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Common Core State Standards for Mathematics: The Key Shifts. Professional Development Module 2. The Background of the Common Core. Initiated by the National Governors Association (NGA) and Council of Chief State School Officers (CCSSO) with the following design principles :

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the background of the common core
The Background of the Common Core

Initiated by the National Governors Association (NGA) and Council of Chief State School Officers (CCSSO) with the following design principles:

  • Result in College and Career Readiness
  • Based on solid research and practice evidence
  • Fewer, higher and clearer
what the disconnect means for students
What The Disconnect Means for Students

Nationwide, many students in two-year and four-year colleges need remediation in math.

Remedial classes lower the odds of finishing the degree or program.

Need to set the agenda in high school math to prepare more students for postsecondary education and training.


The CCSS Requires Three Shifts in Mathematics

Focus: Focus strongly where the standards focus.

Coherence: Think across grades, and linkto major topics

Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency,andapplication

shift 1 focus strongly where the standards focus
Shift #1: Focus Strongly where the Standards Focus

Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom.

Focus deeply on what is emphasized in the standards, so that students gain strong foundations.


Move away from "mile wide, inch deep"curricula identifiedin TIMSS.

Learn from international comparisons.

Teach less, learn more.

“Less topic coverage can be associated withhigher scores on those topics covered becausestudents have more time to master thecontent that is taught.”

– Ginsburg et al., 2005


The shape of math in A+ countries

Mathematics topics intended at each grade by at least two-thirds of A+ countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

group discussion
Group Discussion

Shift #1: Focus strongly where the Standards focus.

In your groups, discuss ways to respond to the following question, “Why focus? There’s so much math that students could be learning, why limit them to just a few things?”


Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades

Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years.

Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

coherence think across grades
Coherence: Think Across Grades

Example: Fractions

“The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”

Final Report of the National Mathematics Advisory Panel (2008, p. 18)



4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Grade 4

5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Grade 5

6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Grade 6

Informing Grades 1-6 Mathematics Standards Development: What Can Be Learned from High-Performing Hong Kong, Singapore, and Korea? American Institutes for Research (2009, p. 13)


Alignment in Context: Neighboring Grades and Progressions

One of several staircases to algebra designed in the OA domain.



Coherence: Link to Major Topics Within Grades

Example: Data Representation

Standard 3.MD.3


Coherence: Link to Major Topics Within Grades

Example: Geometric Measurement

3.MD, third cluster

group discussion1
Group Discussion

Shift #2: Coherence: Think across grades, link to major topics within grades

In your groups, discuss what coherence in the math curriculum means to you. Be sure to address both elements—coherence within the grade and coherence across grades. Cite specific examples.

engaging with the s hift investigate c oherence in the s tandards with r espect to f ractions
Engaging with the Shift: Investigate Coherence in the Standards with Respect to Fractions

In the space below, copy all of the standards related to multiplication and division of fractions and note how coherence is evident in these standards. Note also standards that are outside of the Number and Operations—Fractions domain but are related to, or in support of, fractions.


Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application


The CCSSM require a balance of:

  • Solid conceptual understanding
  • Procedural skill and fluency
  • Application of skills in problem solving situations

Pursuit of all threes requires equal intensity in time, activities, and resources.

solid conceptual understanding
Solid Conceptual Understanding

Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives

Students are able to see math as more than a set of mnemonics or discrete procedures

Conceptual understanding supports the other aspects of rigor (fluency and application)


The standards require speed and accuracy in calculation.

Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts


Students can use appropriate concepts and procedures for application even when not prompted to do so.

Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

group discussion2
Group Discussion

Shift #3: Rigor: Expect fluency, deep understanding, and application

In your groups, discuss ways to respond to one of the following comments: “These standards expect that we just teach rote memorization. Seems like a step backwards to me.” Or “I’m not going to spend time on fluency—it should just be a natural outcome of conceptual understanding.”

engaging with the shift making a t rue s tatement
Engaging with the shift: Making a True Statement

This shift requires a balance of three discrete components in math instruction. This is not a pedagogical option, but is required by the standards. Using grade __ as a sample, find and copy the standards which specifically set expectations for each component.

Rigor = ______ + ________ + _______

it s tarts with focus
It Starts with Focus

The current U.S. curriculum is "a mile wide and an inch deep."

Focus is necessary in order to achieve the rigor set forth in the standards.

Remember Hong Kong example: more in-depth mastery of a smaller set of things pays off.

content emphases by cluster grade four
Content Emphases by Cluster:Grade Four

Key: Major Clusters; Supporting Clusters; Additional Clusters

cautions imp lementing the ccss is
Cautions: Implementing the CCSS is...
  • Not about “gap analysis”
  • Not about buying a text series
  • Not a march through the standards
  • Not about breaking apart each standard