Increased Rigor in the 2009 Mathematics Standards of Learning January 2013

1. Increased Rigor in the 2009 Mathematics Standards of LearningJanuary 2013 Michael Bolling, Director Office of Mathematics and Governor’s Schools

2. What is “Rigor”? • Is it: • Assigning more mathematics problems? • Issuing zeroes for incomplete work? • Weeding out students from honors classes? • Or rather: • Providing challenging content through effective instructional approaches that lead to the development of cognitive strategies that students can use when they do not know what to do next.

3. What is “Rigor”? • What is “Rigor”? • Increased Rigor of the 2009 Mathematics Standards of Learning • New Assessments that Reflect the Increased Rigor of the Standards • Instructional Rigor

4. What is “Rigor”? • Rigor requires active participation from both teachers and students. • Rigor asks students to use content to solve complex problems and to develop strategies that can be applied to other situations, make connections across content areas, and ultimately draw conclusions and create solutions on their own.

5. What is “Rigor”? • Rigor requires students to not only learn the foundational knowledge of the mathematics, but to apply it to real-world situations. • Rigor requires teachers to create a learning environment where students use their knowledge to create meaning for a broader purpose. • Rigor requires students learn how to develop alternative strategies if their first attempts are unsuccessful.

6. Increased Rigor in the 2009 Mathematics Standards of Learning • Explicit content changes • Movement of content between and among grade levels • Increased content expectations • Content additions

7. Increased Rigor in the 2009 Mathematics Standards of Learning • Explicit content changes • Movement of content between and among grade levels • Increased content expectations • Content additions

8. Explicit Content Changes • 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.

9. Explicit Content Changes • 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.

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

11. Explicit Content Changes • 2001 SOL A.1 The student will solve multistep linear equations and inequalities in one variable … • 2009 SOL A.5 The student will solve multistep linear inequalities in two variables …

12. Increased Rigor in the 2009 Mathematics Standards of Learning • Explicit content changes • Movement of content between and among grade levels • Increased content expectations • Content additions

13. Content Additions • Properties in elementary grades • Describing mean as “fair share” in grade 5 • Describing mean as “balance point” in grade 6 • Modeling one-step linear equations in grade 5 • Modeling multiplication and division with fractions in grade 6 • Percent increase/decrease in grade 8 These examples do not provide a comprehensive listing of content additions.

14. Content Additions • Standard deviation, mean absolute deviation, and z-scores in Algebra I • Equations of circles in Geometry • Normal distributions and the Standard Normal curve in Algebra II • Permutations and combinations in Algebra II These examples do not provide a comprehensive listing of content additions.

15. Increased Rigor in the 2009 Mathematics Standards of Learning Assessments • Increased rigor reflective of the SOL • Comprehensive interpretation of SOL and Curriculum Framework • Additional ways for students to demonstrate understanding

16. Increased Rigor in the 2009 Mathematics Standards of Learning Assessments • Increased rigor reflective of the SOL • Comprehensive interpretation of SOL and Curriculum Framework • Additional ways for students to demonstrate understanding

17. Increased Rigor Reflected in SOL Assessments OLD Grade 3

18. Increased Rigor Reflected in SOL Assessments NEW Grade 3

19. Increased Rigor Reflected in SOL Assessments OLD Grade 4

20. Increased Rigor Reflected in SOL Assessments NEW Grade 4

21. Increased Rigor Reflected in SOL Assessments OLD Algebra 1

22. Increased Rigor Reflected in SOL Assessments OLD NEW Algebra 1

23. Increased Rigor in the 2009 Mathematics Standards of Learning Assessments • Increased rigor reflective of the SOL • Comprehensive interpretation of SOL and Curriculum Framework • Additional ways for students to demonstrate understanding

24. SOL, Curriculum Framework,and SOL 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.” – 2009 Mathematics Curriculum Framework

25. Comprehensive Interpretationof the SOL and Curriculum Framework SOL 3.11 The student will- a) tell time to the nearest minute, using analog and digital clocks; and b) determine elapsed time in one-hour increments over a 12-hour period.

26. Comprehensive Interpretationof the SOL and Curriculum Framework Under Essential Knowledge and Skills, the third bullet says: • When given the beginning time and ending time, determine the elapsed time in one-hour increments within a 12-hour period (times do not cross between a.m. and p.m.). There are three elements in this type of problem: a beginning time, an ending time, and the amount of time that has elapsed. If given ANY two of these three elements, the students should be able to find the missing piece.

27. Comprehensive Interpretationof the SOL and Curriculum Framework G.12 The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Using the Curriculum Framework bullets and their converses, students can be given combinations of the following and asked to find other parts: • the coordinates of the center • the radius • the diameter • the coordinates of a point on the circle • the equation of a circle

28. SOL, Curriculum Framework,and SOL 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.” – 2009 Mathematics Curriculum Framework

29. Comprehensive Interpretationof the SOL and Curriculum Framework Use of Prior Knowledge: • Even and odd numbers are taught in grade 2 (SOL 2.4), so numbers on a spinner in a grade 3 item can be referenced as even or odd (the chance that a spinner will land on an even number…).

30. Comprehensive Interpretationof the SOL and Curriculum Framework Use of Prior Knowledge: • Stem-and-leaf plots are taught in grade 5 (SOL 5.15) and can be used to display data sets in Algebra I (SOL A.9). • Solving multistep equations are taught in grade 8 (SOL 8.15) and Algebra I (SOL A.4), and this skill can be used to find missing measures throughout many of the geometry standards.

31. Increased Rigor in the 2009 Mathematics Standards of Learning Assessments • Increased rigor reflective of the SOL • Comprehensive interpretation of SOL and Curriculum Framework • Additional ways for students to demonstrate understanding

32. Additional Ways for Students to Demonstrate Understanding Addition of non-multiple choice items called technology-enhanced items (TEI): • Fill-in-the-blank • Drag and drop • Hot-spot: Select one or more “zones/spots” to respond to a test item; i.e. select answer option(s), shade region(s), place point(s) on a grid or number line • Creation of bar graphs/histograms

33. Example of Fill-in-the-Blank

34. Examples of Drag and Drop

35. Examples of Hot Spot

36. Examples of Hot Spot

37. Examples of Hot Spot

38. Creation of Graphs

39. How Can Teachers Achieve and Maintain Instructional “Rigor”? • Engage students in the learning process, providing relevant activities and tasks that require a high level of cognitive demand • Ask high-leverage questions that require students to think, process, and communicate • Require students to justify their thinking and reasoning

40. How Can Teachers Achieve and Maintain Instructional “Rigor”? • Provide instruction that requires students to • become mathematical problem solvers that • communicate mathematically; • reason mathematically; • make mathematical connections; and • use mathematical representations to model and interpret practical situations Virginia’s Process Goals for Students

41. Mr. Michael Bolling – Michael.Bolling@doe.virginia.gov Director, Office of Mathematics and Governor’s Schools, Dr. Deborah Wickham – Deborah.Wickham@doe.virginia.gov Mathematics Specialist, K-5 Mrs. Christa Southall – Christa.Southall@doe.virginia.gov Mathematics Specialist