1 National Council of Supervisors of Mathematics Illustrating 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

2 National Council of Supervisors of Mathematics Illustrating 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!

3 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Common Core State Standards Mathematics Standards for Content Standards for Practice

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

5 National Council of Supervisors of Mathematics Illustrating 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)

6 National Council of Supervisors of Mathematics Illustrating 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.

7 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Structuring the Practices

8 National Council of Supervisors of Mathematics Illustrating 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?

9 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision The Nature of Tasks Used in the Classroom … Tasks as they appear in curricular materials Student learning Will Impact Student Learning!

10 National Council of Supervisors of Mathematics Illustrating 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 curricular materials Student learning Tasks as they appear in curricular materials Student learning Tasks as set up by teachers Tasks as enacted by teachers and students

11 National Council of Supervisors of Mathematics Illustrating 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 ). Hillsdale, NJ: Lawrence Erlbaum. Geometric/ Graphical Verbal - Written and Oral Tabular Contextual Symbolic Pictures Oral Language Manipulative Models Real-World Situations Written Symbols Representation Stars Elementary Secondary

12 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Exploring Quadrilaterals Preparation for Problem Solving Ms. Humphreys Overview…

13 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Exploring Quadrilaterals Doing Mathematics The kite manufacturer builds only quadrilateral kites, but it doesnt 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.

14 National Council of Supervisors of Mathematics Illustrating 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.

15 National Council of Supervisors of Mathematics Illustrating 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:

16 National Council of Supervisors of Mathematics Illustrating 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).

17 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Exploring Quadrilaterals Implications 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?

18 National Council of Supervisors of Mathematics Illustrating 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.

19 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving and Precision Todays 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 studentsperseverance and precision within a problem-solving context

20 National Council of Supervisors of Mathematics Illustrating 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.

21 National Council of Supervisors of Mathematics Illustrating 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!

22 National Council of Supervisors of Mathematics Illustrating 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

23 National Council of Supervisors of Mathematics Illustrating 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: