Implementing Standards and Incorporating Mathematical Practices

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

2. Student Achievement Partners – Who We Are • 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. Our Principles – How we approach the work We 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. We 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. We 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. 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”

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!

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

7. Implications • What implications do the CCSS have on what we teach? • What implications do the CCSS have on how we teach? 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. Mathematics: 3 shifts • Focus: Focus strongly where the standards focus.

9. The shape of math in A+ countries 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 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

10. Traditional U.S. Approach

11. Focusing attention within Number and Operations

12. Priorities in Mathematics

13. Where to focus in mathematics – K example

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

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

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

19. Conceptual understanding of place value…?

20. Conceptual understanding of place value…?

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

22. Required Fluencies in K-6

23. 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. Don’t Bureaucratize

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

25. Am I Doing the Core?

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.

30. Core Action 3: Provide all students with opportunities to exhibit mathematical practices in connection with the content of the lesson. 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. 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. Am I doing the Core?

33. Am I doing the Core?

34. Evidence-Centered Design (ECD) ECD is a deliberate and systematic approach to assessment development that will help to establish the validityof the assessments, increase the comparability of year-to year results, and increase efficiencies/reduce costs.

35. 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). Claims Structure: Mathematics Sub-Claim B: Additional & Supporting Content2 with Connections to Practices The student solves problems involving the Additional and Supporting Content2 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. Sub-Claim A: Major Content1 with Connections to Practices The student solves problems involving the Major Content1 for her grade/course with connections to the Standards for Mathematical Practice. 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.  Total Exam Score Points: 82 (Grades 3-8), 97 or 107(HS) Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content3 (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. ~37 pts (3-8), ~42 pts (HS) ~14 pts (3-8), ~23 pts (HS) 14 pts (3-8), 14 pts (HS) 4 pts (Alg II/Math 3 CCR) 7-9 pts (3-6) 12 pts (3-8), 18 pts (HS) 6 pts (Alg II/Math 3 CCR) 1For 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.

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