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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

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cgcs 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 mathematics1
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
Common Core Mathematics Standards


  • 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

Focus in mathematics: The new version

Everyone’s Time and Effort

why focus
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
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
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
Conceptual and Procedural Understanding

Describe how you would solve this problem?

shift 2 coherence
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
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
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
Example explanation

Why does 5 x 6 = (6x5) + (6 x ) ?


5 1/3 = 5 + 1/3

6(5 1/3) =

6(5 + 1/3) =

(6x5) + (6x1/3) because a(b + c) = ab + ac

  • 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
Connected directly to the content

(happens in the context of solving real problems)

Mathematical Practices

william schmidt
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

Good News

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

  • 90% of teachers are positive about the CCSS
ugly news
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
reviewing secondary materials
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 materials1
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 materials2
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.