## Thursday, February 2, 2012

### Tiles in the Bag

Earlier in the week, the 7th grade teacher told me that the next unit that she was covering with her classes was Probability and Statistics, which is a huge part of the 7th grade curriculum and makes up 30% of the State Exam.  Since I had taught 7th grade in the past, she asked me for any thoughts or suggestions.  I shared with her some of my past unit plans and offered my thoughts on teaching certain topics, and decided to share the Tiles in the Bag activity from Marilyn Burns during this week's math team meeting.

Burns actually has two versions of this activity, and for our team meeting, I choose Version2.  For this activity, I filled three brown paper bags with red and blue tiles.  One bag had 25 red & 5 blue.  One bag had 20 red & 10 blue.  And the last bag had 10 red & 20 blue.  I told my fellow math teachers this information and had it written on the Smart Board.  We chose a bag at random (I didn't even know) and then we went around, and each person drew a tile from it, noted its color (red or blue), and then replaced it.  One of the teachers kept a record of the colors on a sheet of paper.  We all took turns participating till we had 25 random samples with replacement.  After we had done that, we computed the percentages of red tiles for: the first five samples, the first 15 samples, the first 20 samples, and finally all 25 samples.  We briefly talked about the importance of being comfortable working with percentages and the misconceptions that scholars sometimes have with percents.  As a group, some of the things we noted were: "Not understanding that percent represents a whole," "Converting between fractions, decimals, and percents," and "Percents less than 1 and greater than 100."

Going back to the activity, we had to decide which bag, of the three possibilities, we think we used, and which bag would we have chosen if our decision was based on five samples?  Ten?  Fifteen?  How many samples do we think we needed?  We each took turns sharing what we thought and then explaining why.  After we had shared and talked with each other for about 15 minutes, we opened up the bag and actually counted the tiles.

What am I learning about collaboration?
What I noted, as everyone was sharing out their predictions and reasoning, was how into the conversation I got.  I try to write myself notes during our team meetings, of things to remember to write about on here, but I found myself really listening to my fellow colleagues, and focusing on the math that is going on.  And although, it is challenging because I do want to keep these entries authentic, I think the fact that I am getting draw into the conversation says a lot.  I wasn't aware of it, but my focus wasn't "What am I learning about collaboration by doing this activity with my colleagues?" but "How can I use what I know about probability and statistics to come up with an viable argument to share?" I was thinking about the math!

Although I was very pleased with this experience and the other teachers thought that this was an awesome activity, it did make me wonder about what better ways I could possibly record data during our meetings?  That way, I could really focus all of my attention on the math we are doing, and less on gathering data for my action research.  Plus, with video clips I would have another record of authentic data, in addition this this blog, for my research purposes.  This may be something to look into...

1. So it seems like putting yourself in the students' shoes enabled you to predict some of the struggles that they will have with the activity, and also plan more deeply.

How do you think doing the "kid" math together is different than doing "adult" math together, as far as your collaboration goes?

I think that the recording is a real struggle! Maybe something simple like your question on a piece of paper so you can take jots in the moment, or right after the meeting might help.

2. Hi Anna.
It’s very powerful for teachers to be allowed to share what are common misunderstandings around a math concept. I think it helps us work through our own misunderstandings. Not sure what the teacher meant by “Not understanding that percent represents a whole.” I don’t understand that statement. A percent represents a whole?

I agree with you that getting drawn into the conversation, even though it’s a challenge to then remember everything and reflect on details afterward, says a lot about the authenticity of your work and experience.

Certainly video would help you gather data. But I also think that blogging immediately after the fact might help you reflect on details that are still current. I think you have a lot of data for your question about collaborative professional development. To begin with, you don’t separate yourself from authentically engaging in the activity yourself. What do you think?

Robin

3. I loved this entry! I think that it is so important to not only think about the math and interact with it yourself but also have dialog about what you might expect from your students. You mentioned with your colleagues some concepts and skills that students would need to know or that they might have difficulty with. I wondered if you all discussed what scaffolds you would have in place in the event your students did struggle with content or skills.