## Saturday, December 1, 2012

### How does a home workshop work?

This past week, Esther Billings, John Golden, and I presented Making Workshop Work in Mathematics at the NCTM Regional Conference in Chicago. One of the problems with presenting at these conferences is that the session description is due almost a year before the presentation. So while the program says, "explore several mathematics lessons and assignments that use the workshop model," we decided that the session would be more meaningful to participants if we worked through a single workshop, highlighted the workshop phases and research, and discussed how the workshop structure could support exploring the Standards of Mathematical Practice.

Although we provided a few minutes for participants to reflect on how they might apply what they learned about workshop to their classes, we were not explicit about using the approach on assignments. I hope to remedy this oversight by sharing a home workshop I used recently in my Teaching and Learning Middle Grades Mathematics course. This comes near the end of a unit on rational numbers.
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Doing Math Workshop (CGI Grouping Stories)

Objective: The learner will use representations to support their thinking and make their thinking visible to others as they find solutions to grouping stories involving rational numbers.

Needs: One hour and a copy of CGI Grouping Stories

Schema Activation: Reviewing Grouping Stories (no more than five minutes)
Recall that we used Grouping Stories from Cognitively Guided Instruction to provide context to multiplying and dividing integers. Review the different stories provided below and consider what it might look like as learners use the given contexts to compute their answers.

 Buschman, L. (2001). Using Student Interviews to Guide Classroom Instruction - An Action Research Project. Teaching Children Mathematics, 8(4), 222-227.
Focus: Goldilocks Problems (no more than five minutes)
As you read through the CGI Grouping Stories, you will notice that the values in each story have been left for you to choose. The goal is to select the row of values that is not too soft (so easy that it does not require any thought on your part) and not too hard (so difficult that you would not be able to make progress without a significant amount of help). In other words, find the "just right" numbers. In the space on the right, record the representations you used to support your thinking so you can make it visible to others.

Activity: CGI Grouping Stories (no more than forty minutes)

Reflection: What? So What? Now what? (at least ten minutes)
As you look back at your efforts, pick the one record that best demonstrates your ability to use representation to support and share your thinking.

• What support did the representations provide as you worked on this story?
• So what would you want others to see as you share your efforts?
• Now what does this mean for you as a teacher - as you consider designing rational number computation lessons?
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The next class period, we usually have a math congress where some of the students share their work with their peers and discuss their reflections. If there is any interest, I will try to provide some generic examples of these in a future post. Please leave your interest or your questions in the comments.