1. Process and Content Standards in Mathematics: Thoughts and Reflections V 2 CTM - Valley of Virginia Council of Teachers of Mathematics November 13, 2012 Michael Bolling, Acting Director, Office of Mathematics and Governor’s Schools

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3. Curve of Change Implementation 3 Past Practice Denial Anger Fear Depression Understanding Acceptance Progress

4. VDOE Professional Development Focus 2009 Specific SOL changes (content) 2010 Vertical articulation of the SOL and areas of greatest challenge (content and pedagogy) 2011 Process goals (standards) in mathematics 2012 Using formative assessments (performance tasks) to inform instruction 4

5. “The content of the mathematics standards is intended to support the five goals for students” - 2009 Mathematics Standards of Learning 5

6. Five goals…for students to become mathematical problem solvers that communicate mathematically; reason mathematically; make mathematical connections; and use mathematical representations to model and interpret practical situations 6

7. Virginia’s Process Goals for Students Mathematical Problem Solving Mathematical Communication Mathematical Reasoning Mathematical Connections Mathematical Representations 7

8. Direct Instruction Modeling Cooperative Learning Kinesthetic Learning Graphic Organizers Independent Work Scaffolded Instruction Differentiation Problem Solving Communication Reasoning Connections Multiple Representations

9. 9 Store AStore BStore C Buy 2, get 3 rd one free2 packs for $7.00Buy 1, get one ½ price A recipe requires ½ cup of butter to make a dozen cookies. If you have 3 ¾ cups of butter, do you have enough to make at least 4 cookies for each of the 24 students in your math class? Explain why or why not. Show at least two different ways to solve the problem. You compare the price of butter from different store ads. If the original price of butter for a 1 pound pack is $3.99 at all three stores, explain which store has the best price to make your cookies the most affordable:

10. Standards of Learning 6.4 The student will demonstrate multiple representations of multiplication and division of fractions. 6.2 The student will a)investigate and describe fractions, decimals and percents as ratios; b)identify a given fraction, decimal or percent from a representation; c)demonstrate equivalent relationships among fractions, decimals, and percents; and compare and order fractions, decimals, and percents. 10

11. Vertical Articulation Documents

12. Assessment Types Formal – Formative (prior to or during instruction) – Summative (following instruction) Informal – Listening – Questioning – Observing 12

13. Formative Assessment ‘Assessment FOR learning’ Checking in on understanding and on the formation of learning Diagnostic in nature – should lead to changes in instruction Class tasks, homework, quizzes, benchmark tests Includes a lot of student feedback

14. Summative Assessment ‘Assessment OF learning’ Typically provides a level of student performance (grade) Tests, projects, simulation tests Less student feedback

15. Format of Assessment Items Multiple choice Open response – Short response Fill in the blank Solve, simplify Explain why/justify – Open-ended doesn’t have a predefined answer synthesizes multiple concepts

16. Instruction, Assessment, and Backwards Design 1.What are the content objectives that students should master? 2.How will we assess the content? 3.What instructional experiences will we provide that will assist ALL students to access and master the content? 16

17. Purpose of assessment Improve student learning Checking for student understanding, growth, and progress Determining common misunderstandings Determining common errors Informing instructional and assessment decisions (currently and in the future) 17

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19. Instructional and Assessment Resources Standards of Learning & Curriculum Framework Testing blueprints SOL Practice Items and Tools Practice and Guides SOL Practice Items SOL Institutes (2009, 2010, 2011, 2012 coming soon) SOL Institutes Instructional Videos ESS Sample Lesson Plans Technical assistance documents A.9 AII.11A.9AII.11 Vocabulary resources Statewide Analysis presentations 19

20. We, as teachers, should be… 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 20 Process Goals!

21. We, as teachers, should be… Using formative assessments to learn about the level of student understanding to reflect on and change your own teaching Collaborating to develop a deeper understanding of what needs to be taught and how it should and could be assessed 21

22. Be the teacher that makes a child remember you. 22