5 Practices for Orchestrating Productive Mathematics Discussions

I wanted to start my professional reading this summer with big thinking and I met that goal with 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein.  The five practices guide student's responses to push their mathematical thinking further, striving for understanding.  The practices help teachers plan through a math discussion, focusing on the goal and not over reacting to their in the moment responses.  

The five practices are anticipating, monitoring, selecting, sequencing, and connecting.  These are really key in facilitating a math discussion.  Before the lesson is taught teachers should anticipate all possible solutions, keeping in mind what the students might think of.  During math workshop teachers need to monitor the various responses students are using.  A brilliant idea is to take the solutions from the anticipating thinking and make a chart with each one.  Then as a teacher monitors they can record quickly a student's name and an observation if needed.  After monitoring and finding out what student's are using, the teacher then selects students to share to the whole group, keeping the learning target for today in mind.  However, as we are selecting students to share we need to think about the sequencing in which they share.  The authors offer several ideas but the one I found most interesting was to share what the majority of the students used.  The reason being it validates less sophisticated approaches most likely and moves from the concrete to the abstract.  Then after students have shared, the teacher helps the students make connections between the solutions shared.  I hope this sounds as exciting to you as it does to me.  

The authors offer some insight about selecting and using high level demanding mathematical scenarios for students to work with.  Then they share several examples for each practice descriptions and conversations recorded.  The five practices need the support of good questions and holding students accountable for working through the mathematics and sharing their solutions.  I loved this quote, "What students learn is intertwined with how they learn it."  There are a few good tips for holding students accountable.  The authors provide a lesson plan template which looks quite detailed but as peaked my interest to improve classroom learning.  The authors share vignettes from different ages and classroom settings to help the reader visualize the five practices in action.  This book is filled with reasons to think and plan ahead for richer math discussions.