transferred the ideas to the whiteboard up front. Once a few ideas were up there, more hands and ideas started popping up. I was impressed with the thought that students gave this.

Next, I offered my thoughts on what I was seeing. I explained why a few things were non-negotiables, but left it open for discussion. For example, I do not review immediately before a test. I explained that this is because I try to base every decision that I make on two things: does it help learning, and does it promote accurate assessment. We don't review right before a test because it's not testing true learning - it's testing short-term memory. Not all students liked this, but most understood.

Again, I was impressed with my students' engagement during this discussion. We were truly discussing learning and assessment. They were bring up things that they liked from previous teachers, and then we were discussing it in terms of "will this improve learning?" and "does this promote accurate assessment?" I've got a lot to think about here.

The Plan
To wrap things up, I asked each group to come up with three specific, concrete things that we could change in the context of our discussion. Each group presented their three, and then we voted as a class what three things we could change. There was a remarkable similarity between the three blocks.


This was an incredibly intense day for me. I spent 4.5 hours discussing everything about how I teach. I am emotionally exhausted. It was incredibly powerful, but my energy is gone. 

At the end of my third block, I was speaking to a few students in the last two minutes, and they asked me some innocent sounding questions that really capped off the day:
Why did you decide to teach? Are you sure you like teaching? You should have more fun!
I didn't have time to fully respond, and the questions were asked with true interest. I don't think they were suggesting I shouldn't teach. I think they were picking up on the fact that this job is hard, and this day especially was draining. In the 30 seconds I had, I said that I had been having this discussion for 4.5 hours today, and that it was scary for me. I was letting them write and say anything about my teaching, and I think they understood it.

After the class, I took a walk around the school to let things soak in a bit. I'm tired. I don't know exactly what to do. But, I do know one thing. I need to show students my love. I do love this job, and I love my students. I don't think I share that. Enthusiasm and spirit are tough for me. I've always been a rather reserved, introspective person. People who get to know me learn to pick up my emotion and excitement, but I need to do more than that. But remain who I am.

I need to figure out my way of showing students my love. For them, for my job, for my life.

Tuesday, September 6, 2011

When The Detour Has A Detour

I was driving to pick up my wife today, and the main road I needed was closed for construction. So I took the detour, and then came to a road completely closed off for an emergency. I then took my own detour.

As a new teacher, naturally all that I think about is teaching right now, and I thought this relevant. In the classroom, there will be detours. Sometimes they'll be predictable, sometimes they'll be surprises. The route may change, we may get lost, and maybe we'll see some things we didn't expect to. However, as long as I know where we are going, we'll get there.

I like that.