1. 1 Shifting Instruction to Strengthen the Opportunity to Learn Both Content and English OELAS Conference December 14, 2012 Steve Leinwand American Institutes for Research SLeinwand@air.org

2. 2 So…the problem is: If we continue to do what we’ve always done…. We’ll continue to get what we’ve always gotten.

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8. 8 Algebra: The intense study of the last three letters of the alphabet

9. So what does that result in? Little growth of important content knowledge Little growth in English facility Little preparation for the real world Little preparation for the world of the Common Core State Standards for Mathematics “mathematical practices” 9

10. And what have we gotten? Mountains of math anxiety Tons of mathematical illiteracy Mediocre test scores HS programs that barely work for more than half of the kids Gobs of remediation and intervention A slew of criticism Not a pretty picture! 10

11. 11 If however….. What we’ve always done is no longer acceptable, then… We have no choice but to change some of what we do and some of how we do it.

12. So what does different mean? 12

13. Some data. What do you see? 404 102 304 13

14. Predict some additional data 404 102 304 14

15. How close were you? 404 102 304 203 15

16. All the numbers – so? 454 253 152 404 102 304 203 16

17. A lot more information (where are you?) Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203 17

18. Fill in the blanks Ride??? Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203 18

19. At this point, it’s almost anticlimactic! 19

20. The amusement park RideTimeTickets Roller Coaster454 Ferris Wheel253 Bumper Cars152 Rocket Ride404 Merry-go-Round102 Water Slide304 Fun House203

21. The Amusement Park The 4 th and 2 nd graders in your school are going on a trip to the Amusement Park. Each 4 th grader is going to be a buddy to a 2 nd grader. Your buddy for the trip has never been to an amusement park before. Your buddy want to go on as many different rides as possible. However, there may not be enough time to go on every ride and you may not have enough tickets to go on every ride. 21

22. The bus will drop you off at 10:00 a.m. and pick you up at 1:00 p.m. Each student will get 20 tickets for rides. Use the information in the chart to write a letter to your buddy and create a plan for a fun day at the amusement park for you and your buddy. 22

23. Why do you think I started with this task? -Standards don’t teach, teachers teach -It’s the translation of the words into tasks and instruction and assessments that really matter -Processes are as important as content -We need to give kids (and ourselves) a reason to care -Difficult, unlikely, to do alone!!! 23

24. Join me in Teachers’ Room Chat They forget They don’t see it my way They approach it differently They don’t follow directions They give ridiculous answers They don’t remember the vocabulary THEY THEY THEY BLAME BLAME BLAME An achievement gap or an INSTRUCTION gap? 24

25. Well…..if….. They forget – so we need to more deliberately review; They see it differently – so we need to accommodate multiple representations; They approach it differently – so we need to elicit, value and celebrate alternative approaches; They give ridiculous answers – so we need to focus on number sense and estimation; They don’t understand the vocabulary – so we need to build language rich classrooms; They ask why do we need to know this – so we need to embed the math in contexts. 25

26. Today’s Goal To provoke and inform your thinking about the need to shift instructional practices and mindsets in ways that are aligned with the vision of the new Common Core State Standards and that truly meet the needs of all students. 26

27. Today’s Agenda Three perspectives on our reality The Common Core context Some glimpses at powerful instruction Some challenges to you 27

28. 1. What a great time to be worrying about mathematics! Common Core State Standards adopted by 45 states Quality K-8 instructional materials More access to material and ideas via the web than ever A president who believes in science and data The beginning of the end to Algebra II as the killer A long overdue understanding that it’s instruction that really matters A recognition that the U.S. doesn’t have all the answers 28

29. 29 2. Let’s be clear: We’re being asked to do what has never been done before: Make math work for nearly ALL kids and get nearly ALL kids ready for college. There is no existence proof, no road map, and it’s not widely believed to be possible.

30. 30 3. Let’s be even clearer: Ergo, because there is no other way to serve a much broader proportion of students: We’re therefore being asked to teach in distinctly different ways. Again, there is no existence proof, we don’t agree on what “different” mean, nor how we bring it to scale. (That’s the hope of the CCSSM for Math)

31. Common Core Promises 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. — CCSSM (2010, p.5) 31

32. Some design elements of the CCSSM Fewer, clearer, higher Fairer – rational grade placement of procedures NCTM processes transformed into mathematical practices Learning trajectories or progressions Spirals of expanding radius – less repetitiveness and redundancy A sequence of content that results in all students reaching reasonable algebra in 8th grade Balance of skills and concepts – what to know and what to understand 32

33. 8 CCSSM Mathematical Practices 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. 33

34. 8 CCSSM Mathematical Practices 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. 34

35. So how should this be playing out in every Arizona mathematics classroom? Regular Ed ELL Special Ed Let’s Take a Look 35

36. A Tale of Two Mindsets (and the alternate approaches they generate) Remember How vs. Understand Why 36

37. Mathematics A set of rules to be learned and memorized to find answers to exercises that have limited real world value OR A set of competencies and understanding driven by sense-making and used to get solutions to problems that have real world value

38. Number facts 8 + 9 38

39. Ready, set, 8 + 9 = 17 – know it cold 10 + 7 – decompose the 9 to get to 10 18 – 1 – add 10 and adjust 16 + 1 – double plus 1 20 – 3 – round up and adjust Who’s right? Does it matter? 39

40. Subtracting Whole Numbers 40

41. Find the difference: 1000 - 459 41

42. Find the difference: Who did it the right way?? 9 10 91 0 1 0 - 4 5 9 How did you get 541 if you didn’t do it this way? 42

43. Find the difference: 1000 -459 Counting up (1 is 60, 40 more is 500, …) Moving from left to right! Subtract 400, then 50, then 9 Subtracting 1 from each number (999-458) Eastern European Add-Add algorithm 43

44. Find the difference: Add 10 100 1 0 -4 5 6 9 1 44

45. Find the difference: Add 100 10 1 0 1 0 -4 5 5 6 9 5 4 1 45

46. Adding and Subtracting Integers 5 + (-9) 46

47. Remember How 5 + (-9) “To find the difference of two integers, subtract the absolute value of the two integers and then assign the sign of the integer with the greatest absolute value” 47

48. Understand Why 5 + (-9) -Have $5, lost $9 -Gained 5 yards, lost 9 -5 degrees above zero, gets 9 degrees colder -Decompose 5 + (-5 + -4) -Zero pairs: x x x x x O O O O O O O O O - On number line, start at 5 and move 9 to the left 48

49. Multiplying Decimals 49

50. Remember How 4.39 x 4.2  “We don’t line them up here.”  “We count decimals.”  “Remember, I told you that you’re not allowed to that that – like girls can’t go into boys bathrooms.”  “Let me say it again: The rule is count the decimal places.” 50

51. Understand Why 51 4.2 gallons $ 4.39 Total How many gallons? About how many? Max/min cost?

52. Understand Why 52 4.2 gallons $ 4.39 Total 183.38 Context makes ridiculous obvious, and breeds sense-making

53. Solving Simple Linear Equations 3x + 7 = 22 53

54. 3x + 7 = 22 How do we solve equations: Subtract 7 3 x + 7 = 22 - 7 - 7 3 x = 15 Divide by 3 3 3 Voila: x = 5 54

55. 3x + 7 = 22 1.Tell me what you see: 3 x + 7 2.Suppose x = 0, 1, 2, 3….. 3.Let’s record that: x 3x + 7 0 7 1 10 2 13 4. How do we get 22? 55

56. 3x + 7 = 22 Where did we start? What did we do? x 5 x 3 3x 15 ÷ 3 + 7 3x + 7 22 - 7 56

57. 3x + 7 = 22 X X X IIIIIII IIII IIII IIII IIII II X X X IIIII IIIII IIIII 57

58. Multiplying Whole Numbers 58

59. Remember How 213 X 4 59

60. Understand Why 213 x 4 213 + 213 + 213 + 213 = 852 4 200 10 3 800 40 12 = 852 4 ( 200 + 10 + 3) = 60

61. Which leads to: 4 threes 4 tens 4 two hundreds 213 X 4 12 40 800 852 61

62. Place Value 62

63. Remember How 32,485 What is the value of the 4? What digit is in the thousands place? 63

64. Understand Why 32,485 About how many? 30,000 32,000 32,500 32,490 10 more? 10 less? 100 more? 100 less? 1000 more? 1000 less? 64

65. People won’t do what they can’t envision, People can’t do what they don’t understand, People can’t do well what isn’t practiced, But practice without feedback results in little change, and Work without collaboration is not sustaining. Ergo: Our job, as professionals, at its core, is to help people envision, understand, practice, receive feedback and collaborate. So the key things we know 65

66. To collaborate, we need time and structures Structured and focused department meetings Before school breakfast sessions Common planning time – by grade and by department Pizza and beer/wine after school sessions Released time 1 p.m. to 4 p.m. sessions Hiring substitutes to release teachers for classroom visits Coach or principal teaching one or more classes to free up teacher to visit colleagues After school sessions with teacher who visited, teacher who was visited and the principal and/or coach to debrief Summer workshops Department seminars 66

67. To collaborate, we need strategies 1 Potential Strategies for developing professional learning communities: Classroom visits – one teacher visits a colleague and the they debrief Demonstration classes by teachers or coaches with follow-up debriefing Co-teaching opportunities with one class or by joining two classes for a period Common readings assigned, with a discussion focus on: – To what degree are we already addressing the issue or issues raised in this article? – In what ways are we not addressing all or part of this issue? – What are the reasons that we are not addressing this issue? – What steps can we take to make improvements and narrow the gap between what we are currently doing and what we should be doing? Technology demonstrations (graphing calculators, SMART boards, document readers, etc.) Collaborative lesson development 67

68. To collaborate, we need strategies 2 Potential Strategies for developing professional learning communities: Video analysis of lessons Analysis of student work Development and review of common finals and unit assessments What’s the data tell us sessions based on state and local assessments “What’s not working” sessions Principal expectations for collaboration are clear and tangibly supported Policy analysis discussions, e.g. grading, placement, requirements, promotion, grouping practices, course options, etc. 68

69. So…. While we acknowledge the range and depth of the problems we face, It should be comforting to see the availability and potential of solutions to these problems…. Now go forth and start shifting YOUR school’s mathematics program to better serve our students, our society and our future. 69

70. 70 Thank you! SLeinwand@air.org