1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices The National Council of Supervisors of Mathematics The Common Core State Standards Illustrating the Standards for Mathematical Practice: Getting Started with the Practices

2 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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: Getting Started with the Practices Common Core State Standards Mathematics Standards for Content Standards for Practice

4 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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

5 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 5 “ The Common Core State Standards represent an opportunity – once in a lifetime – to form effective coalitions for change.” Jere Confrey, August 2010

6 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 6 CCSS: A Major Challenge & Opportunity 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

7 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices The expanded version of the CCSS is available at www. mathedleadership.org/

8 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 8 Common Core State Standards for Mathematics 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 content and practice themselves…

9 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 9 History 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 ( )

10 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 10 History

11 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 12 Common Core State Standards 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

13 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 13 Common Core State Standards 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

14 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 14 What’s different about these standards? Accountability

15 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 15 Assessment Consortia Partnership for the Assessment of Readiness for College and Careers (PARCC) SMARTER Balanced Assessment Consortium

16 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Where to Start Implementation? Mathematics Standards for Content Standards for Practice

17 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 18 Underlying Frameworks National Council of Teachers of Mathematics 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

19 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 19 Underlying Frameworks Strands of Mathematical Proficiency Strategic Competence Adaptive Reasoning Conceptual Understanding Productive Disposition Procedural Fluency NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

20 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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. 20

21 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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.

22 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 26 Standards for Mathematical Practice 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.”

27 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 27 On the other hand, they describe the nature of the learning experiences, thinking processes, habits of mind, and dispositions that 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Standards for Mathematical Practice What implications might the Standards for Mathematical Practice have on your classroom? 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.

29 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Implementing CCSS Challenge: –CCSS assessments not available for several years ( ) 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 29

30 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Sample Grade 8 Mathematics Task

33 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Sample Grade 8 Mathematics Task

34 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Sample Grade 8 Mathematics Task

35 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Sample Grade 8 Mathematics Task

36 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Structuring the Practices

37 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices The Nature of Tasks Used in the Classroom … Tasks as they appear in curricular materials Student learning Will Impact Student Learning!

40 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices But, 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

41 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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.

44 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices Join us in thanking the Noyce Foundation for their generous grant to NCSM that made this series possible!

45 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Getting Started with the Practices 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: