Linking Standards, Assessments, and Instruction in Mathematics

1. Linking Standards, Assessments, and Instruction in Mathematics Presented by Gabriela Orozco Gonzalez April 5, 2014 Stockton Common Core Seminar

2. Welcome • Educator, I have taught K-6th Grade, currently teach 1st & 2nd Grade Combination class • Language Arts Performance Task Writer & Mathematics Item Reviewer for the Smarter Balanced Assessment Consortium • CTA Teacher Leadership Cohort and Professional Learning Trainer • NEA Teacher Ambassador for SBAC Representing California Presentation Materials on my blog: Commoncorecafe.blogspot.com

3. Learning Targets Gain an awareness of the content and structure of the Common Core State Standards for Mathematics Understand the meaning of the Mathematical Practices in the CCSSM and apply the practices to your current classroom instruction Become familiar with a performance task and task planner

4. A Balanced Assessment System Summative assessments Benchmarked to college and career readiness Teachers and schools have information and tools they need to improve teaching and learning Common Core State Standards specify K - 12 expectations for college and career readiness All students leave high school college -and career- ready Teacher resources for formative assessment practices to improve instruction Interim assessments Flexible, open, used for actionable feedback

5. Six Item Types • Selected Response • Short Constructed Response • Extended Constructed Response • Performance Tasks • Technology-Enabled • Technology-Enhanced Focus for today

6. The Assessment Challenge . . . to here? How do we get from here . . . Common Core State Standards specify K-12 expectations for college and career readiness All studentsleave high school college- and career-ready . . . and what can an assessment system do to help?

7. Smarter Balanced Assessments are: Standards based NOT textbook based Your text book is an AWESOME resource/ reference book.

9. Standards Based Instruction • Standards-based education is a process for planning, delivering, monitoring and improving academic programs in which clearly defined academic content standards provide the basis for content in instruction and assessment. • Standards help ensure students learn what is important, rather than allowing textbooks to dictate classroom practice. • Student learning is the focus - aiming for a high and deep level of student understanding that goes beyond traditional textbook-based or lesson-based instruction.

10. Teachers guide instruction based on standards “The standards come alive when teachers study student work, collaborate with other teachers to improve their understanding of subjects and students’ thinking, and develop new approaches to teaching that are relevant and useful for them and their students.” - Linda Darling-Hammond, 1997

11. Curriculum Curriculum Mappingis a long-range plan captured in a graphic organizer that represents a collection of Standards-based units. It is informed by the benchmarks and curriculum objective, student data, including an analyses of student work and projected assessment timelines. It is a document that should be modified based on student needs and reviewed and revised yearly.

12. CCSSM Planning and Implementation • Planning meetings with grade level representatives: • Examine Standards, then Prioritize • Pacing Overviews • Assessment Calendar • Unit Overviews and/or Unit Plans • Create Assessments • Revise Assessments

13. Design and Organization Standards for Mathematical Practice • Carry across all grade levels • Describe habits of mind of a mathematically expert student Standards for Mathematical Content • K-8 standards presented by grade level • Domains: • Number and Operations • Counting and Cardinality • Operations and Algebraic Thinking • Number and Operations in Base Ten • Number and Operations—Fractions • Measurement and Data • Geometry

14. Design and Organization • Content standards define what students should understand and be able to do • Clusters are groups of related standards • Domains are larger groups that progress across grades

15. Focal Points & Critical Areas Focal Points Critical Area

16. Prioritizing the CCSS Standards

17. Webb's Depth of Knowledge (DOK) Bloom's Taxonomy vs. Norman Webb's Depth of Knowledge • The Common Core Standards are the cornerstones of the Smarter Balanced assessments, Webb’s Depth of Knowledge (scale of cognitive demand) and Blooms Revised Taxonomy (levels of intellectual ability) are the framework and the structures that will be used to evaluate students. • Depth of knowledge, and complexity of knowledge is the heart of the more rigorous assessments being implemented in 2014. They share many ideas and concepts yet are different in level of cognitive demand, level of difficulty, complexity of verbs vs. depth of thinking required, and the scale of cognitive demand.

18. During the planning process, refer to the DOK Levels

20. 3rd Grade Big Ideas 2-D Shapes Fractions Area Multiplication Division

21. Understanding Assessments • FORMATIVE: checking on learning as students progress • SUMMATIVE: checking on learning at the end of the learning experience • “When the cook tastes the soup, that’s formative; when the guests taste the soup, that’s summative.” (Stake, 2005)

22. Challenges STUDENT TEACHER • Curriculum • Collection of Resources • Assessments • Professional Learning • Collaboration • Explain/Justify • Problem Solving

23. ______ ______

24. Performance Task Planner

25. Performance Task Planner (second Page)

26. Communication, Engagement, and Learning

27. Check your work

29. CCSSM and Real Life Application

30. Student Problem Solving Rubric

31. Students need to engage with • Grade-appropriate materials for exposure to structures, content, vocabulary; • Instructional-level materials that allow them to progress; • Easy materials that allow them to practice. • If familiar/interesting, material can be more challenging. – More at K-12 Teachers: Building Comprehension in the Common Core

32. Timing matters • Greater scaffolding is provided at the beginning of tasks. • Scaffolding supports an increasing level of complexity. • Include a plan for removing the scaffolding.

33. Advice • Time for Planning • Ongoing Professional Development • Follow-up Coaching • Patience and Understanding

34. CCSSM Resources Books Magazines Technology Resources

35. DPI Wiki http://www.ncdpi.wikispaces.net/ http://maccss.ncdpi.wikispaces.net/home

36. CCSSM Resources Common Core State Standards Live Binder: http://www.livebinders.com/edit?id=133724 • Resources: • 21st Century Skills • Common Core State Standards & Essential Standards • Crosswalks • Unpacking Documents • Investigations & CCSSM • Websites

37. Math Resources Aegom Interactive Smartboard Lessons www.aegom.com/

38. Video Resources • Annenberg Media Videos & Resources • http://www.learner.org/resources/ browse. html?discipline=6 • Discovery Education/United Streaming • http://streaming.discoveryeducation.com/

39. Math Resources • National Council of Teachers of Mathematics (NCTM) www.nctm.org http://illuminations.nctm.org/ • Teaching Children Mathematics Magazines

40. Common Core Resources • Tools for the Common Core Standards • http://commoncoretools.wordpress.com/ • Illustrative Mathematics (CCSS Tools & Resources) • http://illustrativemathematics.org/standards • Common Core Wiki (by Drew Polly) • http://elemath.pbworks.com/w/page/30621644/common-core • National Council of Teachers of Mathematics • www.nctm.org • www.nctm.org/standards/mathcommoncore/