Beyond Adoption: Next Steps for the Common Core State Standards for Mathematics in Connecticut

1. Beyond Adoption:Next Steps for the Common Core State Standards for Mathematics in Connecticut Shelbi K. Cole, Ph.D. CAPT Mathematics Consultant CT State Department of Education Bureau of Student Assessment February 3, 2011

2. "The world is small now, and we're not just competing with students in our county or across the state. We are competing with the world," said Robert Kosicki, who graduated from a Georgia high school this year after transferring from Connecticut and having to repeat classes because the curriculum was so different. "This is a move away from the time when a student can be punished for the location of his home or the depth of his father's pockets." Excerpt from Fox News, Associated Press. (June 2, 2010) States join to establish 'Common Core' standards for high school graduation.

3. Focal Points for the Evening • What do the Standards for Mathematical Practice look like in practice? • How should we move forward with the content standards? • What’s the deal with assessment in Connecticut?

4. The CCSS are… • Reflective of core knowledge and skills that students need to be college- and career-ready; • Appropriate in terms of their level of clarity and specificity; • Comparable to expectations of other leading nations; • Informed by available research or evidence; • The result of processes that reflect best practices for standards development; • A solid starting point for adoption of cross-state common core standards; and • A sound basis for eventual development of standards-based assessments. (Findings of the 25 Member Validation Committee, April, 2010)

5. CCSS K-12 Standards for Mathematical Practice What do they look like in action?

6. CCSS K-12 Standards for Mathematical Practice 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.

7. Make sense of problems and persevere in solving them “He tried and he tried, but Spanky could not figure out a way to add three plus four. ☼ Why might 3 + 4 be a harder problem for Spanky to do? ☼ Figure out a way for Spanky to add 3 + 4 using just the six toes on his ‘hands.’” Excerpt from Cole, S. K. (in revision) Spanky the Three-toed Slothematician. Storrs, CT: Creative Learning Press.

8. Make sense of problems and persevere in solving them Help students make sense of problems. MP4. Model with mathematics. pERSERVERENCE CONNECTION TO CONTENT STANDARDS K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

9. Reason abstractly and quantitatively Concrete Abstract CC.7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. CC.8.G.5 Use informal arguments to establish facts about the angle sum of triangles.

10. Extending Students’ Abilities to Think Abstractly • What can we learn about other polygons using what we know about the angle sum of triangles? (180 x 5) – 360 = 900 – 360 = 540

11. So They Knew that a Circle had 360o… But did you ask them why?

12. Reason abstractly and quantitatively • 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.Illustrate and explain the calculation by using equations,rectangular arrays, and/or area models. • 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

13. Learning Task – Grade 5 CCSS • Divide 365/4 (by hand) using three different methods.

14. Method 1 of ∞

15. Method 2 of ∞

16. Method 3 of ∞

17. Method 4 of ∞

18. Reason abstractly and quantitatively 112/4 = 28 112/4 = 28 112/4 = 28 24/4 = 6 5/4 = 1 R1 365 = 112+112+112+24+5= 28+28+28+6+1+¼ =91¼ 4 4

19. Construct viable arguments and critique the reasoning of others.

20. Suggestions for Improving School-Level Implementation of Practice Standards • Use of flexible grouping for instruction • Questioning techniques (Classroom Discussions and using “talk moves”) • Task selection and “trajectory” mapping • Accountability – Teacher self-evaluations with administrator support • Ongoing professional development and collaboration • Collaborative lesson planning and purposeful incorporation of practice standards within the lesson framework

21. Content Standards

22. Common Core State Standards for MathematicsK-8 Mathematics Content

23. CCSS for MathematicsHigh School Conceptual Categories • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability

24. Implementation of Content Standards • Transition should occur between now and 2014 • Assess student prior knowledge to determine readiness for standards that have shifted from higher grades • Immediate transition for grades K-2 is feasible since these grades do not have the same accountability mandates • Curriculum leaders & teachers should be using crosswalk documents and other curriculum documents to examine alignment with CCSS • Identify both major and minor shifts • Shift emphases – decide that teachers will pay more attention to x and yin 2011-2012 and less attention to z

25. Grade Level Comparisons

26. What Impact Will the CCSS Have on Assessment?

27. Looking to 2015… • The current generations of CMT & CAPT will remain in effect through 2014 • In 2015, there will be a new assessment system for the content areas English Language Arts and Mathematics based on the Common Core State Standards

28. Smarter Balanced Assessment Consortium (SBAC)

29. Overview of SBAC • On Sept. 2, 2010, the SBAC was awarded a four-year, $176 million Race to the Top assessment grant by the US Department of Education (USDE) to develop a student assessment system aligned to a common core of academic standards. • SBAC will create state-of-the-art adaptive online exams, using “open source” technology. • The online system will provide accurate assessment information to teachers and others on the progress of all students, including those with disabilities, English language learners and low- and high-performing students.

30. Assessment System Components • The system will include: • the required summative exams, which include performance tasks in addition to the online adaptive component; • optional formative, or benchmark, exams; and • a variety of tools, processes and practices that teachers may use in planning and implementing informal, ongoing assessment. This will assist teachers in understanding what students are and are not learning on a daily basis so they can adjust instruction accordingly.

31. Summative Assessments Under SBAC • Mandatory comprehensive accountability measures that include computer adaptive assessments and performance tasks, administered in the last 12 weeks of the school year in grades 3–8 and in high school for English Language Arts (ELA) and mathematics; • Designed to provide valid, reliable, and fair measures of students’ progress toward the knowledge and skills required to be college and career ready; • Capitalize on strengths of computer adaptive testing, i.e., efficient and precise measurement across the full range of achievement and quick turnaround of results; • Produce composite content area scores, based on the computer-adaptive items and performance tasks.

32. Interim Assessments • Optional comprehensive and content-cluster measures that include computer adaptive assessments and performance tasks, administered at locally determined intervals; • Item sets that provide actionable information about student progress; • The source for interpretive guides that use released items and tasks; • Grounded in cognitive development theory about how learning progresses across grades; • Involve a large teacher role in developing and scoring constructed response items and performance tasks; • Afford teachers and administrators the flexibility to: • select item sets that provide deep, focused measurement of specific content clusters embedded in the CCSS; • administer these assessments at strategic points in the instructional year; • use results to better understand students’ strengths and limitations in relation to the standards; • support state-level accountability systems using end-of-course assessments.

33. Formative Tools and Processes • Provides resources for teachers on how to collect and use information about student success in acquisition of the CCSS; • Can be used by teachers and students to diagnose a student’s learning needs, check for misconceptions, and/or to provide evidence of progress toward learning goals.

34. “The whole is greater than the sum of its parts.” -Aristotle >

35. Questions? Shelbi Cole shelbi.cole@ct.gov (860) 713-6878