Intentional Talk Book Study- Chapter 3 "Compare and Connect"

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

I joined this book study because I really want to learn "how to structure and lead productive mathematical discussions" in my 7th grade math classes this coming school year.  I use the workshop model of delivery and students already do a wonderful job of working collaboratively.  I would like to improve the mathematical discourse during group work time and during whole class discussions.

Better photo of the planning template.

Question 1:  Can you think back to a lesson where students really benefitted from sharing two solutions? Sketch out the solutions and snap a picture.  There are several lessons in my Carnegie curriculum where we look at different ways to solve a problem.  My book calls it "Peer Analysis".  This sometimes shows two different methods for solving the same problem.  Sometimes it shows how two students solve the using the same method, however, one has a misconception in their solution so they are incorrect.  This is a very powerful tool for students analyzing worked examples of others. 

Question 2:  Do you find it useful to think what your board will look like as a result of a discussion? Why or why not? I think it is very useful to anticipate student solutions of problems in advance.  It can help you to place in certain order to show progression in thinking and strategy.

Question 3:  One idea for "Compare and Connect" is to link notation used in a standard algorithm to notations of invented ones.  Can you share a photo of what that might look like?  If you do -8 + 2, 8 + (-2), -8 + (-2), and 8 +2 all represented with a number line model (or you could also do a +/- counter model).  Students begin to see that when you add a negative and a positive number the sum ends up being the difference between the absolute values of the two numbers and the sign will be of the number farther away from zero on the number line.

Question 4:  Compare and Connect can be used to compare strategies, representations, tools.  What's an important connection students at your grade level need to make?  When we are talking about direct variation it's important for students to understand how the equation, table, and graph all represent the same thing and how those different representations look when it's a direct variation vs. when it's not a direct variation.

Question 5:  How do we know if students are understanding the goals we set for discussion?  What do you do to help students stay in the discussion?  We need to be checking in with individuals students and groups during discussion to hear their thinking.  We can also look at their work shown to see if they are making the connections we want them to make.  Having a sharing and reflection at the end with a problem that wraps up the goal of the days lesson can help us see which students really got it and are ready to move on and which students may need a small group lesson or individual conference.

Sorry I was unable to snap any photos of actual problems I do with students.  I am currently unable to access my shared folders where my SMARTBoard files are located.  Technical difficulties are a pain.