A Sorted Beginning

First day of Geometry and Measurement for K-8 Teachers today.  I did some improvising that turned out well, and wanted to think about that a bit. So, quick blogpost.

We were starting with Piece of Me, an activity I've stolen or modified from David Coffey. (I called it Piece of Mind today. I have a pun problem.)  The idea is that instead of the instructor droning on, not looking at you, students find out what they're interested in. One modification I do sometimes is to have them start in their groups. Develop two questions for your tablemates, then ask the person on your right. When they were done, I asked for the questions. I often write down student responses on the whiteboard, just from the principle that it helps them feel listened to. If I'm doing it, I write down them all. Just on impulse, I decided to sort them as they came in.

Now what? I said that I had sorted them. Each group should come up one more question for each list. A few minutes to discuss, then everyone stands up. After you give another question you can sit down. I don't call on people, just first to speak. The only rule was that we had to have one for each column before another one in a used column. When one was suggested, I just asked the class "Agree or disagree?" and we put it where the majority agreed. Sign one of a good semester: no one asked me if they were right! Actually that's sign two. Sign one was that they started on questions without a single person asking me what the columns were. Not that there's anything wrong with that, but the willingness to just give it a go is great.

Then they picked one question to all answer at their table. After all this (about 25 minutes) I asked: were we doing math when we did this? Some yes and no, but when a yes argued that we were noticng, sorting and analyzing by characteristics, plus looking for patterns she crushed the opposition.  I made a point that I want class to be free for people to speak, even if they are the only ones with an opinion.

Finally we did the teacher piece. Lots of why am I teaching, why I am a prof questions, with too long of stories from me. Questions about the course were about working with students, how are they being assessed, what does homework look like.

The next activity is one of my favorites for attributes, and I have used this with all ages.

Game: In or Out?

Set up: draw a circle-ish shape, or lay down a rope, or divide the room in half... two regions is what we're looking for. Players standing around a circle works best in my experience.

One player comes up with a rule that can be determined to be true or false for each player. True, they're in, false they're out. Starting with the player to the rule maker's left, they guess if they're in or out. If they are correct, they can try to guess the rule.

If you need winners, coming up with a rule that no one guesses is a win or a point.

I started with are you wearing sandals. 5 or 6 and they got it. We had rules about shorts, shirts, hair color. One fellow who's rule was at least as tall as me when he was the tallest in the class. I had an every other rule, that went about 15 deep. One great rule was whether you were standing in the shade or not. The rule maker was just at the edge, so we had 15 no's, then yes's until someone got it. We talked about the math we were doing, and I was able to connect their comments to the importance of non-examples. I also talked about the activity being accessible to many different learners and free for different kinds of participation.

When we came back inside, they talked about these questions in their groups:
1)    What were some of the rules used? 
2)    Was there a rule that was easy to guess?  Why?
3)    Was there a rule that was difficult to guess?  Why?
4)    What is a rule that would divide our class into two groups of roughly the same size?
5)    What are two rules that would divide our class into 4 groups of roughly the same size?
6)    Why do two rules divide a population into 4 groups?  Give an example.
Extension: Into how many groups would 5 rules divide a population? N Rules?

To reflect we tried for number 6 as a class. They came up with three ways to visualize in the classroom:

• hand up, stand up. One question you stand for a yes, the other you raise your hand for a yes. (New to me!) It was neat to be able to look at an individual and interpret, but not a good display to get a sense of the group.
• end, middle, end, double no's elsewhere. Worked okay, but not as well as ...
• four corners for four groups. Once we tried it, they divided by a Cartesian scheme, with one direction the first question and the othe question the perpendicular direction. This they liked, and appreciated how there was a dividing line for each question.

We tried:

• sibling & more than 1 sibling: It turned out we all had siblings, and someone noticed that even if someone didn't, they wouldn't be divided on the other question.
• wearing shorts & wearing denim: four groups, but it's hot so not many non-shorts.
• curly hair & shoulder length or longer hair: not many short and curly. This prompted the question - do they have to be linked? No? Well, then...
• pet & eat a good breakfast: yes fish count as pets. Not many non pets, but good division on breakfast. I mean bad because people, it is the most important meal of the day.
• TV in the bedroom & eat a good breakfast: computer in the bedroom doesn't count, even if you watch TV on it. (Hmmm.) This was almost perfect, 6,6,5,5.

They jotted down their take aways, then shared in group. Good stuff about nature of the activity, how much of the problem solving they did,  how engaging the sorting questions being about themselves were. I shared how a teacher had students write down sorting ideas, which she could then screen for sensitivity.

I am looking forward to a semester with these people!