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1National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
The National Council of Supervisors of Mathematics
The Common Core State Standards Illustrating the Standards for
Mathematical Practice:Reasoning about Problems and Unpacking Others’ Reasoning
www.mathedleadership.org
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2National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Module Evaluation
Facilitator: At the end of this Powerpoint, you will find a
link to an anonymous brief e-survey that will help us
understand how the module is being used and how well it
worked in your setting.
We hope you will help us grow and improve our NCSM
resources!
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3National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Common Core State Standards
Mathematics
• Standards for Content
• Standards for Practice
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4National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Today’s Goals• To explore the mathematical standards for
Content and Practice• To consider how the Common Core State
Standards (CCSS) are likely to impact your mathematics program and plan next steps
In particular, participants will• Examine opportunities to develop skill in
reasoning about problems and unpacking others’reasoning
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5National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Standards for Mathematical Practice
“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” (CCSS, 2010)
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6National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the
reasoning of others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated
reasoning.
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7National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Structuring the Practices
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8National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Standards for Mathematical Practice
What implications might the Standards for Mathematical Practice have on your classroom?
1. Individually review the Standards for Mathematical Practice.
2. Choose a partner at your table and discuss a new insight you had into the Standards for Mathematical Practice.
3. Then discuss the following question.
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9National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Buttons TaskGita plays with her grandmother’s collection of black and white buttons. She arranges them in patterns. Her first 3 patterns are shown below.
Pattern #1 Pattern #2 Pattern #3 Pattern #4
1. Draw pattern 4 next to pattern 3.2. How many white buttons does Gita need for Pattern 5 and
Pattern 6? Explain how you figured this out.3. How many buttons in all does Gita need to make Pattern 11?
Explain how you figured this out.4. Gita thinks she needs 69 buttons in all to make Pattern 24.
How do you know that she is not correct?How many buttons does she need to make Pattern 24?
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10National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Buttons Task
1. Individually complete parts 1 - 3.
2. Then work with a partner to compare your work and complete part 4. Look for as many ways to solve parts 3 and 4 as possible.
3. Consider each of the following questions and be prepared to share your thinking with the group:
a) What mathematics content is needed to complete the task?
b) Which mathematical practices are needed to complete the task?
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11National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
The Nature of Tasks Used in the Classroom …
Tasks as they appear in curricular
materials Studentlearning
Will Impact Student Learning!
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12National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
But, WHAT TEACHERS DO with the tasks matters too!
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
The Mathematical Tasks Framework
Tasks as they
appear in
curricularmaterials
Studentlearning
Tasks as they
appear in
curricular materials
Student learning
Tasks as set up by teachers
Tasks as enacted
byteachers
andstudents
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13National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
www.InsideMathematics.org
A re-engagementlesson using the Buttons Task
Francis DickinsonSan Carlos ElementaryGrade 5
http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/218-numerical-patterning-lesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8
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14National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Learner A
Pictorial RepresentationWhat does Learner A see staying the same? What does Learner A see changing? Draw a picture to show how Learner A sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy.
Verbal RepresentationDescribe in your own words how Learner A sees this pattern growing. Be sure to mention what is staying the same and what is changing.
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15National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Learner B
Pictorial RepresentationWhat does Learner B see staying the same? What does Learner B see changing? Draw a picture to show how Learner B sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy.
Verbal RepresentationDescribe in your own words how Learner B sees this pattern growing. Be sure to mention what is staying the same and what is changing.
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16National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Buttons Task Revisited
• Which of the Standards of Mathematical Practice did you see the students working with? Cite explicit examples to support your thinking.
• What did Mr. Dickinson gain from using the same math task two days in a row, rather than switching to a different task(s)?
• How did the way the lesson was facilitated support the development of the standards of practice for students?
• What implications for teachers implementing CCSS does this activity suggest to you?
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17National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Again, WHAT TEACHERS DO with the tasks matters too!
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
The Mathematical Tasks Framework
Tasks as they
appear in
curricularmaterials
Studentlearning
Tasks as they
appear in
curricular materials
Student learning
Tasks as set up by teachers
Tasks as enacted
byteachers
andstudents
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18National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Planning to Support Students’ Opportunity to Learn
Select a typical task (or a related set of problems) from your instructional materials and design a lesson so that it offers more opportunities for students to develop both the content and practice standards.
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19National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Next Steps and Resources
Review the implications you listed earlier and discuss with your table group one or two next steps you might take as a district, school, and classroom teacher.
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20National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Today’s Goals• To explore the mathematical standards for
Content and Practice• To consider how the Common Core State
Standards (CCSS) are likely to impact your mathematics program and plan next steps
In particular, participants will• Examine opportunities to develop skill in
reasoning about problems and unpacking others’reasoning
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21National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
End of Day Reflections
1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain.
2. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.
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22National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Join us in thanking the
Noyce Foundation
for their generous grant to NCSM that made this series possible!
http://www.noycefdn.org/
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23National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Project Contributors• Geraldine Devine, Oakland Schools, Waterford, MI• Aimee L. Evans, Arch Ford ESC, Plumerville, AR• David Foster, Silicon Valley Mathematics Initiative, San José
State University, San José, California• Dana L. Gosen, Ph.D., Oakland Schools, Waterford, MI• Linda K. Griffith, Ph.D., University of Central Arkansas• Cynthia A. Miller, Ph.D., Arkansas State University• Valerie L. Mills, Oakland Schools, Waterford, MI• Susan Jo Russell, Ed.D., TERC, Cambridge, MA• Deborah Schifter, Ph.D., Education Development Center,
Waltham, MA• Nanette Seago, WestEd, San Francisco, California• Hope Bjerke, Editing Consultant, Redding, CA
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24National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Reasoning and Explaining
Help Us Grow!The link below will connect you to a
anonymous brief e-survey that will help us
understand how the module is being used
and how well it worked in your setting.
Please help us improve the module by completing a short ten question survey at:
http://tinyurl.com/samplesurvey1