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

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 school math?

Traditional Secondary Mathematics Course sequence

Grade 6 Grade 7 Grade 8 Algebra I Geometry Algebra II Precalc Calculus

Acceleration Options

Outlined in the Draft 2013 CA

Math Frameworks

The Bird’s

Eye View

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!

No Acceleration

Grade 6 Grade 7 Grade 8 Algebra I Geometry Algebra II Precalc Calculus

Grade 6 Grade 12Grade 11Grade 7 Grade 9 Grade 10Grade 8 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.

About CCSS-M at the Secondary Level

First some Background

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

• 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

Math III

Math II

Math IAlgebra I

Geometry

Algebra II

Pre-Calculusor

Statistics & Probability

10

N-Q 1-3A-SSE 1

A-CED 1-4A-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 1-3A-SSE 2-3A-APR 1A-REI 4, 7F-IF 8F-BF 4F-LE 6

G-CO 1-8, 12-13G-GPE 4, 5, 7

Algebra I Math I

Underlined standard is California revised addition11

G-CO 9-11G-STR 1-8, 8.1

G-C 1-5G-GPE 1-2, 4

G-GMD 1, 3, 5, 6S-CP 1-9S-MD 6-7

G-CO 1-8, 12-13G-SRT 9-11GPE 5-7G-GMD 4G-MG 1-3

Geometry Math IIN-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, 7F-IF 4-7, 8, 9F-BF 1, 3, 4 F-LE 3, 6F-TF 8

Underlined standards are California revised addition.Standards in blue are also in Math I.

12

N-CN 1-2, 7A-REI 3.1F-TF 8

Algebra II Math III N-CN 8-9A-SSE 1, 2, 4 A-APR 1, 2-7A-CED 1-4A-REI 2, 11F-IF 4-9F-BF 1, 3, 4F-LE 4, 4.1, 4.2, 4.3F-TF 1, 2, 2.1, 5G-GPE 3.1S-ID 4S-IC 1-6S-MD 6-7

G-SRT 9-11G-GMD 4G-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

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 AssessmentsGrades 3-8 and 11

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.

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

Significantly Higher Rigor

• 1997CA Algebra 1 ≠ CCSSM Algebra I

• 1997CA Geometry ≠ CCSSM Geometry

• 1997CA Algebra 2 ≠ CCSSM Algebra II

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

3rd Grade MAC Below MAC At/Above Total

CST Below 15.9% 5.2% 21.1%

CST At/Above 13.7% 65.4% 79.1%Total 29.6% 70.6% 100%

4th Grade MAC Below MAC At/Above Total

CST Below 16.9% 2.8% 19.7%



CST Below 20.6% 3.8% 24.4%


MAC vs CST 2012: Elementary Grades

MAC vs CST 2012: Middle School


CST Below 37.2% 1.4% 38.6%



CST Below 33.3% 2.1% 35.4%


Grade 8 Alg 1 MAC Below MAC At/Above Total

CST Below 34.5% 3.6% 38.1%


8th Graders Taking HS Geometry

Grade 8 Geometry

MAC Below

MAC At/Above Total

CST Below 3.1% 0.8% 3.9%CST At/Above 51.3% 44.8% 96.1%

Total 54.4% 45.6% 100%

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As outlined in the 2013 draft version of the CA Mathematics Framework

Five Acceleration Options

Compacting in Middle School

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.

• 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

http://www.corestandards.org/the-standards%20page%2082

https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx

https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx

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


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


Accelerated Integrated Pathway

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

http://www.doe.mass.edu/candi/commoncore/EnhancedPathway.pdf

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

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.

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.

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.

Acceleration Options

Outlined in the Draft 2013 CA

Math Frameworks

The Bird’s

Eye View

Survey Results

Technology Preparedness

• 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.

Confidence To Administer Sbac Today

Percentage of Respondents with

Complete/ Considerable Confidence2

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 Equipment3 40% 36% 24%

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.

Confidence to Administer in 12-week window

Percentage of Districts

with Complete/ Considerable Confidence2


with Some Level of Confidence


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 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.

Technological Need


ReportingHigh Need


Reporting Moderate Need


ReportingLow Need

Desktop 27% 38% 35%

Laptops 44% 34% 22%

Tablets 44% 28% 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 2014–151

1 Row totals may not equal 100 percent due to rounding.

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

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