## Talking Math Over Piggy Banks

Six year old Lil’ Dardy accompanied me on a bank errand and she asked the clerk for a new piggy bank – her third now. Two of them are actual pigs while one is a sheep. She decided to name the pigs Pig and Peg. Pig gets dollar bills and change while Peg and Sheepy both get only coins. We emptied all of her money out and sorted for awhile. She has accumulated tons of coins, she has a great eye for coins on the floor. After we filled Pig with all of the bills, we started filling all of them with coins. Because I have a touch of OCD about this sort of thing, I started by picking up three pennies at a time and giving each container a coin. Then I moved on to nickels, etc. Lil’ Dardy mentioned that she, too, was going around the circle giving each one a coin but I noticed that she was not giving each one the same coin. So, I thought this would be a good opportunity to have a lil’ math chat. I asked her if she thought that each container would get the same amount of money and she quickly said no. So far, so good. I next asked her if she thought that they would have the same number of coins. Here, I was already planning her discovered instead of letting her discovery happen by itself. I am a little annoyed with myself for this. But, when I asked if they would have the same number of coins she again said no. I repeated that we were each ‘going around the circle’ putting in coins, but she said that she had just had this thought- she did not start out this way. Have to say I was pretty proud that she point this out in the face of my question. Hooray for Lil’ Dardy on this counting task this morning.

## Brief Notes on a Good First Week Back

As I wrote about the other day, I tried something brand new with my Geometry kiddos this week. I had found online somewhere recently a three day packet exploring reasoning and proof (you can find it here) and I had my students in small groups. I had three groups of three and one group of four (I know, I am very lucky (spoiled?) to have such small classes) and they all grappled with one of the open problems in the set and gave brief presentations on Tuesday. Yesterday we conducted a fishbowl discussion. I had never done this before as a teacher or as a student, so I felt a little anxious about it. Since I had not taken the time to ‘train’ my class, I left this as a pretty open exercise. There are two pages of definitions to grapple with in the handout linked above. I had seven students in the fishbowl for the first round and I joined the other six in the fishbowl in the second round. Every student drew a card at random as they came in to decide which group they were in. I instructed the outside group to just quietly observe rather than to take notes on the inside participants.  Both rounds went pretty well – in my opinion – but what was best about the day was the talk at the end looking back on the exercise. I have tried to make this first week back for Geometry rather open – ended. I wanted to try and make some important points about learning, and about classroom culture, about proof and logic.

I wrote already about the frustration one girl expressed during the spaghetti exercise where she wanted A right answer to the exercise. I took that opportunity to talk about different approaches, to try and emphasize our desire for efficiency when we can find it, but, more importantly, my desire to hear their voice and thoughts not just an echo of my voice and thoughts. They get too much of that from adults already. Yesterday as we reflected on the exercise two girls shared really interesting observations. One said that when she was inside the fishbowl (I was outside at the time) she felt really anxious about saying something out loud that might be wrong. She said she was more relaxed when she was outside but she felt she understood definitions better when she was inside. This is HUGE. This kind of self-awareness is so important. I asked her to think about that and think how she can use that realization moving forward in our class. I hope that she decides that she understands better when she is more actively engaged in the conversation around her. The other girl remarked that she knew that she understood better when she talks and I seized on that and challenged her to make talking in class a real commitment.

It’s been fun to be back – our school’s last full day of classes before this week was November 12. I appreciated the rest (other than grading finals – a post for another time) and I am glad to finally be prepared in advance for all three of my courses, but I sure did miss the interaction of the classroom and I have been thrilled with how my Geometry students (my youngest class) have come back ready to go. I have asked them to deal with different situations than they normally do and they played along beautifully. I am so pleased and I hope that we have made some important points about our time together. I also hope that I can hold myself to the most important lesson I learned this week. Unfortunately, it is one I have ‘learned‘ numerous times – my students are better off when they speak more and I speak less. I need to make this my mantra – especially if I want to effectively integrate some other changes in my classroom in the upcoming new year. That’s right, I do not want to let myself wait until August, 2016. I want some serious changes as of January, 2016.