1. Common Core-Aligned DDI Primer in Math: Designing and Leading DDI Using Assessment Guidance Documents July 9, 2014

2. Session Objectives Assessment Design: Know the elements of a high-quality Common Core-aligned mathematics assessment Know how to create and choose assessment tasks that reflect a balance of rigor and give comprehensive information about students at all levels

3. Session Objectives Data Analysis: Be able to describe what to look for when analyzing student work for a Common Core- aligned assessment Be able to create a data tracker for assessments Develop questions that drive data-analysis meetings around Common Core-aligned assessment data

4. Agenda Introduction I. What makes a high quality assessment? Sorting Task: Why Do We Assess? Balance of Rigor Students At All Levels II. How can we analyze assessment data? Looking at Student Work Tracking Data Leading a Data Meeting

5. Introduction High Quality, Common Core- Aligned Assessments Data Analysis and Action Part II Part I

6. Why Assess At All? To learn information about students

7. Why Assess At All? 1. Compare the assessments (Documents A, B, and C). What kinds of information would we learn about students from each one? 2. What are the strengths and weaknesses of each?

11. So… What kinds of information do we want to learn about our students?

12. Two Big Ideas About Assessment Design: 1. The assessment should reflect a balance of rigor, helping us understand students’ procedural abilities, conceptual understanding, and abilities to apply. 2. The assessment should give us information about students at all levels.

13. Other Considerations (Not Our Focus Today) Focus: Strong majority of questions assess the Major Work of the grade/course Coherence: Supporting Content is assessed in ways that engage students in the Major Work Practices: Items signal the Standards for Mathematical Practice (not necessarily all items)

14. What Not To Do: -From the Publishers’ Criteria (K-8 and HS Math)

15. 1. Balance of Rigor Procedural Fluency Conceptual Understanding Application

16. From the Publishers’ Criteria:

17. Procedural Fluency $64,000 Question: Are there items that ask or imply that students “do” math procedures? Some good verbs: solve, add, subtract, divide, multiply, graph, compute, find Practice Connections MP.7 Look for and make use of structure MP.8 Look for and express regularity in repeated reasoning *Note fluency expectations named at each grade level. While these are not named for HS level courses there should still be procedural assessment.

18. “But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.” From the New York State Common Core Learning Standards

19. Conceptual Understanding $64,000 Question: Are there items that ask students to explain their thinking? Some good verbs: Explain, determine, prove, show, compare, justify Practice Connections MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. *More important in standards that begin with “understand.”

20. Application $64,000 Question: Does the item have a real-world context? Some good examples: Single-step word problems, multi- step word problems, model-building Practice Connections MP.1 Make sense of problems and persevere in solving them. MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. *Application Paradox: The more directed the task, the more we can be sure it aligns to the standard, but the less authentic it becomes.

21. 7.RP.1 Let’s look at a standard together. What would assessment items based on procedural, conceptual, and application aspects look like?

22. Three Free, Public On-Line Resources To Support A Balance of Rigor 1. www.illustrativemathematics.org 2. EngageNY: Curriculum Modules 3. EngageNY: Annotated Items

23. Illustrative Math Task

26. Annotated Item

27. Module Assessment

28. Connect To Your Practice What is an activity that you could do yourself or lead others in to promote a balance of rigor in assessments?

29. 2. Students at All Levels

30. From the K-8 Publishers’ Criteria: The natural distribution of prior knowledge in classrooms should not prompt abandoning instruction in grade level content, but should prompt explicit attention to connecting grade level content to content from prior learning. To do this, instruction should reflect the progressions on which the CCSSM are built. For example, the development of fluency with division using the standard algorithm in grade 6 is the occasion to surface and deal with unfinished learning with respect to place value. Much unfinished learning from earlier grades can be managed best inside grade level work when the progressions are used to understand student thinking.

31. Three Free, Public On-Line Resources To Support Learning About Students at All Levels 1.EngageNY: Performance Level Descriptions 2.Common Core Learning Standards 3.Progressions

32. Performance Level Descriptions Describe the trajectory of knowledge and skills at each grade level. Provide rich information about what students in each performance category know and can do. Serve as basis of discussion among educators about the specific knowledge and skills that distinguish the “just barely” Level 3 proficient student, or the “just barely” Level 2 student.

33. Performance Level Descriptions

35. Important Questions What performance levels does the item tell us about? How could the item be modified to tell us information about different performance levels?

36. Annotated Item

37. Use Cluster and Domain Headings

38. Illustrative Math Task

40. Connect To Your Practice What is an activity that you could do yourself or lead others in to promote assessments that provide information about students at a variety of levels?

41. Two Big Ideas Revisited 1. The assessment should reflect a balance of rigor, helping us understand students’ procedural abilities, conceptual understanding, and abilities to apply. 2. The assessment should give us information about students at all levels.

42. AET

44. Check In With The Pyramid High Quality, Common Core- Aligned Assessments Data Analysis and Action Part II Part I

45. *Analysis is hard. We don’t want to “granularize” content… …but we have to do something to look “under the hood” We want our students engaged in rich tasks… …but we want to dig into the work associated with the tasks to learn specifics about what our students know and can do We don’t want to put rigor in silos or to create a “checklist” for rigor… …but we want usable information about how are kids are doing with respect to the demands of the Common Core

46. Sample Assessment: Ms. Alonzo’s Class What makes this assessment Common Core-aligned? How could it be improved?

47. Think Aloud… I knew some of my students were functioning below grade level, so I used the NF domain heading to locate similar understandings at the 3 rd grade level. This drove instruction for my unit and allowed for more differentiation. I tried to vary performance level using PLDs by mixing identifying equivalent fractions and generating equivalent fractions. I tried to include a variety of prompts/question types that would offer a balance of rigor. This drove instruction for my unit and ensured a balance of rigor throughout the unit.

48. Examine Sample Assessment First Focus Question: “Imagine looking at some student work associated with this assessment. What kinds of errors do you think you’d see? What would these errors reveal about students?”

49. P C

50. P C

51. P P C

52. A

53. Two Big Ideas About Data Analysis: Analyze student work based on: 1. The grade level standard(s) being measured 2. The type of error, viewed through a rigor* lens

54. Looking At Student Work Second Focus Question: “Look at the work from Caitlin. What kinds of errors do you see? What do these errors reveal about Caitlin, through a rigor lens?”

55. Caitlin

59. Truman

63. Summary Notice: 1. The grade level standard(s) being measured 2. The type of error, viewed through a rigor* lens

64. Connect To Your Practice What is an activity that you could do yourself or lead others in to promote error analysis through a rigor lens?

65. How Do We Track Data?

66. Tracking The Class

67. Each Item, Through Multiple Lenses

68. Useful Disaggregation

70. Possible Modifications Break down data to show strategies employed (e.g., table, equation, picture) Break down P, C, A further (e.g., “P – Division of fractions”) Include other “lenses” (e.g., vocabulary, writing) Also tag items at performance levels, using PLDs Tag items to more than one standard

71. Connect To Your Practice What is an activity that you could do yourself or lead others in to promote tracking data using a rigor lens?

72. Using Questions to Lead Data Meetings “Bambrick Model”—Based on Paul Bambrick- Santoyo’s Driven By Data We’ll look at: “Pre-Cursors” (what happens before a data meeting) “Conversation Starters and Re-Directors” (what happens during a data meeting) $64,000 Question: How might these look different using a Common Core-aligned assessment?

73. “Pre-Cursors”

74. How would we prepare differently for a Common Core assessment meeting? – What different activities would we ask teachers to do? – What different questions would we pose?

75. “Conversation Starters & Re-Directors”

76. What would be different during a Common Core assessment meeting? – What different activities would we ask teachers to do? – What different questions would we pose?

77. Recap High Quality, Common Core- Aligned Assessments Data Analysis and Action Part II Part I

78. Two Big Ideas About Assessment Design: 1. The assessment should reflect a balance of rigor, helping us understand students’ procedural abilities, conceptual understanding, and abilities to apply. 2. The assessment should give us information about students at all levels.

79. Two Big Ideas About Data Analysis: Analyze student work based on: 1.The grade level standard(s) being measured 2.The type of error, viewed through a rigor lens

80. Session Objectives Assessment Design: Know the elements of a high-quality Common Core-aligned mathematics assessment Know how to create and choose assessment tasks that reflect a balance of rigor and give comprehensive information about students at all levels

81. Session Objectives Data Analysis: Be able to describe what to look for when analyzing student work for a Common Core- aligned assessment Be able to create a data tracker for assessments Develop questions that drive data-analysis meetings around Common Core-aligned assessment data

82. Thanks! Q & A