5 PRACTICES FOR ORCHESTRATING PRODUCTIVE MATHEMATICS DISCUSSIONS Why

3 PHASES OF HIGH LEVEL INSTRUCTIONAL TASKS v LAUNCH • Introduce the problem •

Too much focus on accountability can undermine students’ authority and sense making, and unwittingly,

SUCCESSFUL OR SUPERFICIAL? v Lecture, Show & Tell • Without expert guidance, discussions in

HOW COULD MR. CRANE’S CLASSROOM MORE FIRMLY SUPPORT STUDENT ACCOUNTABILITY WITHOUT UNDERMINING STUDENT AUTHORITY?

1. SET CLEAR GOALS v Have a learning objective in mind v Identify those

2. CONNECT KNOWN MATHEMATICAL STRATEGIES v Did the students’ work include examples of different

3. DISPLAY INCORRECT ANSWERS TO HELP STUDENTS RECOGNIZE FAULTY REASONING

4. STEER DISCUSSIONS v You’re the expert. You can use their work and their

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5 PRACTICES FOR ORCHESTRATING PRODUCTIVE MATHEMATICS DISCUSSIONS Why is our approach to teaching changing? Students need: 1. high level tasks 2. teachers that support student engagement

3 PHASES OF HIGH LEVEL INSTRUCTIONAL TASKS v LAUNCH • Introduce the problem • Introduce the tools available to work on the problem • Nature of the products students are expected to produce v EXPLORE • Students work on the problem • Discuss/work on the problem in pairs or small groups v DISCUSS & SUMMARIZE • Variety of approaches to the problem are displayed for the whole class to view and discuss

Too much focus on accountability can undermine students’ authority and sense making, and unwittingly, encourage increased reliance on teacher directions.

SUCCESSFUL OR SUPERFICIAL? v Lecture, Show & Tell • Without expert guidance, discussions in mathematics classrooms can easily devolve into the teacher taking over the lesson and providing a “lecture” or the students presenting an unconnected series of “show and tell” demonstrations v Guide them toward strategies that are most useful, efficient, accurate, etc. v Teachers shape the quality of students’ mathematical thinking

SUCCESSFUL OR SUPERFICIAL?

HOW COULD MR. CRANE’S CLASSROOM MORE FIRMLY SUPPORT STUDENT ACCOUNTABILITY WITHOUT UNDERMINING STUDENT AUTHORITY?

1. SET CLEAR GOALS v Have a learning objective in mind v Identify those students whose work illustrated the multiplicative relationship well

2. CONNECT KNOWN MATHEMATICAL STRATEGIES v Did the students’ work include examples of different ways of illustrating the relationship? This assessment could help him be more deliberate about what students he selects to present and in what order.

3. DISPLAY INCORRECT ANSWERS TO HELP STUDENTS RECOGNIZE FAULTY REASONING

4. STEER DISCUSSIONS v You’re the expert. You can use their work and their explanations to steer the math to a conclusion which purposefully meets your goals.

LESSON PLAN FORMAT

INTRODUCING THE 5 PRACTICES

MONITORING