1. Ensuring State Assessments Match the Rigor, Depth and Breadth of College- and Career- Ready Standards Student Achievement Partners Spring 2014

2. PAGE 2 Section C: Align to Standards – Mathematics The purpose of this presentation is to provide a high-level overview of the CCSSO Criteria for Procuring and Evaluating High-Quality Assessments for Mathematics in order to illustrate the criteria and how to apply them. Topics discussed in this presentation include: Criterion C.1: Focusing strongly on the content most needed for success in later mathematics Criterion C.2: Assessing a balance of concepts, procedures, and applications Criterion C.3: Connecting practice to content Criterion C.4: Requiring a range of cognitive demand Criterion C.5: Ensuring high-quality items and a variety of item types

3. PAGE 3 Not all math topics are created equal.

4. PAGE 4 College and career readiness has specific implications for math content.

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7. PAGE 7 Research on high-performing countries has specific implications for math content.

8. PAGE 8 Mathematics topics intended at each grade by at least two-thirds of A+ countries Mathematics topics intended at each grade by at least two- thirds of 21 U.S. states The shape of math in A+ countries 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

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11. PAGE 11 CCSSO Criterion C.1 Focusing strongly on the content most needed for success in later mathematics: The assessments help educators keep students on track to readiness by focusing strongly on the content most needed in each grade or course for later mathematics.

12. PAGE 12 C.1 – Focusing strongly on the content most needed for success in later mathematics K 12 Number & Operations Measurement & Geometry Algebra &Functions Statistics & Probability Grade Band ElementaryMiddleHigh School Topics Assessed by Vast Majority of Score Points Number and Operation Ratio, Proportional Relationships, Pre-algebra, and Algebra Algebra, Functions, and Modeling

13. PAGE 13 C.1 – Evidence Descriptions Test blueprints and other specifications are provided, demonstrating that the vast majority of score points in each assessment focuses on the content that is most important for students to master in that grade band in order to reach college and career readiness. For each grade band, this content consists of: – Elementary grades – number and operations; – Middle School – ratio, proportional relationships, pre-algebra, and algebra; and – High School – prerequisites for careers and a wide range of postsecondary studies, particularly algebra, functions, and modeling applications. Test blueprints and other specifications are provided, demonstrating that the vast majority of score points in each assessment focuses on the content that is most important for students to master in that grade band in order to reach college and career readiness. For each grade band, this content consists of: – Elementary grades – number and operations; – Middle School – ratio, proportional relationships, pre-algebra, and algebra; and – High School – prerequisites for careers and a wide range of postsecondary studies, particularly algebra, functions, and modeling applications.

14. PAGE 14 CCSSO Criterion C.2 Assessing a balance of concepts, procedures, and applications: The assessments measure conceptual understanding, fluency and procedural skill, and application of mathematics, as set out in college- and career-ready standards.

15. PAGE 15 C.2 – Assessing a balance of concepts, procedures, and applications. Procedures and Fluency (Grade 6) 6.NS.A.3 1. Divide 1.08 by 0.02. 2. 42 ÷ _______ = 105 From: http://achievethecore.org/page/910/extending-previous-understandings-of-properties-mini-assessment- detail-pghttp://achievethecore.org/page/910/extending-previous-understandings-of-properties-mini-assessment- detail-pg 6.EE.A.2

16. PAGE 16 C.2 – Assessing a balance of concepts, procedures, and applications. Concepts (Grade 8) From: http://achievethecore.org/page/911/simultaneous-linear-equations-mini-assessment-detail-pghttp://achievethecore.org/page/911/simultaneous-linear-equations-mini-assessment-detail-pg

17. PAGE 17 C.2 – Assessing a balance of concepts, procedures, and applications. Application (HS): From: https://www.illustrativemathematics.org/illustrations/1306https://www.illustrativemathematics.org/illustrations/1306

18. PAGE 18 C.2 – Evidence Descriptions The distribution of score points reflects a balance of mathematical concepts, procedures/fluency, and applications, as the state’s standards require. All students, whether high performing or low performing, are required to respond to items within the categories of conceptual understanding, procedural skill and fluency, and applications, so that they have the opportunity to show what they know and can do. The distribution of score points reflects a balance of mathematical concepts, procedures/fluency, and applications, as the state’s standards require. All students, whether high performing or low performing, are required to respond to items within the categories of conceptual understanding, procedural skill and fluency, and applications, so that they have the opportunity to show what they know and can do.

19. PAGE 19 CCSSO Criterion C.3 Connecting practice to content: The assessments include brief questions and also longer questions that connect the most important mathematical content of the grade or course to mathematical practices, for example, modeling and making mathematical arguments.

20. PAGE 20 C.3 – Evidence Descriptions Assessments for each grade and course meaningfully connect mathematical practices and processes with mathematical content (especially with the most important mathematical content at each grade), as required by the state’s standards. Explanatory materials (citing test blueprints and other specifications) describe the connection, for each grade or course, between content and mathematical practices and processes. Assessments for each grade and course meaningfully connect mathematical practices and processes with mathematical content (especially with the most important mathematical content at each grade), as required by the state’s standards. Explanatory materials (citing test blueprints and other specifications) describe the connection, for each grade or course, between content and mathematical practices and processes.

21. PAGE 21 CCSSO Criterion C.4 Requiring a range of cognitive demand: The assessments require all students to demonstrate a range of higher-order, analytical thinking skills in reading and writing based on the depth and complexity of college- and career-ready standards, allowing robust information to be gathered for students with varied levels of achievement. Assessments include questions, tasks, and prompts about the basic content of the grade or course as well as questions that reflect the complex challenge of college- and career-ready standards.

22. PAGE 22 C.4 – Evidence Descriptions Test blueprints and other specifications are provided to demonstrate that the distribution of cognitive demand for each grade level is sufficient to assess the depth and complexity of the state’s standards, as evidenced by use a of generic taxonomy (e.g., Webb’s Depth of Knowledge) or, preferably, classifications specific to the discipline and drawn from mathematical factors, such as: – Mathematical topic coverage in the task; – Nature of reasoning; – Nature of computation; – Nature of application; – Cognitive actions Test blueprints and other specifications are provided to demonstrate that the distribution of cognitive demand for each grade level is sufficient to assess the depth and complexity of the state’s standards, as evidenced by use a of generic taxonomy (e.g., Webb’s Depth of Knowledge) or, preferably, classifications specific to the discipline and drawn from mathematical factors, such as: – Mathematical topic coverage in the task; – Nature of reasoning; – Nature of computation; – Nature of application; – Cognitive actions

23. PAGE 23 CCSSO Criterion C.5 Ensuring high-quality items and a variety of item types: High-quality items and a variety of item types are strategically used to appropriately assess the standard(s).

24. PAGE 24 C.5 – Evidence Descriptions Specifications are provided to demonstrate that the distribution of item types for each grade level and content area is sufficient to strategically assess the depth and complexity of the standards being addressed. To support claims of quality the following are provided: – The list and distribution of the types of work students will be asked to produce; – Exemplar items for each item type used in each grade band; – Rationales for the use of the specific item types; Specifications are provided to demonstrate that the distribution of item types for each grade level and content area is sufficient to strategically assess the depth and complexity of the standards being addressed. To support claims of quality the following are provided: – The list and distribution of the types of work students will be asked to produce; – Exemplar items for each item type used in each grade band; – Rationales for the use of the specific item types;

25. PAGE 25 C.5 – Evidence Descriptions To support claims of quality the following are provided (con’t): – Specifications showing the proportion of item types on a form; – For constructed response items, a scoring plan (i.e., AI machine-scored, hand-scored, by whom, how trained), scoring rubrics, and sample student work to confirm the validity of the scoring process; and – A description of the process used for ensuring the technical quality, alignment to standards, and editorial accuracy of the items. To support claims of quality the following are provided (con’t): – Specifications showing the proportion of item types on a form; – For constructed response items, a scoring plan (i.e., AI machine-scored, hand-scored, by whom, how trained), scoring rubrics, and sample student work to confirm the validity of the scoring process; and – A description of the process used for ensuring the technical quality, alignment to standards, and editorial accuracy of the items.

26. Thank You!