The National Council of Supervisors of Mathematics

1. The National Council of Supervisors of Mathematics The Common Core State Standards Illustrating the Standards for Mathematical Practice: Seeing Structure and Generalizing In Grades K-5 www.mathedleadership.org

2. 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. Mathematics Standards for Content Standards for Practice Common Core State Standards

4. 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 seeing structure and generalizing Today’s Goals

5. 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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Standards for Mathematical Practice

7. Structuring the Practices

8. Standards for Mathematical Practice • Individually review the Standards for Mathematical Practice. • Choose a partner at your table and discuss a new insight you had into the Standards for Mathematical Practice. • Then discuss the following question. What implications might the Standards for Mathematical Practice have on your classroom?

9. Building Walls Maya is using blocks to make a wall grow.

10. Building Walls • Draw the 4th wall below. • How many blocks are needed to make the 4th wall? _____ blocks • Tom wants to build the 5th wall. Tell Tom how to build the 5th wall. • How many blocks would it take to build the 7th wall? _____blocks Show how you know your answer is correct. 5. Tom and Maya’s teacher gave them 21 blocks. Can they build a wall with exactly 21 blocks? Yes or No _______ Why or Why not?

11. Building Walls • Individually complete parts 1-5. • Compare your work with a partner’s work. Look for as many plausible explanations for part 5 as possible. • 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?

12. Tasks as they appear in curricular materials Student learning The Nature of Tasks Used in the Classroom … Will Impact Student Learning!

13. Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) Tasks as enacted by teachers and students Tasks as they appear in curricular materials Tasks as set up by teachers Tasks as they appear in curricular materials Student learning Student learning But, WHAT TEACHERS DO with the tasks matters too! The Mathematical Tasks Framework

14. Oral Language Verbal - Written and Oral Real-World Situations Pictures Geometric/ Graphical Contextual Written Symbols Manipulative Models Symbolic Tabular Representation Stars Elementary Secondary 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.

15. www.InsideMathematics.org

16. Student F

17. Student G

18. Comparing Students F and G • Try to translate each student’s explanation into a mathematical expression. • What would these expressions be if the 5 was replaced by n? • How do these students differ in the way they see the structure of the walls?

19. Student L

20. Student Z

21. Comparing Students Z and L • Do you think Student Z is seeing structure or regularity in repeated reasoning? Justify your position. • Do you think Student L is seeing structure or regularity in repeated reasoning? Justify your position.

22. Student K

23. Student E

24. Comparing Students K and E • Do you think Student K is seeing structure or regularity in repeated reasoning? Justify your position. • Do you think Student E is seeing structure or regularity in repeated reasoning? Justify your position.

25. 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.

26. 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 seeing structure and generalizing

27. End of Day Reflections • 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.

28. Join us in thanking theNoyce Foundationfor their generous grant to NCSM that made this series possible! http://www.noycefdn.org/

29. 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

30. 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