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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
2National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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!
3National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
Common Core State Standards
Mathematics
• Standards for Content
• Standards for Practice
4National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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
5National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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)
6National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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.
7National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
Structuring the Practices
8National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
Standards for Mathematical Practice
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?
9National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
The Nature of Tasks Used in the Classroom …
Tasks as they appear in curricular
materials Studentlearning
Will Impact Student Learning!
10National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
. . . 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
11National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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
12National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
Exploring QuadrilateralsPreparation for Problem Solving
Ms. Humphreys’ Overview…
www.insidemathematics.org
13National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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.
14National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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.”
15National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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:
16National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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).
17National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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?
18National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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.
19National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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
20National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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.
21National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
Join us in thanking the
Noyce Foundation
for their generous grant to NCSM that made this series possible!
http://www.noycefdn.org/
22National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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
23National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Problem Solving and Precision
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