September 20, 2012 William and Mary Math Day

1. Changes in the SOL and assessments: How will it impact you and your instruction? September 20, 2012William and Mary Math Day Michael Bolling, Acting Director, Office of Mathematics and Governor’s Schools Michael.Bolling@doe.virginia.gov

2. TEACHERS YOU REMEMBER Who made an impact on you? Why do you remember them?

3. What should be happening in classrooms? Interactions among students and the teacher Communication of mathematical ideas by students Students analyzing, interpreting, and developing processes for solving mathematical tasks Teachers facilitating learning by asking strategic questions and building on ideas that students bring to mathematical tasks Teachers facilitating students’ sharing of ideas, processes, and conclusions

4. We, as teachers, should be… Process Goals! Engaging students in the learning, providing relevant and rigorous activities and tasks Asking high-leverage questions – make students work harder than you Requiring students to communicate their thinking and listen carefully to them Making students justify their thinking Using multiple models

5. We, as teachers, should be… Using formative assessments to learn about the level of student understanding and reflect on your own teaching Collaborating on a deeper understanding of what needs to be taught and how it should and could be assessed

6. Process Goals for Students Students will become mathematical problem solvers that communicate mathematically; reason mathematically; make mathematical connections; and use mathematical representations to model and interpret practical situations

7. Changes to the Mathematics SOL Content Increase rigor through an emphasis on multistep problems and application Move content between grade levels/subjects to improve the vertical progression Remove content from grade levels/subjects Remove content repeated among grade levels Add new content   Reduce language that limits content

8. SOL, Curriculum Framework, and Assessments “The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.”

9. Changes to the SOL Assessments • Increased rigor reflective of the SOL • Comprehensive interpretation of SOL and Curriculum Framework (CF) • Testing blueprint changes • Previous reporting categories combined • Specific listing of SOL tested without a calculator included • Grade 3 SOL test only includes grade 3 content • Geometry SOL test increased by 5 questions to 50 operational items

10. Changes to the SOL Assessments • Addition of non-multiple choice items • Fill in the blank • Drag and drop • Hot-spot: Select one or more “spots” to respond to a test item, i.e. select answer option(s), shade region(s), place point(s) on a grid • Creation of graphs

11. NEW OLD Grade 3

12. NEW Grade 5

13. NEW Grade 6

14. OLD NEW Grade 7

15. Understanding the “increased rigor” of the new SOL comes through analysis of the SOL and the Curriculum Framework

16. Comparing the 2001 SOL to the 2009 SOL 2001 SOL 3.8 The student will solve problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation. 2009 SOL 3.4 The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping.

17. Comparing the 2001 SOL to the 2009 SOL • 2001 SOL 7.22 The student will • b) solve practical problems requiring the solution of a one-step linear equation. • 2009 SOL 7.14 The student will • b) solve practical problems requiring the solution of one- and two-step linear equations.

18. Comparing the 2001 SOL to the 2009 SOL • 2001 SOL 7.7 The student, given appropriate dimensions, will • b) apply perimeter and area formulas in practical situations. • 2009 SOL 6.10 The student will • c) solve practical problems involving area and perimeter • 2009 SOL 8.11 The student will • solve practical area and perimeter problems involving composite plane figures.

19. What makes a good mathematical task a good one?

20. Characteristics of ‘Rich’Mathematical Tasks High cognitive demand (Stein et. al, 1996; Boaler & Staples, 2008) Significant content(Heibert et. al, 1997) Require Justification or explanation (Boaler & Staples, in press) Make connections between two or more representations (Lesh, Post & Behr, 1988) Open-ended (Lotan, 2003; Borasi &Fonzi, 2002) Allow entry to students with a range of skills and abilities Multiple ways to show competence (Lotan, 2003)

21. Instruction, Assessment, and Backwards Design STEPS • Analyze an SOL and Curriculum Framework - What students should be able to do? • Brainstorm ways to assess the SOL • Develop an assessment • Brainstorm instructional strategies • Develop instructional resources/lesson plans

22. Instruction, Assessment, and Backwards Design STEPS • Analyze an SOL and Curriculum Framework - What students should be able to do? • Brainstorm ways to assess the SOL • Develop an assessment • Brainstorm instructional strategies • Develop instructional resources/lesson plans

23. SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers. • Create single-step and multistep problems involving the operations of addition, subtraction, multiplication, and division with and without remainders of whole numbers, using practical situations. • Solve single-step and multistep problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers, using paper and pencil, mental computation, and calculators in which – sums, differences, and products will not exceed five digits; – multipliers will not exceed two digits; – divisors will not exceed two digits; or – dividends will not exceed four digits.

24. Instruction, Assessment, and Backwards Design STEPS • Analyze an SOL and Curriculum Framework - What students should be able to do? • Brainstorm ways to assess the SOL • Develop an assessment • Brainstorm instructional strategies • Develop instructional resources/lesson plans

25. Modifying Assessments

26. VDOE Mathematics Instructional Resources Standards of Learning Curriculum Framework Testing blueprints SOL Practice Items and Tools Practice SOL Institutes (2009, 2010, 2011) Instructional Videos ESS Sample Lesson Plans Technical assistance documents Vocabulary resources

27. 2012 Mathematics SOL Institutes Focus on formative assessment Focus on process goals through “performance tasks” Provide modular online professional development for teachers in grade level/subject area teams (30-40 minute length per module)

28. No Pain, No Gain If you are more tired than the kids, it’s not because you are old Make kids estimate/predict and think before calculating Don’t ask questions that solicit one word answers Let kids struggle to make sense of the mathematics

29. Be the teacher that makes students remember you.

30. Questions? Michael.Bolling@doe.virginia.gov