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: Getting Started with the Practices 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: Become familiar with the components and history of the CCSS Today’s Goals

5. “ The Common Core State Standards represent an opportunity – once in a lifetime – to form effective coalitions for change.” Jere Confrey, August 2010

6. College and career readiness expectations Rigorous content and applications Stress on conceptual understanding as well as procedural skills Organized around important mathematical themes developed across grade levels based on research-based learning progressions whenever possible Greater focus and coherence CCSS: A Major Challenge & Opportunity

7. The expanded version of the CCSS is available at www.mathedleadership.org/

8. Expanded Version of CCSS Introduction Standards-setting criteria Standards-setting considerations Application of CCSS for ELLs Application to Students with Disabilities Appendix A: Model Pathways for High School Courses And, of course, the standards for contentand practice themselves… Common Core State Standards for Mathematics

9. National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (1989) Professional Standards for Teaching Mathematics (1991) Assessment Standards for School Mathematics (1995) Principles and Standards for School Mathematics (2000) Curriculum Focal Points (2006) High School Reasoning and Sense Making (2009 - ) History

10. History

11. A Challenging Opportunity! “These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.” — CCSS (2010, p.5)

12. National Governors Association (NGA) Council of Chief State School Officers (CCSSO) Standards for College and Career Readiness for Mathematics and English/Language Arts Achieve The College Board ACT Common Core State Standards

13. CCSS Mathematics Standards were developed by the following groups Lead writers: Phil Daro, Bill McCallum, Jason Zimba Writing teams Review teams Two rounds of public review and feedback States have option to adopt Verbatim 85% of State Standards must be CCSS Common Core State Standards

14. Accountability Accountability Accountability What’s different about these standards?

15. Partnership for the Assessment of Readiness for College and Careers (PARCC) http://www.fldoe.org/parcc/ SMARTER Balanced Assessment Consortium http://www.smarterbalanced.org/ Assessment Consortia

16. Mathematics Standards for Content Standards for Practice Where to Start Implementation?

17. 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)

18. Underlying Frameworks National Council of Teachers of Mathematics 5 ProcessStandards • Problem Solving • Reasoning and Proof • Communication • Connections • Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

19. Conceptual Understanding Strategic Competence Productive Disposition Adaptive Reasoning Procedural Fluency Underlying Frameworks Strands of Mathematical Proficiency NRC (2001). Adding It Up. Washington, D.C.:National Academies Press.

20. Strands of Mathematical Proficiency • Conceptual Understanding– comprehension of mathematical concepts, operations, and relations • Procedural Fluency– skill in carrying out procedures flexibly, accurately, efficiently, and appropriately • Strategic Competence– ability to formulate, represent, and solve mathematical problems • Adaptive Reasoning– capacity for logical thought, reflection, explanation, and justification • Productive Disposition– habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

21. 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

22. The Standards for Mathematical Practice Take a moment to examine the first three words of each of the eight mathematical practices… what do you notice? Mathematically proficient students…

23. The Standards for Mathematical Practice What are the verbs that illustrate the student actions for your assigned mathematical practice? Circle, highlight or underline them for your assigned practice… Discuss with a partner: How does this practice compare to your current practice?

24. The Standards for Mathematical Practice #1: Explain and make conjectures… #2: Make sense of… #3: Understand and use… #4: Apply and interpret… #5: Consider and detect… #6: Communicate precisely to others… #7: Discern and recognize… #8: Notice and pay attention to…

25. The Standards for Mathematical Practice On a scale of 1 (low) to 6 (high), to what extent are you or your school/district promoting all students’proficiency in the practice you discussed? What evidence might you site for your rating?

26. On one hand, the Standards for Mathematical Practice describe mathematical content students need to learn. SP1. Make sense of problems “… students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.” Standards for Mathematical Practice

27. On the other hand, they describe the nature of the learning experiences, thinking processes, habits of mind, and dispositionsthat students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end. SP1. Make sense of problems “….they [students] analyze givens, constraints, relationships and goals. ….they monitor and evaluate their progress and change course if necessary. …. and they continually ask themselves “Does this make sense?” Standards for Mathematical Practice

28. 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?

29. Implementing CCSS Challenge: CCSS assessments not available for several years (2013-2014) although the assessment specifications and sample items will be available sooner Recognizing that CCSS are a departure from “business as usual” Where not to start-- Aligning CCSS Standards grade-by-grade with existing mathematics standards

30. Practices & Assessment Tasks What might we expect mathematics assessment tasks in the new national assessments to look like, given the CCSS Standards for Mathematical Practice?

31. Practices & Assessment Tasks As you read through the sample assessment tasks from SBAC and PARCC, consider the following questions with a partner and be prepared to share your thinking with the whole group: • Which of the Standards for Mathematical Practice do you see being utilized in these tasks? • How are these tasks similar to and different from the mathematics tasks on your current classroom and state assessments?

32. Sample Grade 8 Mathematics Task

33. Sample Grade 8 Mathematics Task

34. Sample Grade 8 Mathematics Task

35. Sample Grade 8 Mathematics Task

36. Structuring the Practices

37. Practices & Assessment Tasks As you read through the sample assessment tasks from SBAC and PARCC, consider the following questions with a partner and be prepared to share your thinking with the whole group: • Which of the Standards for Mathematical Practice do you see being utilized in these tasks? • How are these tasks similar to and different from the mathematics tasks used on your current classroom and state assessments?

38. Standards for Mathematical Practice The eight standards for mathematical practice place an emphasis on students doing mathematics and demonstrating learning. • Equitable achievement will begin with an understanding of how the • selection of tasks, • assessment of tasks, and • student learning environment • can support or undermine equity in our schools.

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

40. 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

41. 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.

42. 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: • Become familiar with the components and history of the CCSS

43. 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.

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

45. 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

46. 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