1. ACCELERATING MATH In the Common Core State Standards’ Era Curriculum Council 10-25-13

2. UNDERLYING QUESTION At what point and under what conditions do we accelerate students in their mathematics sequence to reach advanced courses in high school math?

3. TRADITIONAL SECONDARY MATHEMATICS COURSE SEQUENCE Grade 6Grade 7Grade 8Algebra IGeometryAlgebra IIPrecalcCalculus

4. Acceleration Options Outlined in the Draft 2013 CA Math Frameworks The Bird’s Eye View

5. WHY ACCELERATE STUDENTS THROUGH MATH? State & district requirements Desire to take college mathematics in high school (e.g., Pre-Calculus, AP Statistics, Calculus AB, Calculus BC) Highest level of HS math course-taking correlates with college success Because some kids can handle it!

6. NO ACCELERATION Grade 6Grade 7Grade 8Algebra IGeometryAlgebra IIPrecalcCalculus Grade 6Grade 12Grade 11Grade 7Grade 9Grade 10Grade 8Grade ??? In the past there was a great deal of repetition in topics for grades 6-8. With the CCSS-M the amount of repetition has been greatly reduced.

7. About CCSS-M at the Secondary Level FIRST SOME BACKGROUND

8. adapted from Foster (2011) Assessment for Learning The CCSS-M high school standards are organized in conceptual categories (not courses): Number and Quantity Algebra Functions Modeling (*) Geometry Statistics and Probability

9. Outlines Conceptual Categories & Model Courses Model Courses are outlined in two pathways: Traditional & Integrated No high school courses outlined in the main text of the standards HS Courses are outlined by Conceptual Category Appendix A: Designing HS Courses Based on the CCSS COURSIFICATION OF HIGH SCHOOL MATHEMATICS 2010 National CCSS-M 2013 CA CCSS-M 2010 CA CCSS-M did not have Appendix A

10. Math III Math II Math IAlgebra I Geometry Algebra II Pre-Calculus or Statistics & Probability 10

11. N-Q 1-3 A-SSE 1 A-CED 1-4 A-REI 1, 3, 3.1, 5, 6, 10, 11, 12 F-IF 1-7, 9 F-BF 1-3 F-LE 1-3, 5 S-ID 1-3, 5-9 N-RN 1-3 A-SSE 2-3 A-APR 1 A-REI 4, 7 F-IF 8 F-BF 4 F-LE 6 G-CO 1-8, 12- 13 G-GPE 4, 5, 7 Algebra I Math I Underlined standard is California revised addition 11

12. G-CO 9-11 G-STR 1-8, 8.1 G-C 1-5 G-GPE 1-2, 4 G-GMD 1, 3, 5, 6 S-CP 1-9 S-MD 6-7 G-CO 1-8, 12-13 G-SRT 9-11 GPE 5-7 G-GMD 4 G-MG 1-3 GeometryMath II N-RN 1-3 N-CN 1-2, 7-9 A-SSE 1, 2, 3 A-APR 1 A-CED 1, 2, 4 A-REI 4, 7 F-IF 4-7, 8, 9 F-BF 1, 3, 4 F-LE 3, 6 F-TF 8 Underlined standards are California revised addition. Standards in blue are also in Math I. 12

13. N-CN 1-2, 7 A-REI 3.1 F-TF 8 Algebra II Math III N-CN 8-9 A-SSE 1, 2, 4 A-APR 1, 2-7 A-CED 1-4 A-REI 2, 11 F-IF 4-9 F-BF 1, 3, 4 F-LE 4, 4.1, 4.2, 4.3 F-TF 1, 2, 2.1, 5 G-GPE 3.1 S-ID 4 S-IC 1-6 S-MD 6-7 G-SRT 9-11 G-GMD 4 G-MG 1-3 Underlined standards are California revised addition. Standards in purple are also in Math I, II and Algebra 1. Standards in Purple are also in Math II 13

14. All grade 11 students will be required to take the SMARTER balanced assessment aligned to all non-plus (+) standards in each of the conceptual clusters. 14 SBAC Assessments Grades 3-8 and 11

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16. CCSSM GRADE 8 STANDARDS OF SIGNIFICANTLY HIGHER RIGOR THAN ALGEBRA I Grade 8 addresses the foundations of algebra by including content that was previously part of the Algebra I course, such as more in- depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers. Grade 8 also includes geometry standards that relate graphing to algebra in a way that was not explored previously. Grade 8 includes statistics in a more sophisticated way that connect linear relations with the representation of bivariate data.

17. ALGEBRA I MISCONCEPTION [The vocabulary] around names of math courses … is likely to cause confusion not only for educators but also for parents. Algebra 1 is a course that, prior to CA CCSSM, has been taught in 8 th grade to an increasing number of students. That same course name will be the default for most students who moving forward will complete the CA CCSSM for grade 8 – a course that is more rigorous and more demanding than earlier versions of “Algebra 1.” From the draft version of the CA Mathematics Framework, 2013

18. SIGNIFICANTLY HIGHER RIGOR 1997CA Algebra 1 ≠ CCSSM Algebra I 1997CA Geometry ≠ CCSSM Geometry 1997CA Algebra 2 ≠ CCSSM Algebra II

19. Silicon Valley Mathematics Initiative Mathematics Assessment Collaborative Performance Assessment Exam 2012 MAC used MARS tasks as the assessment instrument The MARS tasks demand substantial chains of reasoning and non-routine problem solving MAC VS. CST 2012 19

22. 3rd GradeMAC BelowMAC At/AboveTotal CST Below 15.9%5.2%21.1% CST At/Above 13.7% 65.4%79.1% Total 29.6%70.6%100% 4th GradeMAC BelowMAC At/AboveTotal CST Below 16.9%2.8%19.7% CST At/Above 20.3%60.0% 80.3% Total 37.2%62.8%100% 5th GradeMAC BelowMAC At/AboveTotal CST Below 20.6%3.8%24.4% CST At/Above 18.7% 56.9%75.6% Total 39.3%60.7%100% MAC vs CST 2012: Elementary Grades

23. MAC vs CST 2012: Middle School 6th GradeMAC BelowMAC At/AboveTotal CST Below 37.2%1.4%38.6% CST At/Above 25.1% 36.5%61.6% Total 62.3%37.9%100% 7th GradeMAC BelowMAC At/AboveTotal CST Below 33.3%2.1%35.4% CST At/Above 27.4% 37.1%64.5% Total 60.7%39.2%100% Grade 8 Alg 1MAC BelowMAC At/AboveTotal CST Below 34.5%3.6%38.1% CST At/Above 30.3% 31.5%61.8% Total 64.8%35.1%100%

24. 8 TH GRADERS TAKING HS GEOMETRY Grade 8 Geometry MAC Below MAC At/AboveTotal CST Below 3.1%0.8%3.9% CST At/Above 51.3% 44.8%96.1% Total 54.4%45.6%100% 24

25. As outlined in the 2013 draft version of the CA Mathematics Framework FIVE ACCELERATION OPTIONS

26. COMPACTING IN MIDDLE SCHOOL Grade 6 Grade 7 + Part of Grade 8 Part of Grade 8 + Algebra I or Integrated I Geometry or Integrated II Algebra II or Integrated IIIC Precalc Calculus Acceleration Decision Point Compact grade 7, grade 8, and Algebra I or Mathematics I in the middle school. Compacted means to compress content, which requires a faster pace to complete, as opposed to skipping content Details of the compacted pathway example can be found in CCSS Mathematics Appendix A at http://www.corestandards.org/the-standards, page 82.http://www.corestandards.org/the-standards, page 82 Example: Georgia Department of Education has published a 6/7a and 7b/8 course at https://www.georgiastandards.org/Common-Core/Pages/Math-6- 8.aspxhttps://www.georgiastandards.org/Common-Core/Pages/Math-6- 8.aspx

27. DOUBLING UP Students take two math courses simultaneously (such as geometry and Algebra I or Algebra II, or precalculus and statistics). More difficult to do in the integrated pathway. Doubling Up in High School Acceleration Decision Point

28. ACCELERATED INTEGRATED PATHWAY Standards from Mathematics I, II and III course could be compressed into an accelerated pathway for students for two years, allowing students to enter precalculus in the third year Acceleration Decision Point Accelerated Integrated Pathway

29. ENHANCED PATHWAY Spreads 4 year curriculum into 3-year time frame, allowing students to go into Calculus in 12 th grade. Example: Massachusetts Department of Education has developed model courses for a tradition enhanced sequence. These are available at: http://www.doe.mass.edu/candi/commoncore/EnhancedPathway.pdf http://www.doe.mass.edu/candi/commoncore/EnhancedPathway.pdf Integrated Example from Shasta County Office of Education Grade 6Grade 7Grade 8 Enhanced Algebra I/Integrated I Enhanced Geometry/Int egrated II Enhanced Algebra II/Integrated III Calculus Acceleration Decision Point Enhanced Pathway

30. COMPACTING OVER HOW MANY YEARS? 5 years into 4 – Singapore model 2 years into 1 – common US model 3 years into 2 – Pathways Approach (Appendix A) Why 3 years into 2? Moves quickly without overdoing it Doesn’t skip important content or practices Avoids semi-permanent tracking Make a clean break between middle and high school

31. LATE HIGH SCHOOL ACCELERATION Creating a hybrid Algebra II and Precalculus course or Mathematics III and Precalculus that allows students to go straight into Calculus in 12 th grade.

32. CAUTIONS 1.DO NOT RUSH decisions to accelerate students into the Common Core State Standards for higher mathematics before ninth grade. 2.Decisions to accelerate students into higher mathematics before ninth grade must require solid evidence of mastery of prerequisite CA CCSSM. Avoid permanent or overly-early tracking. 3.Compacted courses should include the same CCSS as the non-compacted courses. Avoid skipping content. 4.A menu of challenging options should be available for students after their third year of mathematics – and all students should be strongly encouraged to take mathematics in all years of high school. 5.Insure that all students have access to rigorous mathematics (procedures, concepts and applications) and to the Mathematical Practice Standards.

33. DISTRICTS SHOULD Work with their mathematics leadership, teachers, parents and curriculum coordinators to design pathways that best meet the needs of their students. Enrichment opportunities should allow students to increase their depth of understanding by developing expertise in the modeling process and applying mathematics to novel and complex contexts.

34. Acceleration Options Outlined in the Draft 2013 CA Math Frameworks The Bird’s Eye View

35. Survey Results TECHNOLOGY PREPAREDNESS

36. The Technology Preparedness Survey was available for LEAs to complete between June 21, 2013 and September 5, 2013. A total of 880 respondents, representing 683 school districts and 197 charter schools, completed the Technology Preparedness Survey. The responding LEAs serve approximately 87 percent of students enrolled in California public schools. All of California’s 25 largest school districts, which serve approximately 1.8 million students, responded to this survey.

37. CONFIDENCE TO ADMINISTER SBAC TODAY Percentage of Respondents with Complete/ Considerable Confidence 2 Percentage of Respondents with Some Level of Confidence Percentage of Respondents with Little Confidence Ability to Test all Eligible Students within a 12-Week Testing Window 67%26%8% Adequate Number of Computers with Minimum Operating System 58% 27%15% Adequate Network Bandwidth 70%20%10% Adequate Technical Support Personnel 46%34%20% Adequate Facilities 61%31%9% Additional Equipment 3 40%36%24% Table 1. Reported Levels of Confidence for Currently Meeting the Minimum Technology Requirements to Administer Smarter Balanced Assessments 1 1 Row totals may not equal 100 percent due to rounding. 2 Responses from the “complete” and “considerable” confidence scale points were combined into one category, “complete/considerable” confidence. 3 Examples include keyboards, headphones, printers, and assistive technology products.

38. CONFIDENCE TO ADMINISTER IN 12-WEEK WINDOW Percentage of Districts with Complete/ Considerable Confidence 2 Percentage of Districts with Some Level of Confidence Percentage of Districts with Little Confidence Small (1,000 or fewer students; N=268) 68%24%8% Medium (1,001 to 20,000 students; N=377) 70%26%5% Large (20,001 or more students; N=38) 59%30%12% Table 2. Administering the Smarter Balanced Assessments within a 12- Week Window: Response Rates by District Size 1 1 Row totals may not equal 100 percent due to rounding. 2 Responses from the “complete” and “considerable” confidence scale points were combined into one category, “complete/considerable” confidence.

39. TECHNOLOGICAL NEED Percentage of Respondents Reporting High Need Percentage of Respondents Reporting Moderate Need Percentage of Respondents Reporting Low Need Desktop 27%38%35% Laptops 44%34%22% Tablets 44%28% Keyboards 18%27%55% Headphones 50%34%16% Printers 20%40%41% Assistive Technology 32%40%28% Internet Bandwidth 26%24%50% Internal Bandwidth 29%27%43% Wireless Access 42%26%32% Professional Development 53%38%10% Facilities 27%40%33% Table 4. Reported Levels of Technological Need to Administer Smarter Balanced Assessments in 2014–15 1 1 Row totals may not equal 100 percent due to rounding.