Transcript High School Pathways - Contra Costa County Office of Education

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
Grade 9
Grade 10
Grade 11
Grade 12
Grade ???
Grade 6
Grade 7
Grade 8
Algebra I
Geometry
Algebra II
Precalc
Calculus
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.
FIRST SOME BACKGROUND
About CCSS-M at the Secondary Level
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
COURSIFICATION OF HIGH SCHOOL
MATHEMATICS
2010 National CCSS-M
• 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
2013 CA CCSS-M
• Outlines Conceptual
Categories & Model
Courses
• Model Courses are
outlined in two
pathways: Traditional &
Integrated
Pre-Calculus
or
Statistics & Probability
Algebra II
Math III
Geometry
Math II
Algebra I
Math I
10
Algebra I
N-RN 1-3
A-SSE 2-3
A-APR 1
A-REI 4, 7
F-IF 8
F-BF 4
F-LE 6
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
G-CO 1-8, 1213
G-GPE 4, 5, 7
Underlined standard is California revised addition
11
Geometry
G-CO 1-8,
12-13
G-SRT 9-11
GPE 5-7
G-GMD 4
G-MG 1-3
Math II
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
Underlined standards are California revised addition.
Standards in blue are also in Math I.
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
12
Algebra II
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
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
Math III
G-SRT 9-11
G-GMD 4
G-MG 1-3
13
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 indepth 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
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
MAC vs CST 2012: Elementary Grades
3rd Grade
CST Below
CST At/Above
Total
4th Grade
CST Below
CST At/Above
Total
5th Grade
CST Below
CST At/Above
Total
MAC Below
15.9%
13.7%
29.6%
MAC Below
MAC At/Above
5.2%
65.4%
70.6%
MAC At/Above
16.9%
2.8%
20.3%
60.0%
37.2%
62.8%
MAC Below
20.6%
18.7%
39.3%
MAC At/Above
3.8%
56.9%
60.7%
Total
21.1%
79.1%
100%
Total
19.7%
80.3%
100%
Total
24.4%
75.6%
100%
MAC vs CST 2012: Middle School
6th Grade
CST Below
CST At/Above
Total
7th Grade
CST Below
CST At/Above
Total
Grade 8 Alg 1
CST Below
CST At/Above
Total
MAC Below
37.2%
25.1%
62.3%
MAC Below
33.3%
27.4%
60.7%
MAC Below
34.5%
30.3%
64.8%
MAC At/Above
1.4%
36.5%
37.9%
MAC At/Above
2.1%
37.1%
39.2%
MAC At/Above
3.6%
31.5%
35.1%
Total
38.6%
61.6%
100%
Total
35.4%
64.5%
100%
Total
38.1%
61.8%
100%
8TH GRADERS TAKING HS GEOMETRY
Grade 8
Geometry
CST
Below
CST
At/Above
Total
MAC
Below
MAC
At/Above
Total
3.1% 0.8% 3.9%
51.3% 44.8% 96.1%
54.4% 45.6% 100%
24
FIVE ACCELERATION OPTIONS
As outlined in the 2013 draft version of the CA Mathematics Framework
COMPACTING IN MIDDLE SCHOOL
Grade 7
Grade 6
+ 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.
• Example: Georgia Department of Education has published a 6/7a and 7b/8
course at https://www.georgiastandards.org/Common-Core/Pages/Math-68.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
Grade 6
Grade 7
Grade 8
Algebra I
Geometry
Acceleration Decision Point
Algebra II
Precalc
Calculus
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
Grade 6
Grade 7
Grade 8
Acceleration Decision Point
Part of
Integrated I
and Integrated
II
Part of
Integrated II
and Integrated
III
Precalc
Calculus
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
• Integrated Example from Shasta County Office of Education
Enhanced Pathway
Grade 6
Grade 7
Grade 8
Enhanced
Algebra
I/Integrated I
Acceleration Decision Point
Enhanced
Geometry/Int
egrated II
Enhanced
Algebra
II/Integrated
III
Calculus
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 12 th grade.
CAUTIONS
1.
2.
3.
4.
5.
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.
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
TECHNOLOGY PREPAREDNESS
Survey Results
•
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
Table 1. Reported Levels of Confidence for Currently Meeting the Minimum
Technology Requirements to Administer Smarter Balanced Assessments1
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%
1
Row totals may not equal 100 percent due to rounding.
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.
2
CONFIDENCE TO ADMINISTER IN 12-WEEK
WINDOW
Table 2. Administering the Smarter Balanced Assessments within a 12Week Window: Response Rates by District Size1
Percentage of
Districts
with Complete/
Considerable
Confidence2
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%
1
Row totals may not equal 100 percent due to rounding.
Responses from the “complete” and “considerable” confidence scale points
were combined into one category, “complete/considerable” confidence.
2
TECHNOLOGICAL NEED
Table 4. Reported Levels of Technological Need to Administer Smarter
Balanced Assessments in 2014–151
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%
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%
1
Row totals may not equal 100 percent due to rounding.