PARCC Model Content Frameworks for Mathematics and Item Prototypes August 30, 2012

1. PARCC Model Content Frameworks for Mathematics and Item Prototypes August 30, 2012

2. Objectives • Gain better understanding of the revisions to the Model Content Frameworks • Gain better understanding of the PARCC assessment system and the alignment between the Model Content Frameworks and the PARCC item prototypes • Provide suggestions for communications and supporting materials • Learn from one another about use of the Model Content Frameworks and item prototypes

3. PARCC Model Content Frameworks

4. Purpose and Audience of the Model Content Frameworks Purpose • Inform development of PARCC assessments • Support implementation of the Common Core State Standards Audience • State and local curriculum directors • Teachers and building administrators

5. Development of the Model Content Frameworks • State-led process that included math content experts in PARCC states and members of the Common Core State Standards writing team • November 2011 release: Three rounds of feedback, including public comment period. K–12 educators, administrators, higher education faculty, school board members, parents, and students provided feedback. • August 2012 final release: Two rounds of review, including public comment period in June 2012. Majority of feedback came from mathematics educators.

6. Approach of the Model Content Frameworks for Mathematics • Analysis of CCSS on how focus, coherence, content and practices all work together • Frame the critical advances in the standards: • Focus and coherence • Content knowledge, conceptual understanding, and expertise • Content and mathematical practices • Grades 3-8; Algebra I, Geometry, Algebra II; Mathematics I, Mathematics II, Mathematics III

7. Development of Major, Supporting, and Additional Clusters (grades 3-8) • The content domains in CCSS vary from grade to grade • CCSS domains with greater specificity (e.g., Expressions and Equations) tend to signal priorities for grade • In grade 6, all EE clusters are major • Three out of five domains in CCSS for grades K-5 are arithmetic; 15/20 arithmetic clusters are major • Other domains in 3-5 support arithmetic • standards relating to area and volume explicitly refer to addition, multiplication and their properties (e.g., 3.MD.7 and 5.MD.5)

8. NEW: High School Pathways • Built from Appendix A in CCSS • Content emphases by cluster and assessment limits for • Algebra I, Geometry, and Algebra II • Mathematics I, Mathematics II, and Mathematics III • Decision rules • Clusters that appear as major in traditional pathway also appear as major in integrated pathway • To support focus, traditional courses have 7-9 major and integrated courses have 10-11 major clusters

9. PARCC Item Prototypes

10. What is Different about PARCC’s Development Process? • PARCC states first developed the Model Content Frameworks to provide guidance on key elements of excellent instruction aligned with the Standards. • Frameworks informed the assessment blueprint design So, for the first time. . . • PARCC is communicating in the same voice to teachers as it is to assessment developers! • PARCC is designing the assessments around the exact same critical content the standards expect of teachers and students.

11. Process to Produce Quality Items and Tasks • Teams of classroom teachers and higher education faculty from The Charles A. Dana Center (University of Texas, Austin) developed conceptual models and prototype items • Additional prototype items came from ETS, Pearson, and members of the CCSS writing team • Reviews and feedback from members of CCSS writing team, members of the PARCC Content Technical Working Groups, PARCC state leaders and content experts, and higher education faculty

12. Task Types for Mathematics • Type I (PBA and EOY): Machine scored; focus on major content and/or fluency. Could be practice forward • Type II (PBA): Hand scored (or machine scored if innovative); focus on expressing reasoning • Type III (PBA): Hand scored (or machine scored if innovative); focus on modeling/application

13. Grade 3 Sample Item • Type I Task – Part A is machine-scored • Assessing the standard 3.NF.1- a major focus in grade 3 • Assessing MP.7 (Look for and make sure of structure) • Technology-enhanced • Unlike traditional multiple choice, there is more than one correct solution and difficult to guess.

14. Grade 3 Sample Item • Type II Task – Part B is partial machine-scored and partial hand-scored • Assessing the standard 3.NF.3b - a major focus in grade 3 • Assessing MP.2 (Reason abstractly and quantitatively) and MP.3 (Construct viable arguments and critique the reasoning of others) • Unlike traditional multiple choice, there is more than one correct solution and difficult to guess.

15. Grade 6 Sample Item • Type I Task –Machine-scored • Assessing the standard 6.RP - a major focus in grade 6 • Assessing MP.8 (Look for and express regularity in repeated reasoning) • Unlike traditional multiple choice, this is a multiple select task where there is more than one correct solution and difficult to guess.

16. Grade 7 Sample Item • Type I Task –Machine-scored and multi-prompt • Integrated task – Part A assesses the standard 7.RP.3 - a major focus in grade 7 • A key advance from grade 6 to grade 7 is students’ ability to solve real-world and mathematical problems by reasoning proportionally with ratios of fractions • Unlike traditional multiple choice, this is a technology-enhanced fill-in-the-blank format • Accommodates partial credit in a machine-scored format

17. Grade 7 Sample Item • Type I Task –Machine-scored and multi-prompt • Integrated Task – Part B assesses the standard 7.EE.3 - a major focus in grade 7 • A key advance from grade 6 to grade 7 is students’ ability to solve real-world and mathematical problems by reasoning proportionally with ratios of fractions • Unlike traditional multiple choice, this is a technology-enhanced fill-in-the-blank format • Accommodates partial credit in a machine-scored format

18. High School Sample Item • Type I Task –Machine-scored • Assessing the standard F-IF.9 which is supporting work in both the integrated and traditional series and relies on the knowledge in the F-IF cluster on function notation which is major work in both series • Assessing MP.6 (Attend to Precision) • Unlike traditional multiple choice, this is a technology-enhanced drop-down format • Accommodates partial credit in a machine-scored format

19. Improved Teaching and Learning

20. Uses of the Model Content Frameworks and Item Prototypes (ELC responses) I have used/will use the Model Content Frameworks and the item prototypes to… Curriculum Development • Guide the direction of curriculum and the appropriate emphases/refine curriculum maps • Help determine the scope, sequence and weight of standards • Develop Depth of Knowledge levels • Guide development of instructional outcomes aligned to the standards

21. Uses of the Model Content Frameworks and Item Prototypes (ELC responses) I have used/will use the Model Content Frameworks and the item prototypes to… Professional Development and Instruction • Provide PD on recognizing the shifts necessary in teaching and thinking, raising cognitive demand of tasks/items, incorporating reasoning and discussion into lessons, increasing rigor of instruction and assessment, understanding demands of the CCSS • Emphasize the interconnectedness of the grade level standards • Help teachers in direct service special education classes make decisions about where to focus their time • Help teachers to understand that it is not just about what is being taught, but that they need to change the way that they teach • Guide pre-service instruction

22. Uses of the Model Content Frameworks and Item Prototypes (ELC responses) I have used/will use the Model Content Frameworks and the item prototypes to… Assessment • Guide development of grade level/course level common assessments • Show relationship between CCSS and PARCC • Compare old state assessment items with the new prototypes • Revise local assessments • Change the culture of assessment

23. Uses of the Model Content Frameworks and Item Prototypes (ELC responses) I have used/will use the Model Content Frameworks and the item prototypes to… Communication and Awareness • Demonstrate critical shifts • Make presentations to raise awareness and share resources with teachers • Build understanding of the expectations of the CCSS from grade to grade • Communicate with parents and community • Share information within my unit and department • Update teachers on expectations and assessments

24. Additional Uses of the Model Content Frameworks and Item Prototypes • Evaluating instructional resources • Building model instructional unit plans • Providing awareness on the balance of tasks • Building understanding of the connection between content and mathematical practices • Supporting increased focus and coherence in instructional programs • Supporting vertical planning

25. Raised expectations (ELC responses) How are the expectations for students changing? • Perseverance and greater autonomy is going to be a key for students • Students will need to communicate conceptual understanding • Students will earn credit for good thinking, not just correct answers • Students are asked to be problem solvers. They need to be able to understand where to start and what strategies to use. • Students need to develop conceptual understanding, procedural fluency and the ability to apply knowledge/learning. It is not okay to just know the math... • Students will lead the instruction/discussions and learn to solve problems

26. Raised expectations (ELC responses) …and what does that mean for how you work with your students? • Integration of the practices is essential • Provide more emphasis on Habits of Mind, transferable knowledge, deeper understanding, and application that inspires engagement • Less on the What and more on the How • Integrate 21st century learning and more technology into instruction • Teachers will need to move into more of a facilitator role (less telling); provide students with more opportunities to discuss their thinking; and support active, student-centered, problem-based learning

27. Resources for Educator Leader Cadres (ELC responses) When PARCC releases the next set of sample items, it will be helpful to have ____ in order to more effectively understand and use the items? • Scoring rubrics • Time limits • Levels of rigor of items • Sample student responses/anchors • Assessment limits • Samples of each task type for all grade levels • Calculator use for items (and how this will work) • Specific technology needs • ECD claims • Reference materials that will be available • Aligned skill building tasks • UDL descriptors • Potential accommodations/embedded supports • Links between standards and questions • Teachers' perspectives on how they will help students achieve success on these prototypes • Progression of samples • How items will be weighted

28. Resources for Educator Leader Cadres (ELC responses) What additional tools, resources, etc. do you need to support your work and the work with your colleagues? • K-2 frameworks and prototypes • Webinars, PowerPoints, and Podcasts that can be viewed on own time and used with peers • Guidance for developing integrated and practice forward tasks • Video vignettes of classroom applications (mathematical practices), models of teaching that lead to successful completion of questions, classrooms that incorporate technology • tools that emphasize CCR as the primary objective vs. at-grade level pacing • and also tools that make the coherence in the standards easier to see • online resources that mimic the functionality of PARCC items for students to use

29. Resources for Educator Leader Cadres (ELC responses) What additional tools, resources, etc. do you need to support your work and the work with your colleagues? • Guidance around assessments: drafting quality classroom assessments, informing formative assessment process, knowing a viable number of standards to be assessed on interim assessments • Information about growth measurement and how reliability and validity will be affirmed • A side-by-side of current state assessment items with the PARCC items • Professional development on recognizing the mathematical practices in items • Examples of how tasks are used in the classroom to inform instruction

30. QUESTIONS?

31. PARCC Model Content Frameworks for Mathematics and Item Prototypes August 30, 2012 www.PARCConline.org http://parcc.ltftraining.org