Learning to Teach: I’m Sorry

This will be my eighth year teaching, and my third school. I left both of the first two because of declining enrollment, but my new school was built to relieve overcrowding and is already (surprise, surprise) getting overcrowded itself. I shouldn’t be able to screw this one up.

My current school is not a charter or selective enrollment. It’s a neighborhood high school, and we teach the kids that live in our neighborhood. We’re also part of a special network of schools within the district (I’ll talk more about this later, but it isn’t my point here.) One of the things we do is have training academies that use experienced mentor teachers (oh look, me) to develop new resident teachers over the course of a year. So this year, I will have two residents working with me the entire year. We shall call them “Boy” and “Girl”. And I will do my best to talk about my interactions with them, and not them as teachers, as that is not our point, nor is it very nice since they are here to learn and both seem lovely so far.

They have no experience. They don’t have teaching degrees or certificates, and they haven’t student taught before. This is on me. And it’s a little bit terrifying.

Our network has a pretty well developed training program, and does generally a strong job of teacher preparation. The program focuses a lot on classroom management (which is super important, especially in a turnaround school) and routines/structure. I particularly love structure, although I’m not always the best at routines.

So what do I want Boy and Girl to be able to do?

Apologize.

?!?!

Yep. I say apologize because that’s what taking ownership of everything that happens in the classroom often seems to boil down to, and if you’re secure in what you’re doing, it helps everyone. See, I want them to be able to manage a classroom. I want them to give clear directions and have their students follow them. But I would be lying if I said I could do that perfectly every time, and I have a pretty forceful personality.

So I apologize:

“Stop. Put your pencils down. I’m sorry guys, I don’t think I was clear about what we’re supposed to do here. Lets ___”

“I think I messed up yesterday. We’re still having trouble with ___ and I need to do a better job. Can I try again?”

Nobody’s wrong. Nobody’s in trouble. Nobody failed. And if anyone did, it was me. I just should have been clearer. Let me try it again. And calmly, we get there. Without “But you said to…” or “I thought we should”, sincere or not. Put a positive spin on it.

I think if they can do that, and pull it off, they will be so far in classroom management.

Oh, and they need an attention getting signal. Cheesy & elementary school but it totally works.

Do you apologize? How do you keep things positive in your classroom?

Favorites: Piecewise Functions

One of my favorite things to teach is piecewise functions in Advanced Algebra. For my Honors classes, it comes pretty early in the year.

Last year, it was the first time I really convinced my class I could teach them something.

I started the year with a quick review of functions and inequalities. My students were unimpressed. This class was supposed to be a challenge, and instead it seemed easy.

I asked if the students knew domain & range, and of course everyone had it down. The x is domain, the y is range. Done.

Yep, sure, sounds good guys.

So lets get to some piecewise functions. And then I lost them. Mostly because they thought they could find me whenever, and could just catch on to whatever I was teaching. [Last year was the first and only section of any kind of Advanced Algebra offered at my high school, so they had no point of comparison. That won’t be the case this year.]

I did a brief lecture of the concept of using just parts of a piece of a function, which went ok. Then I went over how the domain and range worked for a piecewise function. I’ll spare you. It wasn’t very exciting. Also, they didn’t really get it.

The next day, the opener had students graphing one of two functions, depending on which side of the pair they were seated on. I told them to take one piece of paper from either partner and rip it in half (so that they had the same scale). So they each graphed their function, and then I had them fold their papers on the line x = 2 (or whatever, really). This helped a lot with the piece part of it, but the domain and range was still fuzzy.

In retrospect, these two activities should have been the first things I did.

The opener was the same, but then I had students write down the domain and range for ONLY their section of the graph, before they pieced them together. Separating it like this seemed to really help them understand that it was only one part of the equation, and that the composite determined the domain and range.

Then they pieced together the two graphs and wrote the piecewise function. Finally, each student rewrote their domain and range on a number line, and then placed the number lines together to see overlap and draw a new number line to see the domain and range for the piecewise function. For these functions, the range was continuous, but the range had a gap, which I think was helpful.

Then the fun began. Each student (I had 29) got one part of a function, which was labeled 1-10 and A-C—ie. 2B or 9A, and then a piece of graph paper. Each student oriented their graph paper horizontally and then graphed the function they were given.

Then the students found the others with the same # (letters didn’t matter yet). Once they had a group of 3 A-C, I gave each group a full size sheet of paper with a piecewise function laid out—the only thing missing were the parts of each, which the students still had. Those went into blanks labeled 3A, 3B, 3C (etc) on each sheet. I printed them out on a variety of fun colors but that’s totally optional.

Once the students had glued or taped their expression in the correct place, they knew the domain of their portion of the piecewise function. Using that information, they cut their graph according to their domain, then wrote out both domain and range (onto two number lines if needed—it really helped my students).

Finally, each of the graphs was put together on the bottom of the paper, and the domains and ranges were combined to find the domain and range of the piecewise function. I would give them one more piece of graph paper for this, but I didn’t last year. That caused some issues if there was a gap in the domain, since students physically cut the graphs into pieces—if no one had 2<x<3, there was a missing strip between two sides of the graph.

This activity really helped my students understand where piecewise functions were coming from and was really fun to teach as well. Everyone was engaged the whole time, and really into what came next.

What is your favorite subject to teach? Activity structure?

[I can’t post the document or images right now because I’m on vacation with very limited internet, but I have it still. You can email me for it or leave a comment.]

Maps (not directions)

Our (amazing) administration has given us some time and (a little) funding to write maps for all of our courses in the math department. The network we are a part of is supposed to have these, but they are two years old, were written by two people with very little experience (who are no longer employed by the network) and honestly make no sense at all.

We teach the high school standard courses, but our students are tracked (we call is streamed. Whatever.) so we actually have four levels of everything. That means we teach 12 courses. Many of the schools in our network are turnarounds, so in general the students are fairly low level. We have our share of low students, but we also have some very high achievers. Unfortunately, the maps manage to meet no one’s needs.

The AP asked me to manage the process and coordinate the meetings and I thought I would share a little about it in case its helpful to someone else.

First, our goal was yearly maps. We are also required to write quarterly calendars, but my concern was more about making sure that two sections of the same course at the same level taught by different teachers were still comparable. Informative without being directive. That means I wanted one page, divided into quarters, with topics listed (fairly generally) and an approximate number of days. My rationale was that then a new teacher did have something to go off of* and a more experienced teacher still has the flexibility to tweak things.

To start off, I split us into groups of 4. Each group was given four different colored sheets of paper and a pen. No other supplies needed. Each color corresponded to a course (Algebra, Geometry, AAT, Senior Year). I gave the groups about 6 minutes to list the topics that should be covered in each course in their small group. I told them not to worry about overlap, duplication, order or amount of time. Just list.

Then we came back together and I put out the textbooks–we don’t even have seniors yet, but I wanted to make sure we were clear about where things are included. Some topics everyone assumes are covered at another level so they get skipped and others kids see over and over again. We took only a few minutes with this as well, and then split into three groups by course (no levels yet–we started with our on-level students).

Each course had a big poster page of paper and took each groups data so far to list out what was included in each course. Then we took a break and looked over the maps, writing questions on post-its on each chart. Some great comments, questions and missed topics came out of that, so I’m glad we did it. We talked about topics that were duplicated and what that looked like. Duplicating topics is fine (Systems of Equations is a big topic in both Algebra 1 and Algebra 2) but we need to make sure that the content isn’t duplicated as well. Review solving a system in two variables to get ready to introduce the new topic of systems in three variables in AAT.

Next up, everyone got five stickers per map and put them next to the five topics they felt were most important on that map.

That was basically two hours worth of work, but a really good start to writing the maps. One person from each group took the list home with them and started the work of splitting it into quarters and making some guesses on numbers of days.

For our next meeting, we plan on finalizing the on-level maps for each course, and then starting on the two iterations of below level students. Honors will be last.

Have you written a curriculum map? Any good advice for us?

*My first year teaching Algebra 1 I asked what I was supposed to teach:

“Whatever you want”

“We’re very flexible.”

“Its really up to you.”

….I want to teach whatever I’m supposed to. I don’t have an opinion here, I don’t know what I’m doing. I wanted someone to say “teach this, then this. You might want to try this.” No one did. (Now of course, I want to do my own thing, since I think I know better than everyone else. Or something.)

Hello world!

This could be one of those things that sounds like a great idea and then proves to be impossible to keep up with. We’ll see.
I plan on talking about curriculum, planning, teacher training and math–algebra at several levels and AP Stats. Welcome!