Michael Bolling, Director of Mathematics and Governor’s Schools michael.bolling@doe.virginia

1. Mathematics Standards of Learning Instruction and AssessmentRegion I and II Teachers – Franklin City HSAugust 28, 2013 Michael Bolling, Director of Mathematics and Governor’s Schools michael.bolling@doe.virginia.gov

2. What would you like to discuss today?

3. Instruction and Assessment

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

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

6. Level of Cognitive Demand in Activities

7. Level of Cognitive Demand in Activities High Level of Cognitive Demand Med Med Low

8. Level of Cognitive Demand in Activities Write a real-world problem using this expression. Is the value of this expression more or less than 1? How do you know? Level of Cognitive Demand Simplify.

9. So how could we increase cognitive demand ? The bill at a store is $150. A 10% coupon is applied. What is the amount of the discount? Write the equation of the line that passes through the points (2,3) and (4, 8).

10. Collaboration is Key

11. Effective Strategies for Success • Instructional Support • Curriculum resources • links to SOL, CF, and local resources • Professional development • content, pedagogy, process • Administrative leadership and support • frequent observations and instructional involvement

12. Effective Strategies for Success • Collaboration on Instruction and Assessment • analysis and discussion about student objectives and instructional/assessment strategies • common assessments • analysis of student work and performance data

13. School-level Administrators When observing, notice who is doing the most thinking – teachers or students Facilitate common planning periods for teachers (general and special education) of the same subjects (when possible) Provide guidelines and expectations for planning (learning community) meetings and attend all of them

14. Learning Community Meetings Long-term and short-term planning/pacing Instruction – What’s being taught? Instruction – How’s it being taught? Creation/review of common assessment items Review/analysis of data/student performance Review and analysis of student work

15. School-level Administrators • Reach out within your division/region • Bring teachers together for collaboration • Facilitate the development of guidelines for their time • Analysis of the SOL and Curriculum Framework • Analysis of student performance through use of the school-and/or division-level SPBQ • Development of common assessments • Discussion of instructional strategies, resources, and pacing

16. Increased Rigor in Daily Instruction and Assessment Consider the level of cognitive demand that instructional activities and assessments require Consider the engagement level of the activity Reflect on the kinds of questions that you are asking students Let students struggle with the mathematics

17. Effective Questioning When Kids Struggle Ask students what they know Ask about their approach to solve Ask them where they ran into trouble Ask them why Restate what they’ve said Ask them to reflect on possible other routes

18. Effective Questioning and Discourse Ask students to justify and explain their thinking Have students share their problem solving approaches with others Ask them to explain others’ approaches in their own words Ask them to evaluate others’ approaches (error analysis) Ask them “what if” questions

19. Reflection

20. Virginia Department of Education Standards of Learning Curriculum Framework Testing blueprints SOL Institutes (2009, 2010, 2011, 2012) Instructional Videos ESS Sample Lesson Plans Technical assistance documents SOL Practice Items and Tools Practice Vocabulary resources

21. SOL Institutes – FOCUS

22. 2013 Mathematics SOL Institutes Analyzing existing assessments to evaluate alignment with the SOL and Curriculum Framework and make improvements to alignment and level of rigor Modifying existing mathematical resources to promote problem solving and critical thinking Continuing the emphasis on process goals for students

23. Professional Development

26. Mathematics Instructional Resources

27. Mathematics Instructional Resources

28. Mathematics Instructional Resources

29. ESS Sample Lesson Plans

30. ESS Sample Lesson Plans

31. Instructional Videos

32. Algebraic Properties

33. Mathematics Vocabulary Word Wall Cards

34. Practice SOL Items Practice SOL Items: Available for grades 3-8, Algebra I, Geometry, and Algebra II Grades 3-8 Practice Tool:  Practice measuring with the ruler, measuring angles with the protractor, using the four function calculator, and provides a grid for open practice with tools EOC Practice Tool: Practice with geometric constructions and provides a grid for open practice with tools

35. Practice SOL Items • It is essential that students have experiences with the Practice SOL Items prior to testing. • Teacher use of the Practice Item Guides with students isSTRONGLY recommended. • Practice Item Guides provide: • Guided practice with tools • Information specific to TEI functionality • Information on item format

36. Current Projects (some of them) • Mathematics Vocabulary Word Wall Cards • Algebra, Spring ‘14 • FAQ and technical assistance • Models for algebraic properties • Work with divisions through OSI • Algebra Readiness Diagnostic Test (ARDT)

37. Frequently Asked Questions Based on Frequently Asked Questions from teachers and school divisions Provides additional information intended to clarify the intent of standards and Curriculum Framework Bullets

38. Test Development 3R4 x<3 ABC 1/2 • TEI: Fill-in-the-Blank Items Frequently asked question: Will a student be marked wrong for not spelling a word correctly in fill-in-the-blank items? Currently, there are no items that require students to spell a word to correctly answer a question. Students do not need to enter words. May require letters, numbers, and/or characters.

39. Test Development • TEI: Fill-in-the-Blank Items Frequently asked question: Do students have to give an exact answer for FIB items that require them to use a ruler or protractor? There is a range of acceptable answers for certain items, depending on the type of measure required.

40. Test Development • TEI: Fill-in-the-Blank Items Frequently asked question: Can students enter a decimal equivalent when asked specifically for a fraction? Acceptable character keys are controlled for student responses. In this case, the decimal would not be an allowable character.

41. “TEI-Like” Items in the Classroom TEI reflect many classroom activities and questions. TEI Item Types: • Drag and Drop • Hot spot • Fill-in-the-blank • Bar Graph/Histogram

42. “TEI-Like” Items in the Classroom Drag and Drop: • Use of a paper cut out, index card, sticky note, that can be manipulated to answer a question (sort and categorize, order, label, pull from word bank, etc.) • Any matching item or activity

43. “TEI-Like” Items in the Classroom Drag and Drop SOL 1.7b The student will determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less. Use of matching

44. “TEI-Like” Items in the Classroom Drag and Drop SOL 4.2a The student will compare and order fractions and mixed numbers.

45. “TEI-Like” Items in the Classroom Drag and Drop SOL A.2c Factor completely first-and second-degree binomials and trinomials in one or two variables.

46. “TEI-Like” Items in the Classroom Drag and Drop examples: • Complete sentences or phrases with text • Match a figure to a description (ray, line, line segment, point) • Create change with money • Complete the pattern with a missing figure • Justify each step of solving an equation • Place justifications into a two-column proof • Match properties to equations • Match equations to one solution, no solution, infinite solution • Match statement to the converse, inverse and contrapositive

47. “TEI-Like” Items in the Classroom Hot Spot: • “Circle all of these that are ---” • “Circle the two of these that show---” • “Plot the points that---” • “Shade the part of the model that---”

48. “TEI-Like” Items in the Classroom Hot Spot SOL 1.7b The student will determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.

49. “TEI-Like” Items in the Classroom Hot Spot SOL 4.2a The student will compare and order fractions and mixed numbers

50. “TEI-Like” Items in the Classroom Hot Spot SOL 7.3b The student will add, subtract, multiply, and divide integers.