West Virginia’s Adoption of the Common Core State Standards for High School Mathematics

1. West Virginia’s Adoptionof the Common Core State Standards forHigh School Mathematics Lou Maynus, NBCT Mathematics Coordinator Office of Instruction, WVDE

2. Adoption of the Standards • May 2010 WVBE Adopted the Common Core State Standards for Mathematics • August 2010 – April 2011 WVDE placement of the standards into the WV framework including the study and organization of the High School Standards into courses

3. Considerations • WV’s performance on the 12th grade NAEP • Current ACT scores • Performance on WESTEST 2

4. Benefits for States and Districts • Allows collaborative professional development to be based on best practices • Allows the development of common assessments and other tools • Enables comparison of policies and achievement across states and districts • Creates potential for collaborative groups to get more mileage from: • Curriculum development, assessment, and professional development

5. Characteristics • Fewer and more rigorous. The goal was increased clarity. • Aligned with college and career expectations – prepare all students for success on graduating from high school. • Internationally benchmarked, so that all students are prepared for succeeding in our global economy and society. • Includes rigorous content and application of higher-order skills. • Builds on strengths and lessons of current state standards. • Research based.

6. Intent of the Common Core • The same goals for all students • Coherence • Focus • Rigor

7. The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed by research on children’s cognitive development and by logical structure of mathematics.

8. Coherence • Articulated progressions of topics and performances that are developmental and connected to other progressions • Conceptual understanding and procedural skills stressed equally

9. Focus • Key ideas, understandings, and skills are identified • Deep learning of concepts is emphasized • That is, adequate time is devoted to a topic and learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

10. CCSS 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.

11. The CCSSO math standards (including the high school standards organized by conceptual category – not by courses) were provided to us in one document is found at http://www.corestandards.org/Math • This is how they are given to the states.

12. Domain Format of High School Cluster Standard

13. Regular Standard Modeling STEM

14. Conceptual Categories • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability

15. Common Core - Domain • Overarching “big ideas” that connect topics across the grades • Descriptions of the mathematical content to be learned, elaborated through clusters and standards

16. Common Core - Clusters • May appear in multiple grade levels with increasing developmental standards as the grade levels progress • Indicate WHAT students should know and be able to do at each grade level • Reflect both mathematical understandings and skills, which are equally important

17. Common Core - Standards Progressions of increasing complexity from grade to grade • In high school, this may occur over the course of one year or through several years

18. High School Pathways The CCSS Model Pathways are NOT required. The two sequences are examples, not mandates • Two models that organize the CCSS into coherent, rigorous courses • Four years of mathematics: • One course in each of the first two years • Followed by two options for year 3 and a variety of relevant courses for year 4 • Course descriptions • Define what is covered in a course • Are not prescriptions for the curriculum or pedagogy

19. Appendix A High School Pathways This is a link to Appendix A with four model pathways http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf • Traditional • Integrated • Compacted Traditional • Compacted Integrated

20. High School Pathways • Pathway A: Consists of two algebra courses and a geometry course, with some data, probability, and statistics infused throughout each (traditional) • Pathway B: Typically seen internationally, consisting of a sequence of 3 courses, each of which treats aspects of algebra; geometry; and data, probability, and statistics.

21. Do a quick comparison of the critical areas for the Integrated Math I (page 77)  and the Algebra I (page 69). http://www.projectaero.org/aero_standards/mathstandards/2011AEROHighSchoolMathStandards.pdf Our teacher’s review and comparison found the Math I course provides more time to develop a strong foundation in algebra and functions.  Math I is more rigorous that our old Algebra I and less rigorous than the new Algebra I course.  Our teachers found there are strong interrelationships in algebra and functions and algebra and geometry that the Math I pathway better addresses.

22. What else? • Real life applications of mathematics do not artificially separate problems into discrete topics of algebra, geometry, or statistics. • If the goal of high school mathematics is to boost students’ problem solving ability • Life after high school • Nearly every country in the world

23. Interrelationships • Algebra and Functions • Expressions can define functions • Determining the output of a function can involve evaluating an expression • Algebra and Geometry • Algebraically describing geometric shapes • Proving geometric theorems algebraically

25. Why did WV Choose an Integrated Model for High School Mathematics? The major benefit of the international pathway is a more seamless trajectory of mathematics learning, eliminating learning gaps by making connections within mathematics topics over the course of three years of high school.  Some advisory bodies have referred to the international pathway as a “world-class” curriculum, pointing to its use in high performing countries.  The West Virginia Board of Education adopted the Integrated pathway for High School mathematics after careful deliberation regarding the potential benefits and possible challenges inherent in the adoption of any pathway.