From Standards to Actions: Implementing the Common Core State Standards for Mathematics

1. From Standards to Actions: Implementing the Common Core State Standards for Mathematics Diane J. Briars NCSM Immediate Past President djbmath@comcast.net 2011 NCTM Regional Conference & Exposition Atlantic City, NJ October 20, 2011

2. FYI Presentation slides will be posted on the NCSM website: mathedleadership.org or email me at djbmath@comcast.net

3. Today’s Goals Provide information about NCSM Resources to support implementation of CCSS: • Illustrating the Mathematical Practices • CCSS Curriculum Materials Analysis Tools • Webinars • Websites with valuable resources

4. What is NCSM? International organization of and for mathematics education leaders: Publishers and authors Specialists and coordinators State and provincial directors Superintendents Teachers Teacher educators Teacher leaders Coaches and mentors Curriculum leaders Department chairs District supervisors/leaders Mathematics consultants Mathematics supervisors Principals Professional developers mathedleadership.org

6. NCSM Position Papers • Effective and Collaborative Teams • Sustained Professional Learning • Equity • Students with Special Needs • Assessment • English Language Learners • Positive Self-Beliefs • Technology mathedleadership.org mathedleadership.org

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

8. CCSS: A Major Challenge/Opportunity • College and career readiness expectations • Rigorous content and applications • Stress conceptual understanding as well as procedural skills • Organized around mathematical principles • Focus and coherence • Designed around research-based learning progressions whenever possible.

9. Implementing CCSS: Where to Start? • Build understanding of: • Standards for Mathematical Practice • Standards Progressions: Domains and Clusters • Assess implications of this for current practice • Short-term changes • Long-term changes

10. Illustrating the Mathematical Practices

11. Illustrating the Mathematical Practices • Ready to use professional development modules: • PowerPoint • Video clips • Handouts, including student work • Each module supports a 1.5- to 3-hour session that focuses on one or two of the mathematical practices.

12. Illustrating the Mathematical Practices Each module is: • Anchored by a high demand mathematics task • Situated in classroom practice, with classroom video and/or samples of student work • Presented in PowerPoint format with slide annotations on the Notes pages to support facilitation • Designed to be used individually or in combination with other modules.

13. Insidemathematics.org

14. Insidemathematics.org

15. Illustrating the Mathematical Practices • Illustrating the Standards for Mathematical Practice: Getting Started • Reasoning and Unpacking Others' Reasoning, Grades 4-6 • Modeling and Viable Arguments, Grades 6-8

16. Illustrating the Mathematical Practices • Illustrating the Standards for Mathematical Practice: Getting Started • Reasoning and Unpacking Others' Reasoning, Grades 4-6 • Modeling and Viable Arguments, Grades 6-8

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. Standards for Mathematical Practice • 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.

22. The Standards for Mathematical Practice Take a moment to examine the first three words of each of the 8 mathematical practices… what do you notice? Mathematically Proficient Students…

23. The Standards for [Student] 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: What jumps out at you?

24. The Standards for [Student] Mathematical Practice SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Notice and pay attention to…

25. The Standards for [Student] Mathematical Practice On a scale of 1 (low) to 6 (high), to what extent is your school/district promoting students’ proficiency in the practice you discussed? Evidence for your rating? Individual rating Team rating

26. Standards for Mathematical Practice • 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.

28. Standards for Mathematical Practice • Describe the 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?”

29. Standards for Mathematical Practice AND…. • 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.”

30. Connecting Standards for Content and Practice in a Classroom Create verbal and tabular representations of the 3 DVD rental plans below. Mail Flix $18 per month regardless of the number of movies rented Online Flix $12 per month plus $1 per movie rented Movie Buster $3 per movie rented Do the three plans ever cost the same for renting the same number of DVDs?

31. The DVD Rental Task • Individually do the task. • Then work with a partner to compare your work. • Consider each of the following questions and be prepared to share your thinking with the group: • What mathematics content is needed to complete the task? • Which mathematical practices are needed to complete the task? CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003

32. Connecting Standards for Content and Practice in a Classroom Create verbal and tabular representations of the 3 DVD rental plans below. Mail Flix $18 per month regardless of the number of movies rented Online Flix $12 per month plus $1 per movie rented Movie Buster $3 per movie rented Do the three plans ever cost the same for renting the same number of DVDs?

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

34. Tasks as enacted by teachers and students Tasks as they appear in curricular materials Tasks as set up by teachers Student learning 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

35. www.Inside Mathematics.org http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-comparing-linear-functions/264-comparing-linear-functions-introduction?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8 A reengagement lesson using the DVD Rental Task Cecilio Dimas Ida Price Middle School Grade 7

36. DVD Rental Task In what ways did the teacher give students opportunities to make sense of the task and build perseverance in his launch of the task? What evidence do you see that students are building this standard of practice?

37. Looking at Student Work Examine the tables generated by Student H Given this work, what conclusions has the student made? What mistakes (if any) are evident in the tables? Do the tables make mathematical sense, and do they match the plans?

38. Connecting Standards for Content and Practice in a Classroom Create verbal and tabular representations of the 3 DVD rental plans below. Mail Flix $18 per month regardless of the number of movies rented Online Flix $12 per month plus $1 per movie rented Movie Buster $3 per movie rented Do the three plans ever cost the same for renting the same number of DVDs?

39. Looking at Student Work

40. Looking at Student Work As you watch the video consider: What evidence do you see that suggests students are developing competency with Standards 3 and/or 4 for Mathematical Practice? In what ways did interactions between students support their ability to develop competency with Standards 3 and/or 4 for Mathematical Practice? In what ways did the teacher facilitate/hinder students developing competency with the practices?

42. Tasks as enacted by teachers and students Tasks as they appear in curricular materials Tasks as set up by teachers Student learning Teachers and Tasks Matter Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) The Mathematical Tasks Framework

43. Planning to Support Students’ Opportunity to Learn Select a typical task (or a related set of problems) from your instructional materials and design a lesson it so that it offers more opportunities for students to develop both the content and practice standards.

44. Next steps and resources • Review the implications you listed earlier, then discuss with your table group one or two next steps you might take as a district, school, and teacher.

45. 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.

46. www.Insidemathematics.org

47. CCSS Analyzing curriculum materials Tools

48. Counting and Cardinality (K) Operations and Algebraic Thinking (K-5) Number and Operations in Base Ten (K-5) Measurement and Data (K-5) Geometry (K-HS) Number and Operations —Fractions (3-5) Ratios and Proportional Relationships (6-7) The Number System (6-8) Expressions and Equations (6-8) Statistics and Probability (6-HS) Functions (8-HS) Number and Quantity (HS) Algebra (HS) Modeling (HS) Standards for Mathematical Content

49. K- 5 6-8 High School Expressions and Equations Operations and Algebraic Thinking Algebra Number andOperations―Base Ten The Number System Number and Operations ―Fractions Progressions within and across Domains Daro, 2010

50. Key Advances Daro, 2010 • Operations and the problems they solve • Properties of operations: Their role in arithmetic and algebra • Mental math and “algebra” vs. algorithms • Units and unitizing • Unit fractions • Unit rates • Defining congruence and similarity in terms of transformations • Quantities-variables-functions-modeling • Number-expression-equation-function • Modeling