1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining The National Council of

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

http://www.mathedleadership.org/


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!


Common Core State Standards

Mathematics

• Standards for Content

• Standards for Practice


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


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)



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.


Structuring the Practices



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.


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?


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?


The Nature of Tasks Used in the Classroom …

Tasks as they appear in curricular

materials Studentlearning

Will Impact Student Learning!


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


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





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.


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.


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?


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


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.


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.


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


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.


Join us in thanking the

Noyce Foundation

for their generous grant to NCSM that made this series possible!

http://www.noycefdn.org/

http://www.noycefdn.org/


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


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

http://tinyurl.com/samplesurvey1

Documents

1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Reasoning and Explaining The National Council of