1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools The National Council of.

1National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Modeling and Using Tools

The National Council of Supervisors of Mathematics

The Common Core State Standards Illustrating the Standards for

Mathematical Practice:Modeling with Mathematics and Using Representational Tools

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

modeling real-world problems with mathematics using appropriate tools and representations


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.


The Nature of Tasks Used in the Classroom …

Tasks as they appear in curricular

materials Studentlearning

Will Impact Student Learning!


Maria and Wayne Task

Maria saved $24.

She saved 3 times as much as Wayne.

How much money did Wayne save?

Work the task.

What representations and strategies did you use to solve the task?


Maria saved $24.

She saved 3 times as much as Wayne.

1. In what way(s) did the set-up of the task differ from the “traditional” way we experienced the task?

2. Why do you think Ms. Sherman might have set up the task the way she did?

3. What standards for mathematical practice might be addressed through her delivery?

Teacher Set Up Task as Set Up


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

Four boys discuss their

understanding of the

task.

1. What representational tools do the boys use to engage in the task?

2. What mathematics do they use to model the real-world problem?

3. How does their conversation demonstrate any of the Standards for Mathematical Practice?

http://www.insidemathematics.org/index.php/classroom-video-visits/public-lesson-number-operations/182-multiplication-a-divison-problem-4-part-c?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8


Closer Look at Content4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

1. What made the content of this problem so difficult and led students into thinking the problem might be 3 x 24?

2. What about student approaches reassures you?

3. What about their thinking on this standard needs refinement?


Closer Look at Practices

Model with mathematics.

Use appropriate tools strategically.

How does the revised task support the students’ development of expertise regarding these practices?


Adapted from Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. In C. Janvier, (Ed.), Problems of Representations in the Teaching and Learning of Mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.

Geometric/Graphical

Verbal - Written and Oral

Tabular

Contextual

Symbolic

Pictures

Oral Language

ManipulativeModels

Real-World Situations

WrittenSymbols

Representation Stars

Elementary Secondary


One More Look

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.


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

modeling real-world problems with mathematics using appropriate tools and representations


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

1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Modeling and Using Tools The National Council of.

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