1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision The National Council

1National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision

The National Council of Supervisors of Mathematics

The Common Core State Standards Illustrating the Standards for

Mathematical Practice:Problem Solving and Precision

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

supporting students’ perseverance and precision within a problem-solving context


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



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.

What implications might the Standards for Mathematical Practice have on your classroom?


The Nature of Tasks Used in the Classroom …

Tasks as they appear in curricular

materials Studentlearning

Will Impact Student Learning!


. . . 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


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


Exploring QuadrilateralsPreparation for Problem Solving

Ms. Humphreys’ Overview…

www.insidemathematics.org

http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-properties-of-quadrilaterals/297-properties-of-quadrilaterals-tueasday-introduction-part-a?


Exploring QuadrilateralsDoing Mathematics

The kite manufacturer builds only quadrilateral kites, but it doesn’t make kites only according to the mathematical definition. The manufacturer can make any type of convex quadrilateral.

Manufacturer's Problem: Every time an order comes in, we need to figure out how to make that particular kite. This is not efficient.


Exploring Quadrilaterals Task as Set Up

1. In what ways could this instructional move support perseverance and/or precision within a problem solving context?

2. What might Ms. Humphreys achieve by incorporating this instructional move?

3. What other instructional moves did your facilitator model that supported perseverance and precision?

In the clips you watched during the task facilitation, Ms. Humphreys chose to be explicit about the “investigative process.”


Exploring Quadrilaterals Task as Enacted

1. What do you see or hear that indicates students are developing their abilities to persevere and use precision?

2. In what ways do perseverance and precision appear to be working in interaction to support problem solving?

3. What instructional moves or decisions that the teacher made appear to have supported these practices?

As you are watching the next video clips, consider the following:


Exploring Quadrilaterals Task as Enacted

1. How would you describe what Ms. Humphreys is doing in this clip?

2. Why might this be a productive instructional move to support problem solving and precision?

Ms. Humphreys opens the next class period by sharing samples of student work from the last class period. As she shares the student work, she comments on what she noticed while reviewing their work (e.g., thinking she saw methods students/groups used to communicate developing ideas).


Exploring QuadrilateralsImplications for Instruction

Take a few minutes to reflect on the instructional strategies discussed today.

1. Which of these strategies would you like to integrate into your own toolbox for instruction to promote problem solving and precision?

2. What could you do to prepare yourself and your students to interact with mathematics in similar ways?


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 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

supporting students’perseverance and precision within a problem-solving context


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: Problem Solving and Precision The National Council