Preparing for the Common Core State Standards Mathematics Assessment

1. Preparing for the Common Core State Standards Mathematics Assessment October 30, 2012

2. Today’s Goals Participants will have the opportunity to: • explore the design of the SBAC assessment system • consider the design of abalancedassessment system for your districts

3. Today’s Agenda • Welcome, Context, and Introductions • Opening Comments - Dr. Burkhardt • Explore SBAC Content Specifications and Items • SBAC Basics • Summative Assessment Target Tables • SBAC Tasks • Computer Adapted Test Design • AM Summary & Reflections - Dr. Burkhardt Lunch & District Debrief • A Balanced Classroom and District Assessment System • Introduction to Formative Assessment – Dr. Burkhardt • MAPS Tasks • Closing Remarks - Dr. Burkhardt • District Debrief & End of Day Reflections

4. CCSS States and the Smarter Balanced Assessment Consortium Balanced States CCSSM States

5. SBAC - A Balanced System

6. Assessment Principles • Assessments are grounded in a thoughtful, standards-based curriculum and are managed as part of an integrated system. • Assessments include evidence of student performance. • Teachers are integrally involvedin the development and scoring of assessments. • Assessments are structured to continuously improve teaching and learning. • Assessment, reporting, and accountability systems provide useful information on multiple measures.

7. Hugh Burkhardt, Ph.D. • Shell Center for Mathematics Education • Mathematics Assessment Resources Project (MARS) • Mathematics Assessment Project (MAP)

8. Key Elements of the CCSSM Connected to Issues of Assessment • CCSS Learning Progressions • Within grades • Across Grades • www.TurnonCCMath.net • http://ime.math.arizona.edu/progressions/

9. Key Elements of the CCSSM Connected to Issues of AssessmentStandards for Mathematical Practice Reasoning and explaining William McCallum Standards for Mathematical Practice Tucson, April 2011 Modeling and Using tools Seeing structure and generalizing

10. Smarter Balanced Assessment Consortium Mathematics Content Specifications Beginning with the basics! • Claims • DOK • Cluster Headings • Targets • Item Types

11. SBAC Basics - A Balanced System

12. SBAC Basics: FoundationalBeliefs Assessments should be structured to continuously improve teaching and learning • Assess around learning progressions • Using Computer Adaptive Testing Technology • Creating opportunities for students and teachers to get actionable feedback on student learning throughout the year • Provide curriculum-embedded assessments that offer models of good curriculum and assessment practices • Allowing close examination of student work and moderated teacher scoring as professional development

13. Claim 1: Concepts and Procedures, ≈ 40% • “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” SBAC Basics: Reporting Categories • “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” Claim 2: Problem Solving ≈ 20% “Each claim is a summary statement about the knowledge and skill students will be expected to demonstrate on the assessment related to a particular aspect of the CCSS for mathematics.” • “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Claim 3: Communicating Reasoning ≈ 20% Claim 4: Data Analysis and Modeling ≈ 20% • “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”

14. Same Target, Different Claims For each task consider: Which claim or claims do you see the task supporting? Why?

15. SBAC Basics: Depth of Knowledge (DOK) Measure of Cognitive Rigor The level of task complexity. Level 1: Recall and Reproduction • Requires eliciting information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. Level 2: Basic Skills and Concepts • Requires the engagement of some mental processing beyond a recall of information. Level 3: Strategic Thinking and Reasoning • Requires reasoning, planning, using evidence, and explanations of thinking. Level 4: Extended Thinking • Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.

16. DOK Level 1 Example -Grade 8 Select all of the expressions that have a value between 0 and 1. 87∙ 8–12 74 7–3 1 3 2 1 3 9 ∙ (–5)6 (–5)10

17. DOK Level 2 Example- Grade 8 A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills this tank with water at a rate of 8 cubic feet per minute. How many minutes will it take Jane to completely fill the tank without overflowing at this rate? Round your answer to the nearest minute.

18. DOK Level 3 Example- Grade 8 • The total cost for an order of shirts from a company consists of the cost for each shirt plus a one-time design fee. The cost for each shirt is the same no matter how many shirts are ordered. • The company provides the following examples to customers to help them estimate the total cost for an order of shirts. • 50 shirts cost $349.50 • 500 shirts cost $2370 • Part A: Using the examples provided, what is the cost for each shirt, notincluding the one-time design fee? Explain how you found your answer. • Part B: What is the cost of the one-time design fee? Explain how you found your answer.

19. DOK Level 4 Example - Grade 8 During the task, the student assumes the role of an architect who is responsible for designing the best plan for a park with area and financial restraints. The student completes tasks in which he/she compares the costs of different bids, determines what facilities should be given priority in the park, and then develops a scale drawing of the best design for the park and an explanation of the choices made. This investigation is done in class using a calculator, an applet to construct the scale drawing, and a spreadsheet.

20. Cognitive Rigor Matrix

21. Structure of the CCSSM DOMAIN Number and Operations in Base Ten 4.NBT Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. STANDARD CLUSTER

22. SBAC Basics: Large Scale Assessment Constraints On the large scale summative assessment not everything in the CCSSM can have equal priority given time limitations. Cluster headings at each grade level are categorized as Major (m), or as Additional/Supporting (a/s). • About 75% - 80% of the items should come from Major clusters for Claim 1 • About 20% - 25% of the items should come from Additional/Supportingclusters for Claim 1

23. SBAC Basics: Large Scale Assessment Constraints • Identifying some standards within “major” clusters and others within “additional/supporting” clusters is not to say that anything in the standards can be neglected. To do so would leave gaps in student preparation for later mathematics. In other words, all content is eligible for and should be encompassed in the assessment. (p.29)

24. SBAC Basics: Large Scale Assessment Constraints • Working at the cluster level helps to avoid obscuring the big ideas and getting lost in the details of specific standards (which are individually important, but impossible to measure in their entirety within the bounds of reasonable testing time). p.29

25. SBAC Mathematics Content Specifications

26. Claim 1: Concepts and Procedures, ≈ 40% Content Specifications for the Summative Assessment of CCSSM Claim 2: Problem Solving ≈ 20% • Details of the Assessment Specifications are organized around the four Claims that will be used as reporting categories Claim 3: Communicating Reasoning ≈ 20% Claim 4: Data Analysis and Modeling ≈ 20%

27. Summative Assessment Target TablesCurrently under development by SBAC • Indicates Targets for the summative portion of the Smarter Balanced assessment • Suggests what is taken as evidence of student proficiency for a particular target • Articulates • Content (cluster heading and related standards) • Depth of Knowledge task assignments • Assessment method/Task types

28. Claim 1: Concepts and Procedures, ≈ 40% Summative Assessment Target Tables The cluster headings can be viewed as the most effective means of communicating the focus and coherence of the standards. Therefore, this content specifications document uses the cluster headings as the targets of assessment for generating evidence for Claim #1. (p.29)

29. Structure of the CCSSM DOMAIN Number and Operations in Base Ten 4.NBT Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. STANDARD CLUSTER

30. Summative Assessment Target DClaim 1 - Concepts and Procedures Grade 4 Operations and Algebraic Thinking Target D [m]: Generalize place value understanding for multi-digit whole numbers. (DOK 1, 2) Tasks for this target will require students to compare multi-digit numbers using >, =, and <. Tasks should tap into students’ understanding of place value (e.g., by asking students to give a possible digit for the empty box in 4357 < 43☐9 that would make the inequality true). A smaller number of these tasks will incorporate student understanding of rounding (e.g., explaining why rounding to a certain place would change the symbol < or > to =). In claims 2-4, students should see contextual problems associated with this target that highlight issues with precision, including problems in Claim 3 that ask students to explain how improper estimation can create unacceptable levels of precision and/or lead to flawed reasoning. (pg. 34 - 35)

31. Cluster Headings RULE! • In the CCSSM the cluster headings usually serve to communicate the larger intent of a group of standards. For example, a cluster heading in Grade 4 reads: “Generalize understanding of place value for multi-digit numbers.” Individual standards in this cluster pinpoint some signs of success in the endeavor, but the important endeavor itself is stated directly in the cluster heading. In addition, the word generalize signals that there is a multi-grade progression in grades K-3 leading up to this group of standards. (p.28)

32. Summative Assessment TargetsClaim 1 - Concepts and Procedures Grade 4 Operations and Algebraic Thinking • Use the four operations with whole numbers to solve problems. • Gain familiarity with factors and multiples. • Generate and analyze patterns. • Generalize place value understanding for multi-digit whole numbers. • Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations – Fractions • Extend understanding of fraction equivalence and ordering. • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. • Understand decimal notation for fractions, and comparedecimal fractions.

33. Summative Assessment TargetsClaim 1 - Concepts and Procedures Grade 4 continued Measurement and Data • Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. • Represent and interpret data. • Geometric measurement: understand concepts of angle and measure angles. Geometry • Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

34. Claim 1- Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

35. Summative Assessment Target Tables for Claims 2, 3, and 4 (≈ 60%) Claim 2: Problem Solving ≈ 20% • Assessment Targets for Claims 2, 3, and 4 are not divided into a grade-by-grade description. • A general set of assessment targets applicable across grade levels. Claim 3: Communicating Reasoning ≈ 20% Claim 4: Data Analysis and Modeling ≈ 20% Pages 59 - 68

36. Summative Assessment TargetsClaim 2 – Problem Solving • Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace • Select and use tools strategically • Interpret results in the context of the situation • Identify important quantities in a practical situation and map their relationships. Claim 2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

37. Summative Assessment TargetsClaim 3 – Communicating Reason Claim 3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. • Test propositions or conjectures with specific examples. • Construct, autonomously, chains of reasoning that justify or refute propositions or conjectures. • State logical assumptions being used. • Use the technique of breaking an argument into cases. • Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in the argument—explain what it is. • Base arguments on concrete referents such as objects, drawings, diagrams, and actions. • Determine conditions under which an argument does and does not apply.

38. Summative Assessment TargetsClaim 4 – Modeling and Data Analysis Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. • Apply mathematics to solve problems arising in everyday life, society, and the workplace. • Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. • State logical assumptions being used. • Interpret results in the context of a situation. • Analyze the adequacy of and make improvement to an existing model or develop a mathematical model of a real phenomenon. • Identify important quantities in a practical situation and map their relationships. • Identify, analyze, and synthesize relevant external resources to pose or solve problems.

39. Summative Assessment Targets Tables As a table group select a grade level and skim through the corresponding Targets for Claim 1. • Orient yourself to the grade level • Cluster headings with standards • DOK • Related requirements in Claims 2 – 4 • Read one assessment target and explore related targets in Claims 2 – 4. • Share a feature that may suggest changes at the system and/or classroom level.

40. SBAC Related Assessment Resources • Where can I go for instructional and assessment tasks that reflect the types of thinking students will need to be able to demonstrate on the SBA?

41. SBAC Sample Math Tasks • Explore the SBAC collection www.tinyurl.com/SBsamples • Be sure to push forward to explore a variety of task types (Selected-response, Technology-enhanced, Constructed-response, Performance) • Check out the two right tabs along the top bar for a number of items.

42. SBAC Website Resourceshttp://www.smarterbalanced.org/smarter-balanced-assessments/ Click Here • Content Specifications (with some items at the end) • Item/Task Specifications (with more sample tasks) • Technology Enhanced Items (still more sample tasks) • Performance Tasks (you guessed it, more sample tasks!) • Guidelines

43. SBAC Website Resourceshttp://www.smarterbalanced.org/smarter-balanced-assessments/ • Item and Task Types • Accessibility and Accommodations • For more information: • Visit the support for under-represented students webpage • Download the Accessibility and Accommodations Factsheet Click Here

44. Oakland CCSSInitiative Resources The Common Core State Standards Initiative (CCSSI) Oakland provide support and direction for educators as they move toward full implementation: CCSS aligned curriculum and coherent units of studyto highlight needed shifts in content related and pedagogical practices Highlight Lessons Formative Assessment Resources (video, sample student work, rubrics, instructional websites, etc.)

45. Atlas Curriculum Mapping Units, lessons, formative assessments, and other resources available in Atlas by Rubicon. • http://oaklandk12.rubiconatlas.org/public

46. Online CCSS Curriculum Resources • Units of Study • Lesson resources • Assessment resources • Professional resources • Video • Sample student work • And more

47. Classroom and Systems Implications • As a group discuss implications for your particular roles • instruction • assessments • teacher evaluation • student subgroups • classroom materials such as textbooks, computers, etc. • Be prepared to share your thinking with the whole group.

48. An Introduction to Computer Adaptive Tests (CATs) Not to be Confused with Computer Administered Tests (CATs)! :-O

49. Computer Adaptive Tests… • Place student ability and test question difficulty on the same scale • Modify the test based on student responses • Can assess student ability more efficiently than “fixed-form” tests • Can be used to measure “growth” • Have a set of inherent challenges all of their own.

50. Student 1 Ability /Difficulty More/ Harder More/ Harder Test Scale Score Less/ Easier Less/ Easier Q1 Q2 Q3 Q4 Student 2 Ability /Difficulty Test Scale Score Q1 Q2* Q3* Q4*