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Accelerating Math

Accelerating Math. In the Common Core State Standards ’ Era Curriculum Council 10-25-13. Underlying Question. At what point and under what conditions do we accelerate students in their mathematics sequence to reach advanced courses in high s chool math?. Grade 8. Algebra I. Calculus.

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Accelerating Math

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  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. Grade 8 Algebra I Calculus Grade 6 Grade 7 Geometry Algebra II Precalc Traditional Secondary Mathematics Course sequence

  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. Grade 8 Algebra I Calculus Grade 6 Grade 7 Geometry Algebra II Precalc No Acceleration Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11 Grade 12 Grade ??? 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. First some Background About CCSS-M at the Secondary Level

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

  9. Coursification of High School Mathematics 2010 National CCSS-M 2013 CA CCSS-M • 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 2010 CA CCSS-M did not have Appendix A

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

  11. Algebra I Math I 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 Underlined standard is California revised addition

  12. Geometry Math II N-RN 1-3 N-CN 1-2, 7-9 A-SSE 1, 2, 3 A-APR 1 A-CED 1, 2, 4 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 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.

  13. Math III Algebra II N-CN 8-9 A-SSE 1, 2, 4 A-APR 1, 2-7 A-CED 1-4 A-REI 2, 11 F-IF4-9 F-BF1, 3, 4 F-LE4, 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 N-CN 1-2, 7 A-REI 3.1 F-TF 8 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

  14. SBAC Assessments Grades 3-8 and 11 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

  15. 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.

  16. 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 8th 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

  17. Significantly Higher Rigor • 1997CA Algebra 1 ≠ CCSSM Algebra I • 1997CA Geometry ≠ CCSSM Geometry • 1997CA Algebra 2 ≠ CCSSM Algebra II

  18. MAc vs. CST 2012 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 19

  19. MAC vs CST 2012: Elementary Grades

  20. MAC vs CST 2012: Middle School

  21. 8th Graders Taking HS Geometry 24

  22. Five Acceleration Options As outlined in the 2013 draft version of the CA Mathematics Framework

  23. Compacting in Middle School • 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. • 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.aspx Acceleration Decision Point

  24. 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. Acceleration Decision Point Doubling Up in High School

  25. Accelerated Integrated Pathway Acceleration Decision Point • 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 Accelerated Integrated Pathway

  26. Enhanced Pathway • Spreads 4 year curriculum into 3-year time frame, allowing students to go into Calculus in 12th 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 • Integrated Example from Shasta County Office of Education Enhanced Pathway Acceleration Decision Point

  27. 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

  28. 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 12th grade.

  29. cautions • DO NOT RUSH decisions to accelerate students into the Common Core State Standards for higher mathematics before ninth grade. • 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. • Compacted courses should include the same CCSS as the non-compacted courses. Avoid skipping content. • 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. • Insure that all students have access to rigorous mathematics (procedures, concepts and applications) and to the Mathematical Practice Standards.

  30. 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.

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

  32. Technology Preparedness Survey Results

  33. 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.

  34. Confidence To Administer Sbac Today Table 1. Reported Levels of Confidence for Currently Meeting the Minimum Technology Requirements to Administer Smarter Balanced Assessments1 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.

  35. Confidence to Administer in 12-week window Table 2. Administering the Smarter Balanced Assessments within a 12-Week Window: Response Rates by District Size1 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.

  36. Technological Need Table 4. Reported Levels of Technological Need to Administer Smarter Balanced Assessments in 2014–151 1 Row totals may not equal 100 percent due to rounding.

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