Teaching Geometry - Journal Post #1

I usually try to write blog posts with a point. I don't often have the energy for that lately. But I do want to keep track of how this class goes...

Today was the first day of my geometry class. (It is the first time ever for me to teach geometry. I have done lots and lots of prep.) It goes for 6 weeks, and meets 3 1/2 hours a day. (Yikes!) My students are mostly high school students, though this is a college class. The college screwed up registration. I had 28 students on my list, but a bunch thought they were on a waitlist (only happens when a class is full with 40 students), and came in not yet registered. I now have 35 or 36 students. Of course I ran out of handouts.

I gave what I thought were good directions for our first activity, and students managed to do strange other things.


My directions:

Welcome and Triangle Activity

This activity is an introduction to the themes of the course. The more thought and care you put into it (the activity and the course), the more learning and joy you will get out of it.

With a straightedge, draw a big triangle on this page. Make it as weird as you want as long as it is a triangle. Make sure it looks different than the triangle your neighbor draws.

Now you are going to draw three lines inside it. Each line will go from a corner (aka vertex) to the middle of the opposite side (aka midpoint). These lines are called the medians of the triangle. How will you find the midpoints? Do this as accurately as you can. Now look at what others have drawn. What do you notice?

[Can you guess how this activity connects with the themes of the course?]

***

I should have had them find the midpoints first. And then talk about connecting those to opposite vertices. (Fixing the handout now.) Some people connected the midpoints to each other. Some drew a new triangle inside the first triangle. (Pretty but nothing like what I asked for.)

So the activity took lots longer than I expected. Sadly, I didn't note the time. (I have a tutor working with me in class. I will ask her to keep track of how long things take.)

I thought I could manage to lecture on 4 sections of our textbook in about an hour and a half. No way. I enjoyed what I did with the students, but we only got through 2 sections.

Some of what I did was impromptu. I asked them to each write down their own definition of angle. Then I asked for volunteers to read their definitions. I talked about courage. I waited. Finally I got a volunteer. And then another. I did not criticize their definitions, even though I didn't like them much. The third one was closer. He was struggling for a word for how far the one side is from the other. I repeated his definition, with a big pause where he had been stuck. And then I said rotation. We talked about things that rotate.

One of the book problems we did just asked them to measure a line segment against a ruler printed in the book, and angles on a protractor. It was hard for them. And that was good for me to see. It tells me where we are.

I hated our textbook when I first started reading it, but eventually it seemed fine to me. I think the first chapter has more problems than the rest of the book.

1.1 Reasoning. They talked about types of reasoning and included 'intuition' (along with inductive and deductive reasoning). No. Intuition helps us guess what we might want to try, and helps us see things that might be true. But I don't like them calling it one of 3 types of reasoning.

1.2 on measurement turns out to be more useful than I expected. Looking it over now, there's a lot more there that I haven't gotten to. Good thing I've asked them to turn in their notes on their reading. I hope that helps. (They are supposed ot read the first 4 sections.)

The last hour and a half is devoted to labtime. We will be using lots of labs from Henri Picciotto's Geometry Labs (free). I had hoped to do 3 of them today. We didn't even finish one. (Lab 1.1 involves putting different shapes of blocks around a point.) I had also hoped to introduce them to euclidthegame. We'll do that tomorrow.

Quiz first thing tomorrow. I am hoping to keep them on top of things by quizzing daily.

We are part of a program called High School STEM Connection. 20 of my 35 students are part of that program, and are required to come to tutoring after class. Most of them did. They got most of their homework done. Yay them. I love spending time with them where I'm not in charge. I'm just there to help out when they need me.

I am hoping to complete 5 sections of the book tomorrow. I'm tempted to throw out the cool group activities, but I know I shouldn't. I think I'll just see how far we get, like today. And then tomorrow evening I'll have to think again about how to adjust.