5 Practices for Orchestrating
Productive Mathematics
Discussions
Twitter Math Camp 2016
Kerry Gruizenga and Tony Riehl
Billings, Montana
Skyview High School
Billings, Montana
~ 1600 Students grades 9-12
Kerry Gruizenga
@kgruizenga
Algebra 1
Algebra Foundations
AP Statistics
Skyview High School
Billings, Montana
~ 1600 Students grades 9-12
Tony Riehl
@riehlt
Algebra 1
Algebra 2
College Algebra/Trig
5 Practices for Orchestrating Productive Mathematics Discussions
Goal 1:
Introduce the “5 Practices for
Orchestrating Productive Math
Discussions”
5 Practices for Orchestrating Productive Mathematics Discussions
Goal 2:
Do an activity to demonstrate
the “5 Practices for
Orchestrating Productive Math
Discussions”
5 Practices for Orchestrating Productive Mathematics Discussions
Quick Survey
Raise the number of fingers:
1 – Heard of 5 Practices
2 – Read about them
3 – Considered using them
4 – Tried the process in my class
5 – Successfully used the process
5 Practices for Orchestrating Productive Mathematics Discussions
Let’s do this….
5 Practices for Orchestrating Productive Mathematics Discussions
5 Practices for Orchestrating Productive Mathematics Discussions
• Individual time
• Group time
5 Practices for Orchestrating Productive Mathematics Discussions
5 Practices for Orchestrating Productive Mathematics Discussions
• Sequencing
• Presenting
5 Practices for Orchestrating Productive Mathematics Discussions
5 Practices for Orchestrating Productive Mathematics Discussions
*Margaret S. Smith
and May Kay Stein,
Five Practices for
Orchestrating
Productive
Mathematics
Discussions.
NCTM. 2011
5 Practices for Orchestrating Productive Mathematics Discussions
Five Practices for Orchestrating
Productive Mathematics Discussions
1. Anticipating
2. Monitoring
3. Selecting
4. Sequencing
5. Connecting
5 Practices for Orchestrating Productive Mathematics Discussions
1. Anticipating



Do the problem yourself
What are students likely to produce?
Which strategies advance the
mathematics?
5 Practices for Orchestrating Productive Mathematics Discussions
2. Monitoring
• Listen, observe, identify key strategies
• Keep track of approaches
• Ask questions of students to get them
back on track or to think more deeply
-Advancing and assessing questions
5 Practices for Orchestrating Productive Mathematics Discussions
3. Selecting
• CRUCIAL STEP – what do you want
to highlight?
• Purposefully select those that will
advance mathematical ideas
• Focus on student personalities
5 Practices for Orchestrating Productive Mathematics Discussions
4. Sequencing
• In what order do you want to present the
student work samples?
• Do you want the most common first?
• Do you present misconceptions first?
• Last order – extension examples
5 Practices for Orchestrating Productive Mathematics Discussions
5. Connecting
• Craft questions to make the math visible.
• Compare and contrast 2 or 3 students’
work – what are the mathematical
relationships?
• What do parts of student’s work represent
in the original problem? The solution?
• Connections to the past?
5 Practices for Orchestrating Productive Mathematics Discussions
Part two ….
5 Practices for Orchestrating Productive Mathematics Discussions
5 Practices for Orchestrating Productive Mathematics Discussions
• Individual time
• Group time
5 Practices for Orchestrating Productive Mathematics Discussions
5 Practices for Orchestrating Productive Mathematics Discussions
• Sequencing
• Presenting
5 Practices for Orchestrating Productive Mathematics Discussions
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5 Practices for Orchestrating Productive Mathematics Discussions
4 𝑁+4 −8
5 Practices for Orchestrating Productive Mathematics Discussions
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5 Practices for Orchestrating Productive Mathematics Discussions
(𝑁 +
2
2
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2
5 Practices for Orchestrating Productive Mathematics Discussions
Five Practices for Orchestrating
Productive Mathematics Discussions
1. Anticipating
2. Monitoring
3. Selecting
4. Sequencing
5. Connecting
5 Practices for Orchestrating Productive Mathematics Discussions
Questions?
5 Practices for Orchestrating Productive Mathematics Discussions
1.
2.
3.
4.
5.
6.
7.
8.
The Mathematical Practices
Make sense of problems and persevere in solving
them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated
reasoning.
Credits
Five Practices for Orchestrating Productive
Mathematics Discussions. NCTM. 2011
Margaret S. Smith and May Kay Stein
Mathematics Vision Project
http://www.mathematicsvisionproject.org/
Contact Information
• Kerry Gruizenga
[email protected]
Twitter: @kgruizenga
• Tony Riehl
[email protected]
Twitter: @riehlt