Friday, February 10, 2012

How I Plan: The Triage

Prompted by this, here's what I've figured out so far about planning. I'm a bit embarrassed to post this, because I've always figured that lesson planning is the sort of thing that people learn how to do well during ed school, and that my inability to plan effectively was because I'd never been schooled in the art of schooling. But I think I'm at the point where I'm comfortable enough with what I'm doing that it's worth sharing.

In short: The most important thing I currently do in my planning is reflect on what makes the lesson difficult, and then to figure out some way to react. I write up a reflection on the hard parts, and then anything else that I do is built on top of this.

What I used to do.

Planning was a mess during my first semester of teaching. I would sit down to "plan" and end up googling stuff for 3 hours. I would find something cool, and then try to figure out how it worked so that I could use it in the classroom. Then I would find a problem, and then start looking for another resource. I printed out stacks and stacks of files. I downloaded lots of Mr. Meyer's stuff.

This was the first stage of my lesson planning, when I didn't understand teaching well enough to prepare in advance. If teaching were basketball, I didn't understand the game well enough to conceptually isolate offense from defense, shooting from dribbling.

Towards my second semester I started understanding that a lot of learning involved finding something that students did know and then hitching a new idea to that old knowledge. This lead to a new stage of my planning, where I produced a lot of outlines and mini-scripts of questions. These were almost always scrawled on the back of scraps of paper half an hour before class.* These plans were still pretty awful, though.

*In my desk drawer at work I have a huge stack of these outlines and mini-scripts. They're completely disorganized. I can't quite bring myself to throw them out, but they're entirely useless to me at the moment.

To give you a taste of the awfulness, here's one of the rare mini-scripts that I actually saved on the computer.

There is lot of terribleness* on display here. To start, this is inefficient planning. I don't need to plan out every step of a lesson in this way.  Besides, it's artificial and false to plan out every step of a class in sequence. Truth be told, these sorts of outlines were really just to get me thinking in the right way before class -- I almost never used them during the session. At the same time, these were incredibly time consuming.

*Terriblitude? Teribadingness? 

So when last summer came around, the second thing on my todo list was figuring out a better way to plan lessons. 

The Triage
Here are my guiding principles for lesson planning:
  1. The planning needs to cut the crap, and focus on the crucial bits. I have 4 preps, and zero patience for the sort of purposeless googling that my planning used to involve.
  2. The planning needs to be something reusable. So no more scraps of paper.
  3. The planning needs to anticipate the fact that someday I'll probably look back on it and hate it. I didn't want my planning to prioritize the creation of documents or slides that I'll likely hate as I learn more about teaching. I wanted my planning to be more robust than that.
In short, I want my planning to be efficient, reusable and distinct from the creation of classroom materials.

Here's an example of a lesson I put together this past Monday morning. It took me about 20 minutes for the lesson plan, and probably a half hour more to put together the problem set, and it was used later that afternoon: 

Quadratics Day 5 Lesson Plan
Quadratics Day 5 Problem Set

In case you don't feel like clicking through, my lesson planning basically involves a hierarchy of activities.

At the bottom of the hierarchy is what I need to do before every lesson to be prepared. And, at the moment, my thinking is that I need to reflect on what the hard parts of a lesson are going to be in order to be prepared. Some days this is reflecting on content, others it's reflecting on management issues that I'm having in class, and sometimes it's whatever. In my mind, this is the crucial core of a lesson.

If I've got that down, and I have more time, then the next most important thing for me to do is to reflect on good questions to ask in class. I also like thinking about the warm up questions that I'll ask in class, because this often gets me thinking about the bigger picture of the lesson. In other words, thinking about how I'm actually going to start the lesson helps me think about what I'm actually building this knowledge on top of.

What's great about this is that it's efficient. Reflecting on the hard parts of a lesson and some good questions to ask gets me pretty prepared to teach, even if it's a day when I can't put together an awesome task or a worksheet or a cool visual. In other words, most days. And if I have that time, then I can build on top of the planning, and the things that I produce are more focused and, um, good.

Because I'm recording things that happen before the lesson I'm pretty confident that this stuff will still be valuable to me. It will give me something to bounce off of, a place to pick up my thinking, even when I recognize that the thinking is no longer as on-target as I once thought it was.

This post has gone on long enough, and if you're really curious about how I plan you can click through those links above. But the important point for me is this: break down your teaching into little chunks. Then, find the little chunks that you need to think about the most before walking into the classroom. Make sure you do those every day. Then do everything else.

Sunday, February 5, 2012

VFC: Quadrilaterals

Here is a Virtual Filing Cabinet for resources concerning Quadrilaterals.. This is part of an ongoing experiment in how to better share online teaching resources. If you like this post, then make your own post for a particular topic.

What am I missing here? Point me to your favorite quadrilaterals resource in the comments.

[Last Updated: 2/5/2012]

The Hard Parts

A lot of the traditional proofs of the properties of quadrilaterals depend very heavily on congruent triangles. One of the real challenges in teaching this topic is to change your students' perspectives. When they see a rhombus they should see four congruent triangles; when they see a parallelogram they should see two pairs of congruent triangles; when they see a kite they should see two pairs of congruent triangles arranged differently.

There are lots of challenges for novices that go along with this change in perspective. Students need to see triangles in quadrilaterals, even if the diagonals are absent. Students need to see parallel lines with a transversal even when the sides of the quadrilateral are not extended. 

Another major theme of this unit is the hierarchy of shapes. A square is a rectangle, but it's also a rhombus. They are all parallelograms, though, and so what's true of parallelograms is true of them as well. This, plus a whole slew of new vocabulary.

Quadrilateral Resources

For vocabulary, I like the approach of the Discovering Geometry series. Show kids a bunch of examples of things that are "trapezoids", show them a bunch of things that aren't, and then challenge them to formulate a definition that works. This is a pretty common approach, from what I can tell. Here's a post from misscalcul8 on her version of it.

Once you have the vocab down, you might want to make it more concrete and emphasize the relationships between these shapes. I've posted about an activity that I like where students create "family trees" for quadrilaterals. 

One of the big challenges of this unit is (to my mind) getting students to see quadrilaterals as composed of triangles, as this generates all of the non-obvious properties of the quadrilaterals. I like this activity, which uses a series of tangram challenges of increasing difficult. It literally forces students to compose various quadrilaterals out of smaller shapes, including triangles. This can also serve as a concrete model that can be returned to over the course of the unit.

I'm still looking for resources for the actual nitty gritty of this unit which is the properties of the various quadrilaterals. I'll post resources as I find them, and please let me know if you have resources to add to this page.

Quadrilateral Family Trees

There's not a whole lot to this idea, but it was a good opener for the quadrilaterals unit, and it was a good use of our whiteboards.

One of the things that I'm trying to be more sensitive to in Geometry is just how difficult vocabulary is for students. I feel as if a lot of teachers in my life taught vocabulary as if the hard part was keeping the connection between the concepts and their names straight. That's wrong, though. What's difficult about learning a new term is for the concept to make a clear and distinct impression upon the mind.*

*  "Clear and distinct impressions" is for all my ex-philosophy major brothers and sisters out there.

Anyway, learning vocabulary. It requires real conceptual clarity before we can even talk about these things, let alone prove things about them, and so it's worth the extra time to get those concepts clear.

And it's also important to get the interconnectedness of these shapes clear -- that's a major theme of this unit.

Anyway, start by introducing the concept of a family tree. Know your audience. My boys know about video games, so we drew three big circles containing the words "Sony," "Microsoft" and "Nintendo." They told me video game consoles made by each of those three companies. When we got "Playstation" on the board I asked them whether there were different types of Playstations. Yeah, there are. And all of those things are Playstation machines, and all of those are Sony consoles, etc.

Then they made these.

Nothing ground-breaking here, but it was a good activity.