California Mathematics Council November 2, 2013 Ivan Cheng Jaspreet Sandha

1. The Right Answer Is NOT Enough California Mathematics Council November 2, 2013 Ivan Cheng Jaspreet Sandha icheng@csun.edu jxs9368@lausd.net Lina Kim lina.n.kim@gmail.com

2. Just for Fun – Try This Now • The proportion = can be used to solve • which of the following situations? • Situation 1: For every 1 teacher, there are 2 TAs at Some HS.If there are 10 teachers, how many TAs are there? • Situation 2: Abel is 1 year old and Betty is 2 years old.When Abel is 10 years old, how old will Betty be? • Situation 1 • Situation 2 Both Situations 1 and 2 Neither Situation 1 nor 2 Presented by Jimmy de la Torre at AERA 2013

3. The Right Answer is NOT Enough • The proportion = can be used to solve • which of the following situations? • Situation 1: For every 1 teacher, there are 2 TAs at Some HS.If there are 10 teachers, how many TAs are there? • Situation 2: Abel is 1 year old and Betty is 2 years old.When Abel is 10 years old, how old will Betty be? • Situation 1 • Situation 2 Both Situations 1 and 2 Neither Situation 1 nor 2 Presented by Jimmy de la Torre at AERA 2013

4. The Right Answer is NOT Enough • Suppose on one test… • Period 1 students averaged 75% correct • Half the class scored 100% and the other half scored 50% • Period 2 students averaged 75% correct • Half the class scored 76% and the other half scored 74% • How do these two classes differ?

5. The Right Answer is NOT Enough • Suppose on one test… • Two students both scored 75% • Sample problem: 12 – 2(3 – 5) • One student got –20 for an answer andanother student got 8 for an answer • How do their errors differ? • What does this mean for our teaching practice?

6. The Right Answer is NOT Enough • Mathematical content • Ratios & proportions, the number system, expressions & equations, functions, geometry, statistics & probability • Mathematical practices • 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

7. Depth of Knowledge (DOK) • Cognitive rigor for each type of thinking • Remember (Level 1 only) • Understand (Levels 1 – 4) • Apply (Levels 1 – 4) • Analyze (Levels 1 – 4) • Evaluate (Levels 3 – 4) • Create (Levels 1 – 4) • What is the DOK for current CSTs?

8. Depth of Knowledge (DOK) Yuan & Le (2012); Herman & Lin (2013), from Linda Darling-Hammond Assembly Testimony, 3/6/13

9. Depth of Knowledge (DOK) Yuan & Le (2012); Herman & Lin (2013), from Linda Darling-Hammond Assembly Testimony, 3/6/13

10. Smarter Balanced Blueprints • “Claims” • Assessment “Targets”

11. Smarter Balanced Blueprints • “Claims”integrate content and practices • Assessment “Targets”

12. Smarter Balanced Blueprints • “Claims” integrate content and practices • Assessment “Targets” specify what will be tested

13. Smarter Balanced Blueprints • “Claims” integrate content and practices • Assessment “Targets” specify what will be tested

14. Claim 1–Concepts and Procedures

15. Claim 1–Concepts and Procedures • Assessment Targets–Grade 8 • Numbers (NS.1, NS.2) • Radicals and exponents (EE.1, EE.2, EE.3, EE.4) • Proportional relationships and equations (EE.5, EE.6) • Expressions and equations (EE.7, EE.8) • Functions (F.1, F.2, F.3) • Modeling relationships (F.4, F.5) • Geometric relationships (G.1, G.2, G.3, G.4, G.5) • Pythagorean Theorem (G.6, G.7, G.8) • Volume (G.9) • Data analysis (SP.1, SP.2, SP.3, SP.4)

16. Claim 2–Problem Solving

17. Claim 2–Problem Solving • Assessment Targets–Grades 6–8, 11 • Applying mathematics to solve problems • Select and use appropriate tools strategically • Interpret results in the context of a situation • Identify important quantities in a practical situation and map their relationships

18. Claim 4–Modeling and Data Analysis • Assessment Targets–Grades 6–8, 11 • Apply mathematics • Construct chains of reasoning to justify models, solutions • State logical assumptions being used • Interpret results in the context of a situation • Analyze the adequacy of and improve models • Identify important quantities in a practical situationand map their relationships

19. Claim 3–Communicating Reasoning

20. Claim 3–Communicating Reasoning • Assessment Targets–Grades 6–8, 11 • Test propositions or conjectures with specific examples • Construct chains of reasoning to justify or refute • State logical assumptions being used • Breaking arguments into cases • Distinguishing correct logic • Base arguments on concrete referents • Determine conditions under which arguments apply

21. Item Types for SBAC Assessments

22. Sample Selected Response Item From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.072

23. Sample Constructed Response Item From Smarter Balanced Assessments, MAT.07.CR.1.000EE.D.165

24. Sample Extended Response Item From Smarter Balanced Assessments, MAT.06.ER.2.000EE.C.172

25. Sample Technology Enhanced Item From Smarter Balanced Assessments, MAT.HS.TE.1.0AREI.I.088

26. The Right Answer is NOT Enough • Mathematical content • Ratios & proportions, the number system, expressions & equations, functions, geometry, statistics & probability • Mathematical practices • 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

27. What Do We Need to Do? • Mathematical content • Ratios & proportions, the number system, expressions & equations, functions, geometry, statistics & probability • Mathematical practices • 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. What Do We Need to Do? • Have clear objectives for each test item we make • Use the standards and blueprints • Specify precise learning goals • Create problems that reveal understanding • Use SBAC samples as a guide • Reveal mastery of specific concept or skill • Analyze student work for understanding • Go beyond the score • Look for patterns of errors and misunderstandings

29. Assessment Planning Matrix • Have clear objectives for each test item we make • Use the standards and blueprints • Specify precise learning goals • Create problems that reveal understanding • Use SBAC samples as a guide • Reveal mastery of specific concept or skill • Analyze student work for understanding • Go beyond the score • Look for patterns of errors and misunderstandings

30. Assessment Planning Matrix

31. Creating Assessments with the APM • Have clear objectives for each test item we make • Use the standards and blueprints • Specify precise learning goals • Create problems that reveal understanding • Use SBAC samples as a guide • Reveal mastery of specific concept or skill • Analyze student work for understanding • Go beyond the score • Look for patterns of errors and misunderstandings

32. Creating Assessments with the APM From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.178

33. Creating Assessments with the APM • Claim 1 – Target F – Grade 6 • Concepts & Procedures – Expressions & Equations • Model 1: SR (DOK 2) – Stimulus: The student is presented with a one-variable equation or inequality in a problem and/or problem set. Prompt: The student is prompted to use substitution to identify the solution to one-variable equations and inequalities. • Model 2: SR (DOK 2) – Stimulus: The student is presented with a verbal expression in a real-world or mathematical problem involving a one-variable equation in the form x + p = q or px = q or a one variable inequality in the form of x > c or x < c. Prompt: The student is prompted to identify the variable equations or inequalities that correspond to verbal expressions in real-world and mathematical problems. Or the student is prompted to identify the solution to one-variable equations and inequalities in real-world and mathematical problems. • Model 3: SR (DOK 1, 2) – Stimulus: The student is presented with a one-variable inequality presented in a real-world or mathematical problem. Prompt: The student is prompted to identify a number line that represents the solution to a one-variable inequality presented in a real-world or mathematical problem. From Smarter Balanced Assessments, MAT.06.SR.1.000EE.F.178

34. Creating Assessments with the APM

35. Creating Assessments with the APM

36. Creating Assessments with the APM • Selected Response (SR) • Constructed Response (CR) • Extended Response (ER) • Technology Enhanced (TE) • Performance Task (PT) • Choose one sample as a model • Note the Assessment Target and the DOK • Note the type of stimulus and the prompt • Create a similar task

37. Online Resources • Common Core resources • CA Common Core Standardshttp://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf • Smarter Balanced sample interactive problemshttp://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm • Howard Countyhttps://secondarymathcommoncore.wikispaces.hcpss.org • MARS/Shellhttp://map.mathshell.org/materials/stds.php • Illustrativemathematics.org • Schools.nyc.gov/Academics/CommonCoreLibrary • Achievethecore.org • Serpmedia.org

38. The Right Answer Is NOT Enough Thank You Ivan Cheng Jaspreet Sandha icheng@csun.edu jxs9368@lausd.net Lina Kim lina.n.kim@gmail.com