Laguna Beach Unified School District
November 5, 2014
Transitioning to the Common Core:
All Roads lead to Calculus and Statistics
Dr. Patrick Callahan
Statewide Co-Director, California Mathematics Project
UCLA
• Why Common Core?
Where did the CCSS Come From?
Overriding question:
What do we want HS graduates to
know and be able to do?
Current Adoptions of CCSS
CCSS
Adoptions
as of
11/3/2014
43 State are currently implementing
the CCSS
When will we be fully
implemented?
“fully implemented?”
From a student’s perspective the first time the
Common Core could be fully implemented is
a student graduating in 2024.
Before that time every student will
experience a hybrid of Common Core and
previous mathematics.
“fully implemented?”
From a student’s perspective the first time the Common Core
could be fully implemented is a student graduating in 2024.
Before that time every student will experience a hybrid of
Common Core and previous mathematics.
You have experienced about
7.692% Common Core!
Implementation vs. Transition
The word “implementation” tends to refer to the policy
aspects of adopting the Common Core.
In a policy sense you can be “fully implemented” right away.
Another, more student-centric, approach is to think in
terms of “transition” rather than “implementation”.
This is a pragmatic approach that acknowledges that
student, parents, teachers, and systems are where they are
now and that it will take time to move the system to
the Common Core.
Transition to What?
We use the phrase
“implement the Common Core”
or
“transition to the Common Core”
but what does that mean?
What exactly are the Common Core
Standards?
Common Core Standards, what they
are NOT and what they ARE:
The Common Core standards are not a list of topics
to be covered or taught.
The Common Core State Standards are a description
of the mathematics students are expected to
understand and use, not a curriculum. The standards
are not the building blocks of curriculum, they are
the achievements we want students to attain as the
result of curriculum.
How are the CCSS different?
The CCSS are reverse engineered from an analysis of what
students need to be college and career ready.
The design principals were focus, coherence, and rigor. (No
more mile-wide inch deep laundry lists of standards)
The CCSS in Mathematics have two sections:
CONTENT and PRACTICES
The Mathematical Content is what students should know.
The Mathematical Practices are what students should do.
Real life applications and mathematical modeling are essential.
Mathematical
Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of
others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
REASONING AND EXPLAINING
1. Make sense of problems and persevere in
solving them
6. Attend to precision
OVERARCHING HABITS OF MIND
CCSS Mathematical Practices
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS
4. Model with mathematics
5. Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
What is rigor?
APPLICATIONS
CONCEPTS
PROCEDURES
What is rigor?
Sample Algebra Worksheet
This should look familiar.
What do you notice?
What is the mathematical
goal?
What is the expectation of
the student?
A sample Algebra Exam
A sample Algebra Exam
I typed #16 into
Mathematica
Look at the circled answers.
What do you notice?
“Answer Getting”
As Phil Daro has mentioned:
There is a difference between
using problems to “get
answers” and to learn
mathematics.
This algebra exam sends a
clear message to students:
Math is about getting
answers.
Note that there is no
context, just
numbers and
expressions.
Getting correct answers is necessary,
but students must also understand,
and be able do applications
APPLICATIONS
CONCEPTS
PROCEDURES
Previous Expectations for Mathematics
California STAR test released items 5th Grade
What are these assessing?
The Common Core is NOT just about
shuffling topics around.
The Common Core is fundamentally about
changing the definition of what it means to
be mathematically proficient.
The Target has Changed!
OLD DEFINITION OF
PROFICENCY
NEW DEFINITION OF
PROFICENCY
SBAC Claims
SAT Redesign (2016)
Focus on Math that Matters Most
The exam will focus in depth on three essential
areas of math:
•Problem Solving and Data Analysis
•Heart of Algebra
•Passport to Advanced Math
New SAT items
New expectations require new
Pathways
Changing expectations:
The trouble with course names
In the particular case of mathematics, there is a “vocabulary”
around the names of mathematics courses that 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 ninth grade for most students who moving forward will
complete the CA CCSSM for grade eight – a course that is more
rigorous and more demanding than the earlier versions of “Algebra
1.” Even so, we expect the changes to cause confusion. The single
most practical solution is to describe detailed course contents, in
addition to course names, as a way of clearing up confusion until
“Algebra I” as commonly used, refers to a ninth grade and not an
eighth grade course
Changing expectations
The trouble with course names
In the particular case of mathematics, there is a “vocabulary”
around the names of mathematics courses that 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 ninth grade for most students who moving forward will
complete the CA CCSSM for grade eight – a course that is more
rigorous and more demanding than the earlier versions of “Algebra
1.” Even so, we expect the changes to cause confusion. The single
most practical solution is to describe detailed course contents, in
addition to course names, as a way of clearing up confusion until
“Algebra I” as commonly used, refers to a ninth grade and not an
eighth grade course
An important equation:
Algebra 1 ≠ Algebra 1
Previous 8th grade CA standards
Crosswalks are not the answer
Changing expectations:
Middle School is key
When the expectations for middles school
mathematics were mostly about speed and
accuracy of computations it made sense to
accelerate in middle school, and even skip grades.
This no longer makes sense.
Middle school mathematics is the key to success for
all students. Rushing or skipping is a bad idea for
almost all students.
Sample Common Core
Grade 8 Curriculum Plan
Common Core is
much more rigorous
than previous
middle school
expectations.
CA Framework on Acceleration
1. Decisions to accelerate students into the Common Core State
Standards for higher mathematics before ninth grade should
not be rushed.
Placing students into an accelerated pathway too early should
be avoided at all costs. It is not recommended to compact the
standards before grade seven to ensure that students are
developmentally ready for accelerated content. In this
document, compaction begins in seventh grade for both the
traditional and integrated sequences.
CA Framework on Acceleration
Decisions to accelerate students into higher
mathematics before ninth grade must require
solid evidence of mastery of prerequisite CA
CCSSM.
What it means to be successful at
mathematics
It’s not rushing to get as far ahead as you can.
It means mastering rigorous mathematics.
APPLICATIO
NS
CONCEPTS
PROCEDUR
ES
OLD vs. CC: Same Advanced Options for Students
(A POSSIBLE SET OF CC PATHWAYS)
Grade 6
Grade 7
Grade 8
Grade 9
Grade 10
Grade 11
Grade 12
OLD
GRADE
6
OLD
GRADE
7
OLD
ALG
1
OLD
GEOM
OLD
ALG
2
OLD
PRECALC
AP
CALC
OLD
GRADE
6
OLD
ALG
1
OLD
GEOM
OLD
ALG
2
OLD
PRECALC
AP
CALC
AB
AP
CALC
BC
CC
6
CC
7
CC
8
CC
ALG
1
CC
GEOM
CC
ALG
2
YR 4
or
AP C/S
CC
7
CC
8
CC
ALG
1
CC
GEOM
CC
ALG
2
AP
CALC
AB
AP
CALC
BC
Transitioning to Common Core:
Focus and Purpose
Transitions are like home remodels: they take
time and they can be messy along the way, but it
is worth the effort if you have a vision for
improving mathematics for all students.
I would like to personally thank the teachers and administrators of Laguna
Beach Unified School District.
It has been a pleasure to work with them.
They are committed to providing the best possible education for all your
students.
They are working hard to ensure that all students not only get into the college
of their choice, but to be successful when they get there, and after they
graduate.
Sincerely,
,
Patrick Callahan