Bilingual, Immigrant & Rufugee
Education Directors Meeting
Seattle, Washington
Mathematics
CGCS Mathematics
• Mathematics Retreat, September 21-22, 2011
– Jason Zimba, lead writer of the CCSS Mathematics
• Mathematics Advisory Committee professional development
– Mathematics Learning Progressions, March 19-20, 2012
– Phil Daro, lead writer of the CCSS Mathematics
• Mathematics Retreat
– Learning Progressions, June 19, 2012
– William McCallum, lead writer of the CCSS Mathematics
• Pre-conference in Mathematics
– July 11, 2012
– William McCallum & IM&E
CGCS: Mathematics
• September 21-22, 2011 – Albany, New York
• Audience: District mathematics leaders
• Purpose: Develop a shared understanding of the Common
Core Mathematics Standards and examine assessment
items that probe for deeper conceptual understanding
• Facilitators: Student Achievement Partners (including Jason
Zimba, lead developer of the Common Core Mathematics
Standards)
Common Core Mathematics
Standards
Umbrella
• Balanced approach to mathematics
– Three instructional shifts that correspond
to the design principles underlying the
development of the standards
• Focus
• Coherence
• Rigor: deep understanding, fluency, and
applications
How the curriculum in the U.S.
was organized
The Importance of Focus
Traditional U.S. Approach
K
Number and
Operations
Measurement
and Geometry
Algebra and
Functions
Statistics and
Probability
12
Focusing attention within Number and
Operations
Operations and Algebraic
Thinking
Expressions
 and
Equations
Number and Operations—
Base Ten

K
1
2
3
4
Algebra
The Number
System
Number and
Operations—
Fractions



5
6
7
8
High School
Focus in mathematics: The new version
100
Sample
Additional
Everyone’s
Time and
Effort
Intense Focus
0
Why Focus?
• Provides the time for students to transfer mathematical skills
and understanding across concepts and grade levels
– Mathematical connections
– Deep conceptual understanding
– Connect conceptual and procedural understanding
• Transitions from concrete↔pictorial↔language↔abstract
• Deepens and narrows the scope of how time and energy is
spent in the math classroom
– Communicate focus so that instruction is manageable; it is more
than merely writing a standard a day
Focus– strengthens foundations
• Progression involving fractional concepts (conceptual
understanding) and operations (multiplication and division of
fractions):
– Grade Three:
Develop understanding of fractions as numbers
Develop understanding of fractions as part of a
whole and as a number on the number line
Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size
– Grade Four:
Extend understanding of fraction equivalence and
ordering
Build fractions from unit fractions by applying and
extending previous understandings on whole numbers
(decompose a fraction into a sum of fractions with the
same denominator)
Focus: Number and Operations Fractions
• Grade Four:
Multiply a fraction by a whole number
• Grade Five:
Multiply a fraction by a fraction
Divide unit fractions by a whole number; and whole
numbers by unit fractions
• Grade Six:
Interpret and compute quotients of
fractions and solve word problems
Conceptual and Procedural
Understanding
Describe how
you would solve
this problem?
Shift 2: Coherence
• Coherence provides the opportunity for students to make
connections between mathematical ideas and across
content areas
– Each standard is not a new event, but an extension of
previous learning
– Occurs both within a grade and across grades
– Allows students to see mathematics as inter-connected
ideas
• Mathematics instruction cannot be relegated to merely
a checklist of topics to cover, but instead must be
centered around a set of interrelated and powerful
ideas
Take the number apart?
Tina, Emma, and Jen discuss this expression:
• Tina: I know a way to multiply with a mixed number, like
that is different from the one we learned in class. I call my
way “take the number apart.” I’ll show you.
Which of the three girls do you think is
right? Justify your answer
mathematically.
First, I multiply the 5 by the 6 and get 30.
Then I multiply the by the 6 and get 2. Finally, I
add the 30 and the 2, which is 32.
– Tina: It works whenever I have to multiply a
mixed number by a whole number.
– Emma: Sorry Tina, but that answer is wrong!
– Jen: No, Tina’s answer is right for this one
problem, but “take the number apart” doesn’t
work for other fraction problems.
Example explanation
Why does 5 x 6 = (6x5) + (6 x ) ?
Because
5 1/3 = 5 + 1/3
6(5 1/3) =
6(5 + 1/3) =
(6x5) + (6x1/3) because a(b + c) = ab + ac
Coherence
• At the high school level, students relate their previous
understandings as they learn to multiply binomials
(3x + 5)(2x + 6)
3x(2x + 6) + 5 (2x + 6)
Connected directly to the content
(happens in the context of solving
real problems)
Mathematical Practices
Secondary Focus
William Schmidt
• Keynote speaker, July 2012, Curriculum/Research
Director’s Meeting
– CCSS in Mathematics
• Can potentially elevate the academic performance of our students
• Standards relationship to student achievement is influenced by the
instructional materials/units available for teachers to use
Implementation
Good News
• 90% of teachers are
positive about the CCSS
Bad News
• 80% of teachers indicated
that the CCSSM is pretty
much the same as their
state standards. They
indicated that they would
keep teaching a topic in
their grade level even if
not in the Standards
Ugly news
Teachers self-report
• Grades 1-5: only ½ felt
well-prepared to teach
the standards;
• Grades 6-8; only 60%
feel well-prepared;
• HS; only 70% feel well
prepared
Now what?
What criteria will you use to
review and select
materials/resources
Reviewing secondary materials
• The degree to which specific trajectories
of mathematics topics are incorporated
appropriately across grade-band
curriculum materials.
• The curriculum materials support the
development of students’ mathematical
understanding
Reviewing secondary materials
• The curriculum materials support the
development of students’ proficiency with
procedural skills.
• The curriculum materials assist students in
building connections between mathematical
understanding and procedural skills.
Reviewing secondary materials
• Student activities build on each other within
and across grades in a logical way that
supports mathematical understanding and
procedural skills.
• The materials provide opportunities for students to
develop the Standards for Mathematical Practice as
“habits of mind” (ways of thinking about
mathematics that are rich, challenging, and useful)
throughout the development of the Content
Standards.
Materials/resources/professional
development
A lot to do….