Please sit with a mixture of grade levels.

1. Please sit with a mixture of grade levels.

2. Conditions for Learning • Choose to be present • Choose to be engaged • Be an active listener • Learning is a process not an event • Take 30 seconds each to share one important condition that supports your learning.

3. Objectives • Grounding in the College & Career Readiness Standards and the implications for you and your students.

4. The College & Career Readiness Standards (CCRS) are divided into the: • Standards for Mathematical Content which present a balanced combination of concept development, procedural fluency and application • Standards for Mathematical Practice which rely on processes and proficiencies.

5. College & Career Readiness Standards The Shifts

6. The Background of the College & Career Readiness Standards • Initiated by the National Governors Association (NGA) and Council of Chief State School Officers (CCSSO) with the following design principles: • Result in College and Career Readiness • Based on solid research and practice evidence • fewer, higher,and clearer

7. CCR Standards • What is your comfort and knowledge regarding the defined shifts of math standards? • Read the article “Making the Shifts.” Please use the following code to annotate as you read • Circle your agreements • Box your ponderings • Underline for more information

8. Debrief the Article At your table: • Do a whip around and share one coding you feel most strongly about. If your first choice has been shared, be ready to share an alternate.

9. CCR Standards Require Three Shifts in Mathematics • Focus: Focus strongly where the Standards focus. • Coherence: Thinkacross grades and linkto major topics within grades. • Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency,andapplication.

10. Focus on the Major Work of the Grade Two levels of focus: - What’s in/What’s out - The shape of the content that is in

11. 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).

12. Traditional U.S. Approach

13. Focusing Attention Within Number and Operations

14. Shift #1: Focus Strongly Where the Standards Focus • Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. • Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

15. Key Areas of Focus in Mathematics

16. Engaging with the shift: What do you think belongs in the major work of each grade?

17. Activity Debrief Was there anything that surprised or shocked you?

18. PARCC Content Model Framework • Major standards • K-2: 85% of instructional time • 3-5: 75% of instructional time • Supporting standards • Additional standards

19. Group Discussion Shift #1: Focus strongly where the Standards focus. • In your groups, discuss ways to respond to the following question, “Why focus? There’s so much math that students could be learning, why limit them to just a few things?”

20. What’s in/What’s out It is because of this level of focus that teachers will have the time to go deeper with the math that is most important. Compared to the typical state standards of the past, the College & Career Readiness Standards for math have fewer standards which are manageable and it is clear what is expected of the teachers and students at each grade level.

21. PARCC Example

22. BREAK – 10 MINUTES

23. Coherence Across and Within Grades It’s about math making sense. The power and elegance of math comes out through carefully laid progressions and connections within grades.

24. Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades • Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. • Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

25. Alignment in Context: Neighboring Grades and Progressions One of several staircases to algebra designed in the OA domain. 25

26. Looking for Coherence Across Grades • Coherence is an important design element of the standards. • “The Standards are not so much built from topics as they are woven out of progressions.” Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix

27. Coherence Card Activity • Activity: Place the standards of each color under the appropriate grade (K-8). • Determine a “theme” for each color. • No grade has two of the same color card. • Some “themes” that have only a few cards might represent consecutive grades and some may not. • Read each card in its entirety to help determine placement. • Do not check your Standards until you and your colleagues agree on the final product. • Discuss horizontal and vertical observations with your partners.

28. Check your answers • Use the key to check your answers. • What surprised you? What are your thoughts?

29. Group Discussion Shift #2: Coherence: Think across grades, link to major topics within grades • In your groups, discuss what coherence in the math curriculum means to you. Be sure to address both elements—coherence within the grade and coherence across grades. Cite specific examples.

30. Rigor: Illustrations of Conceptual Understanding, Fluency, and Application Here rigor does not mean “hard problems.” It’s a balance of three fundamental components that result in deep mathematical understanding. There must be variety in what students are asked to produce.

31. Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application • The CCRS-Mathrequire a balance of: • Solid conceptual understanding • Procedural skill and fluency • Application of skills in problem solving situations • Pursuit of all three requires equal intensity in time, activities, and resources.

32. Solid Conceptual Understanding • Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives • Students are able to see math as more than a set of mnemonics or discrete procedures • Conceptual understanding supports the other aspects of rigor (fluency and application)

33. Fluency • The standards require 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 they are more able to understand and manipulate more complex concepts

34. Required Fluencies in K-6

35. Application • Students can use appropriate concepts and procedures for application even when not prompted to do so. • Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. • Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

36. Coherence Card Activity: Rigor Focus • Activity: Identify the type of rigor within each theme for your grade band. • More than one strand of rigor may be assigned to each theme • Underline the word(s) that indicate the strand of rigor identified

37. Group Discussion Shift #3: Rigor: Expect fluency, deep understanding, and application • In your groups, discuss why the balance of the three strands of rigor are important to building student understanding of mathematics and what is balance.

38. Frequently Asked Questions • How can we assess fluency other than giving a timed test? • Is it really possible to assess conceptual understanding? What does it look like? • Are the Standards for Math all about application and meaningful tasks?