1. Improving Student Learning by Transforming Teacher Practice K-12 Mathematics Section NC Department of Public Instruction

2. Agenda Overview of Current Mathematical Practices in the US Structure of Common Core State Standards (CCSS) New, Better, and/or Different in the CCSS Getting started with the Implementation of the CCSS

3. Outcomes for Today An understanding of where the US is with mathematics teaching and practice as compared to the world Exploration of strategies to improve student outcomes through improving teaching practices. A plan to move forward in preparation of implementing the CCSS.

4. When you think about doing mathematics what do you think about?

5. Preconceptions About Mathematics Activity On a note card, write a preconception about mathematics. –Write one explanation of how the preconception impacts instruction.

6. Preconceptions About Mathematics “Mathematics is about learning to compute” (Donovan& Bransford, 2005, p. 220). “Mathematics is about following rules to guarantee correct answers” (Donovan & Bransford, p. 220). “Some people have the ability to do math and some don’t” (Donovan & Bransford, p. 221).

7. Perception

8. Four Teacher-Friendly Postulates Article and Activity Read the article On a sheet of paper, write the statement or thought that was most profound to you.

9. Implementation of CCSS provides us with an opportunity to examine our instructional practices and how those practices effect student outcome. Barbara Bissell K-12 Mathematics Section Chief

10. “ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.” David Hutchens “Outlearning the Wolves”

11. Why is change necessary?

12. 8 + 4 = [ ] + 5

13. Percent Responding with These Answers Grade7121712 and 17 1 st & 2 nd 3 rd & 4 th 5 th & 6 th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

14. 8 + 4 = [ ] + 5 Percent Responding with These Answers Grade7121712 and 17 1 st & 2 nd 558138 3 rd & 4 th 5 th & 6 th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

15. 8 + 4 = [ ] + 5 Percent Responding with These Answers Grade7121712 and 17 1 st & 2 nd 558138 3 rd & 4 th 9492510 5 th & 6 th Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

16. 8 + 4 = [ ] + 5 Percent Responding with These Answers Grade7121712 and 17 1 st & 2 nd 558138 3 rd & 4 th 9492510 5 th & 6 th 276212 Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

17. 8 + 4 = [ ] + 5 Percent Responding with These Answers Grade7121712 and 17 1 st & 2 nd 558138 3 rd & 4 th 9492510 5 th & 6 th 276212 Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School. Carpenter, Franke, & Levi Heinemann, 2003

18. Estimate the answer to (12/13)+ (7/8) A. 1 B. 2 C. 19 D. 21 Only 24% of 13 year olds answered correctly. Equal numbers of students chose the other answers. NAEP

19. Students were given this problem: 168 20 4 th grade students in reform math classes solved it with no problem. Sixth graders in traditional classes responded that they hadn’t been taught that yet. Dr. Ben Klein, Mathematics Professor Davidson College

20. Types of Math Problems Presented

21. How Teachers Implemented Making Connections Math Problems

22. Lesson Comparison Japan and United States The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms The emphasis on understanding is evident in the steps of a typical Japanese lesson Teacher instructs students in concept or skill Teacher solves example problems with class Students practice on their own while teacher assists individual students Teacher poses a thought provoking problem Students and teachers explore the problem Various students present ideas or solutions to the class Teacher summarizes the class solutions Students solve similar problems 22

23. Hong Kong / US Data Hong Kong had the highest scores in the most recent TIMMS. Hong Kong students were taught 45% of objectives tested. Hong Kong students outperformed US students on US content that they were not taught. US students ranked near the bottom. US students ‘covered’ 80% of TIMMS content. US students were outperformed by students not taught the same objectives.

24. BREAK

25. Mathematical Practices

26. Instructional Task I What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know? What do you notice about the relationship between area and perimeter?

27. Instructions Discuss the following at your table –What thinking and learning occurred as you completed the task? – What mathematical practices were used? –What are the instructional implications?

28. Compared to…. 5 10 What is the area of this rectangle? What is the perimeter of this rectangle?

29. Review the completed task Consider the mathematical practices as they relate to the task. Discuss the connections you see between the task and mathematics instruction. Connecting Mathematical Practices and Instruction

30. Mathematical Practices Discuss the following and record responses on chart paper: How will the mathematical practices impact instruction? How will this information impact your work with teachers as you move toward the implementation of the CCSS? What challenges will you face? What is a possible solution for one of the challenges?

31. Mathematical Practices Gallery Walk Each group should post the chart paper with responses. Walk around to review the responses from other groups. Note any information that you will use.

32. Something to Think About The value of the common core is only as good as the implementation of the mathematical practices. What if we didn’t have a requirement for math – how would we lure students in? -- Jere Confrey

33. Lessons Learned Mile wide and inch deep does not work. The task ahead is not so much about how many specific topics are taught; rather, it is more about ways of thinking. To change students’ ways of thinking, we must change how we teach.

34. QUESTIONS COMMENTS

35. Format and Structure of the Common Core State Standards

36. www.corestandards.org

37. Mathematical Practices

38. Grade Level DomainDomain Standards

39. DomainDomain ClusterCluster Conceptual Categories StandardsStandards

40. Common Core Resources Glossary

41. Common Core Glossary Table 1. Common addition and subtraction situations

42. Common Core Resources Operations and Properties Information Tables

43. Property Table Table 3. The properties of operations

44. Other Common Core Resources Appendix A High School Pathways Compacted Middle School Courses

45. New Better Different

46. Common Core Attributes Focus and coherence –Focus on key topics at each grade level –Coherent progression across grade level Balance of concepts and skills –Content standards require both conceptual understanding and procedural fluency Mathematical practices –Fosters reasoning and sense-making in mathematics College and career readiness –Level is ambitious but achievable

47. 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 Standards for Mathematical Practices

48. Grade or course introductions give 2- 4 focal points K-8 presented by grade level Organized into domains that progress over several grades High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability) Standards for Mathematical Content

49. Common Core Standards Fewer Clearer Higher

52. Old Boxes People are the next step If people just swap out the old standards and put the new CCSS in the old boxes –Into old systems and procedures –Into the old relationships –Into old instructional materials formats –Into old assessment tools, Then nothing will change, and perhaps nothing will

53. What can we do NOW to prepare for the implementation of the CCSS?

54. Development of a Team Implementation TeamNO Implementation Team Intervention Effective80%, 3 Yrs14%, 17 Yrs NOT Effective Fixsen, Blasé, Timbers, & Wolf, 2001 Balas & Boren, 2000 Implementation

55. Establish a Professional Culture for Change Book Studies Who moved my cheese? Spencer Johnson, M.D. Outlearning the Wolves David Hutchens The Prime Leadership Framework National Council of Supervisors of Mathematics Sensible Mathematics: A Guide for School Leaders Steven Leinwand

56. Strengthen PLC’s Use as venues for grade level / course studies of the Common Core standards How is an objective in common core different from what we have been teaching? Common Core Standards can be found at www.corestandards.org

57. Strengthening Content Knowledge Math Matters: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin, Art Johnson Teaching Student-Centered Mathematics: Grades 5-8 John A. Van de Walle, LouAnn H. Lovin Focus in High School Mathematics: Reasoning and Sense Making NCTM

58. Instructional Materials Look at current instructional materials and compare to the Common Core Standards Determine where materials can be modified and what is missing.

59. Changing Tasks: Low Level to High Level Traditional Question: If you earned $380 for 2 weeks of work, how much will you earn in 15 weeks? More Open-ended: Kate earns $380 for 2 weeks of work, how much will you earn in 15 weeks? Explain how you arrived at your answer. Kate earns $380 every two weeks. She thinks she will earn enough in 15 weeks to pay for a used car that costs $3000. Write an explanation to convince Kate that this is or is not true.

60. Implement Formative Assessment Modules Share and examine student work (LASW) Book: Formative Assessment: Making It Happen in the Classroom Margaret Heritage

61. Classroom Instruction As Cathy Seeley said: In your math class, who is doing the talking? Who is doing the math?

62. Websites of Interest www.ncpublicschools.org www.ncpublicschools.org/acre www.ncpublicschools.org/stateboard http://math.ncwiseowl.org http://www.k12.wa.us/smarter/

63. “ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.” David Hutchens “Outlearning the Wolves”

64. QUESTIONS COMMENTS

65. Mathematics Section Contact Information 65 Kitty Rutherford Elementary Mathematics Consultant 919-807-3934 krutherford@dpi.state.nc.us Robin Barbour Middle Grades Mathematics Consultant 919-807-3841 rbarbour@dpi.state.nc.us Mary Russell Middle Grades Mathematics Consultant 919-807-3618 mrussell@dpi.state.nc.us Carmella Fair Secondary Mathematics Consultant 919-807-3840 cfair@dpi.state.nc.us Johannah Maynor Secondary Mathematics Consultant 919-807-3842 jmaynor@dpi.state.nc.us Barbara Bissell K-12 Mathematics Section Chief 919-807-3838 bbissell@dpi.state.nc.us Susan Hart Program Assistant 919-807-3846 shart@dpi.state.nc.us