1. achievethecore.org 1 Implementing Standards and Incorporating Mathematical Practices Sandra M. Alberti AMTNJ October 24, 2013

2. achievethecore.org 2 Student Achievement Partners – Who We Are 2 SAP is a nonprofit organization founded by three of the contributing authors of the Common Core State Standards Currently a team of approximately 30; office in NY and team members located throughout the country Funded by foundations: GE Foundation, Hewlett Foundation, Bill & Melinda Gates Foundation and The Helmsley Charitable Trust Our mission: Student Achievement Partners is devoted to accelerating student achievement by supporting effective and innovative implementation of the CCSS.

3. achievethecore.org 3 Our Principles – How we approach the work W E HOLD NO INTELLECTUAL PROPERTY Our goal is to create and disseminate high quality materials as widely as possible. All resources that we create are open source and available at no cost. We encourage states, districts, schools, and teachers to take our resources and make them their own. W E DO NOT COMPETE FOR STATE, DISTRICT OR FEDERAL CONTRACTS Ensuring that states and districts have excellent materials for teachers and students is a top priority. We do not compete for these contracts because we work with our partners to develop high quality RFPs that support the Core Standards. W E DO NOT ACCEPT MONEY FROM PUBLISHERS We work with states and districts to obtain the best materials for teachers and students. We are able to independently advise our partners because we have no financial interests with any publisher of education materials. Our independence is essential to our work.

4. achievethecore.org 4 Why are we doing this? We have had standards. Before Common Core State Standards we had standards, but rarely did we have standards-based instruction. Long lists of broad, vague statements Mysterious assessments Coverage mentality Focused on teacher behaviors – “the inputs” 4

5. achievethecore.org 5 Results of Previous Standards, and Hard Work Previous state standards did not improve student achievement. Gaps in achievement, gaps in expectations NAEP results High school drop out issue College remediation issue This is about more than just working hard! 5

6. achievethecore.org 6 Principles of the CCSS Fewer - Clearer - Higher Aligned to requirements for college and career readiness Based on evidence Honest about time

7. achievethecore.org 7 Implications What implications do the CCSS have on what we teach? What implications do the CCSS have on how we teach? 7 This effort is about much more than implementing the next version of the standards: It is about preparing all students for success in college and careers.

8. achievethecore.org 8 Mathematics: 3 shifts 1. Focus: Focus strongly where the standards focus.

9. achievethecore.org 9 9 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).

10. achievethecore.org 10 achievethecore.org 10 K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability Traditional U.S. Approach

11. achievethecore.org 11 achievethecore.org Focusing attention within Number and Operations Operations and Algebraic Thinking Expressions and Equations Algebra  Number and Operations— Base Ten  The Number System  Number and Operations— Fractions  K12345678High School

12. achievethecore.org 12 achievethecore.org Priorities in Mathematics

13. achievethecore.org 13 achievethecore.org Where to focus in mathematics – K example 13

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16. achievethecore.org 16 achievethecore.org Mathematics: 3 shifts 1. Focus: Focus strongly where the standards focus. 2. Coherence: Think across grades, and link to major topics

17. achievethecore.org 17 achievethecore.org Coherence: Link to major topics within grades Example: data representation Standard 3.MD.3

18. achievethecore.org 18 achievethecore.org Mathematics: 3 shifts 1. Focus: Focus strongly where the standards focus. 2. Coherence: Think across grades, and link to major topics 3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

19. achievethecore.org 19 achievethecore.org Conceptual understanding of place value…?

20. achievethecore.org 20 achievethecore.org 20 Conceptual understanding of place value…?

21. achievethecore.org 21 achievethecore.org Conceptual Understanding of Fractions Resource/Tool: http://www.illustrativemathematics.org/standards/k8

22. achievethecore.org 22 achievethecore.org 22 Required Fluencies in K-6

23. achievethecore.org 23 achievethecore.org Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

24. achievethecore.org 24 achievethecore.org 24 1.Make sense of problems and persevere in solving them 6. Attend to precision 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning Overarching habits of mind of a productive mathematical thinker. Reasoning and explaining Modeling and using tools Seeing structure and generalizing

25. achievethecore.org 25 achievethecore.org AM I DOING THE CORE?

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29. achievethecore.org 29 achievethecore.org 29 Standards for Mathematical Practice There is not a one-to-one correspondence between the indicators for Core Action 3 and the Standards for Mathematical Practice. These indicators and the associated illustrative student behavior collectively represent the Standards for Mathematical Practice that are most easily observable during instruction. 29

30. achievethecore.org 30 achievethecore.org Core Action 3: Provide all students with opportunities to exhibit mathematical practices in connection with the content of the lesson. 30 4 Some or most of the indicators and student behaviors should be observable in every lesson, though not all will be evident in all lessons.

31. achievethecore.org 31 achievethecore.org Evidence Observed or Gathered 1 = The teacher does not provide students opportunity and very few students demonstrate this behavior. 2 = The teacher provides students opportunity inconsistently and very few students demonstrate this behavior. 3 = The teacher provides students opportunity consistently and some students demonstrate this behavior. 4 = The teacher provides students opportunity consistently and some students demonstrate this behavior.

32. achievethecore.org 32 achievethecore.org Am I doing the Core? IndicatorsIllustrative Student Behavior A.The teacher uses strategies to keep all students persevering with challenging problems. Even after reaching a point of frustration, students persist in efforts to solve challenging problems. B.The teacher establishes a classroom culture in which students explain their thinking. Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence. C.The teacher orchestrates conversations in which students talk about each other’s thinking. Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding.

33. achievethecore.org 33 achievethecore.org Am I doing the Core? IndicatorsIllustrative Student Behavior D.The teacher connects students’ informal language to precise mathematical language appropriate to their grade. Students use precise mathematical language in their explanations and discussions. E.The teacher has established a classroom culture in which students choose and use appropriate tools when solving a problem. Students use appropriate tools strategically when solving a problem. F.The teacher asks students to explain and justify work and provides feedback that helps students revise initial work. Student work includes revisions, especially revised explanations and justifications.

34. achievethecore.org 34 achievethecore.org Evidence-Centered Design (ECD) Claims Design begins with the inferences (claims) we want to make about students Evidence In order to support claims, we must gather evidence Tasks Tasks are designed to elicit specific evidence from students in support of claims ECD is a deliberate and systematic approach to assessment development that will help to establish the validity of the assessments, increase the comparability of year-to year results, and increase efficiencies/reduce costs.

35. Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready (or “on- track” to being ready) in mathematics. The student solves grade-level /course-level problems in mathematics as set forth in the Standards for Mathematical Content with connections to the Standards for Mathematical Practice. Sub-Claim A: Major Content 1 with Connections to Practices The student solves problems involving the Major Content 1 for her grade/course with connections to the Standards for Mathematical Practice. Sub-Claim B: Additional & Supporting Content 2 with Connections to Practices The student solves problems involving the Additional and Supporting Content 2 for her grade/course with connections to the Standards for Mathematical Practice. Sub-Claim E: Fluency in applicable grades (3-6) The student demonstrates fluency as set forth in the Standards for Mathematical Content in her grade. Claims Structure: Mathematics Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content 3 (expressing mathematical reasoning) The student expresses grade/course- level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others, and/or attending to precision when making mathematical statements. Sub-Claim D: Highlighted Practice MP.4 with Connections to Content (modeling/application) The student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them (MP. 1),reasoning abstractly and quantitatively (MP. 2), using appropriate tools strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for and expressing regularity in repeated reasoning (MP.8). Total Exam Score Points: 82 (Grades 3-8), 97 or 107(HS) Total Exam Score Points: 82 (Grades 3-8), 97 or 107(HS) 12 pts (3-8), 18 pts (HS) 6 pts (Alg II/Math 3 CCR) 12 pts (3-8), 18 pts (HS) 6 pts (Alg II/Math 3 CCR) ~37 pts (3-8), ~42 pts (HS) ~37 pts (3-8), ~42 pts (HS) ~14 pts (3-8), ~23 pts (HS) ~14 pts (3-8), ~23 pts (HS) 14 pts (3-8), 14 pts (HS) 4 pts (Alg II/Math 3 CCR) 14 pts (3-8), 14 pts (HS) 4 pts (Alg II/Math 3 CCR) 7-9 pts (3-6) 1 For the purposes of the PARCC Mathematics assessments, the Major Content in a grade/course is determined by that grade level’s Major Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. Note that tasks on PARCC assessments providing evidence for this claim will sometimes require the student to apply the knowledge, skills, and understandings from across several Major Clusters. 2 The Additional and Supporting Content in a grade/course is determined by that grade level’s Additional and Supporting Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. 3 For 3 – 8, Sub-Claim C includes only Major Content. For High School, Sub-Claim C includes Major, Additional and Supporting Content.

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37. 37 Implementing Standards and Incorporating Mathematical Practices Sandra M. Alberti AMTNJ October 24, 2013