Deeper Study of the Common Core State Standards for Mathematics

1. Deeper Study of the Common Core State Standards for Mathematics Jennifer Lawler

2. Name, position, school Something you already know about the CCSS for Mathematics? Something you hope to learn more about in terms of CCSS for Mathematics? Who’s In the Room?

3. Why are we here?

4. Why are we here?

5. Why are we here?

6. Day One – Participants will: Know the history of the CCSSM Understand the structure of the document Understand the instructional shifts the standards require Understand the CCSS as second order change Day Two Understand the importance of the Standards for Mathematical Practice Day Three Understand the progression of skills within the Standards and how key fluencies create a coherent and focused curriculum Workshop Goals

7. Please use the sticky notes on your tables to write down any questions you have. Place them in the “Parking Lot” and we will try to address them. Parking Lot

8. 1989 – NCTM Curriculum and Evaluation Standards for School Mathematics 2000 – NCTM Principles and Standards for School Mathematics 2010 – Common Core State Standards for School Mathematics A Brief History of Mathematics Standards

10. Let’s Dive In! Introduction Standards-Setting Criteria Standards-Setting Considerations Application of CCSS for ELLs Application to Students with Disabilities Mathematics Standards Standards for Mathematical Practice Contents Standards: K-8; HS Domains Appendix A: Model Pathways for High School Courses

11. CCSS Scavenger Hunt

12. “These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.” Introduction National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core Standards for Mathematics. Washington, DC: Authors. Retrieved from www.corestandards.org/Math.

13. 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. The Standards for Mathematical Practice

14. Standardsdefine what students should understand and be able to do. Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. The Standards for Mathematical Content

15. How to read the grade level standards (K-8)

16. The high school standards are listed in conceptual categories: • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability High School Standards

17. Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (*). Appendix A provides model course pathways for high school standards High School Standards

18. The Structure is the Standardsby Phil Daro, Bill McCallum, Jason Zimba Once you have read the article, please answer the questions below with an elbow partner. • How do the authors describe the standards? Provide evidence in the text. • How were the Common Core State Standards developed? Point to evidence in the text. • Why did they use the word “structure” in the title? Discuss with your elbow partner. Daro, P., McCallum, B., & Zimba, J. (2012, February 16). The Structure is the      Standards [Web log post]. Retrieved from http://commoncoretools.me/2012/02/      16/the-structure-is-the-standards/ 20

19. “Implementation of the mathematics standards requires much more than new names for old ways of teaching mathematics. Many well-intending educators are spending a great deal of time doing alignment studies to figure out which grade levels various topics have moved to. Quality implementation means more than shuffling topics around; it requires an understanding of three core shifts.” Key Shifts for the CCSSM Alberti, Sandra. "Making the Shifts." Educational LeadershipDec.2012-Jan. 2013: 24-27. Print.

21. Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? Reflection

22. The Standards call for a greater focus in mathematics. Rather than racing to cover topics in today’s mile-wide, inch-deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent in the math classroom. They focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. Shift 1: Focus

24. Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? Reflection

25. Thinking across grades: The Standards are designed around coherent progressions from grade to grade. Principals and teachers carefully connect the learning across grades so that students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. Linking to major topics: Instead of allowing additional or supporting topics to detract from the focus of the grade, these topics can serve the grade level focus. For example, instead of data displays as an end in themselves, they support grade-level word problems. Shift 2: Coherence

27. Read the “Shift” What does the “Shift” mean to you? What does it look like in mathematics classrooms (provide specific examples)? Reflection

28. Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that students have access to more complex concepts and procedures. Application: The Standards call for students to use math flexibly for applications. Teachers provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content. Shift 3: Rigor

29. “But the shift to Common Core State Standards is an example of second order change. It requires a shift in the way we think about the nature of teaching and learning. This shift asks us to reexamine the foundations of traditional teaching methods. Rather than asking students to memorize by rote, to accumulate facts and figures, Common Core calls for nuanced understanding, applicable to real-world problems. Common Core asks students to analyze, to generate and test hypotheses. It asks students to think like mathematicians rather than just do math. To think like writers rather than just churn out five-paragraph essays. To use complex cognitive skills to analyze the complex problems they face as 21st century citizens.” The Common Core Shift "Common Core State Standards and Second Order Change: What Every Adminstrator Should Know." Web log post. Marzano Center Blog. Learning Sciences Marzano Center, 30 Oct. 2012. Web. 18 Dec. 2012.

30. “First-Order” Change • An extension of past knowledge • Implemented with existing knowledge and skills • Within existing paradigms • Consistent with prevailing values and norms • Incremental *Marzano, Waters, McNulty, 2005

31. “Second-Order” Change • A break with the past • Outside of existing paradigms • Conflicts with prevailing values and norms • Complex • Requires new knowledge and skills to implement Marzano, Waters, McNulty, 2005

32. First Order Second Order When stakeholders see the change as: • Consistent with existing values and norms • Advantageous for stakeholders • Readily implement-able with existing knowledge and resources When stakeholders: • Are unclear about how it will make things better for them • Must master new knowledge, practices, or approaches to implement the change • Feel the change conflicts with prevailing personal values and organizational norms

33. Knowing what to do Knowing how to do it Knowing when to do it Knowing why to do it Leading the Change Huffman, Karen. "The 21st Century Leadership Challenge: Leading Second Order Change." Lecture. West Virgina Department of Education Principal's Institute. West Virginia Department of Education. West Virginia Department of Education. Web. 27 Dec. 2012.

34. Initiators Start the requested change immediately 3% - 10% of the community Early Adopters Realize the benefits of the change and begin adopting Not influenced by actions of initiators 5-20% of the community Later Adopters Strongly influenced by earlier adopters’ actions 75-80% of the community Resisters How Adults Change Hull, Ted H., Ruth Harbin. Miles, and Don Balka. The Common Core Mathematics Standards: Transforming Practice through Team Leadership. Thousand Oaks, CA: Corwin, 2012. Print.

35. Changing Paradigms

36. Changing Paradigms

37. Who should get in the car first?

38. Whom do you ask if you have questions concerning: School policy Classroom management School activities or schedules Instructional strategies Course (or grade-level) content Who are your Early Adopters?

39. Compare “The Unadopted Plan” and “Reaching the Earlier Adopters” In each scenario, what was occurring from the principal’s point of view? What was occurring from the teachers’ point of view? Two Scenarios for Change

40. Renewal Integration Refinement Routine Mechanical Preparation Orientation Nonuse Concern Based Adoption Model: Levels of Use

41. Five Fundamental Leadership Areas Collaboration Instruction Content Assessment Intervention A Framework for Second Order Change Kanold, Timothy D., and Matthew R. Larson. Common Core Mathematics in a PLC at Work. Bloomington, IN: Solution Tree, 2012. Print.

42. For each of the five areas: Read the description on pages 3-5, then assess your school’s - Current level of Implementation - Priority score - Opportunity score Where are we?

43. Leading High Performing Collaborative Teams PLC Leaders Guide, Chapter 1 Everyone: Opening paragraphs, p 7 & “Collaborative Protocols”, p 22-23 Group 1: “The Professional Development Paradigm Shift”, p 7-9 Group 2: “Professional Learning Communities, p 9-11 Group 3: “Teacher Collaboration Versus Cooperation or Coordination”, p 11-13 Group 4: “High Leverage Professional Development for the Common Core”, p 21-22

44. “Changing people’s behavior is one of the most difficult aspects of leadership. However, there is much that we know about changing behaviors: people cannot do what they cannot envision; people will not do what they do not believe is possible; people will not implement what they do not understand; people are unlikely to do well what they don’t practice; people who practice without feedback don’t progress efficiently; and people who work without collaboration are unlikely to sustain their effort.” Today’s final thought… Leinwand, Steve. Sensible Mathematics: A Guide for School Leaders in the Era of Common Core State Standards. Portsmouth, NH: Heinemann, 2012. Print.