Understanding the Shifts in the Common Core State Standards A
Focus on Mathematics Wednesday, October 19 th, 2011 2:00 pm 3:30 pm
Doug Sovde, Senior Adviser, PARCC Instructional Supports and
Educator Engagement, Achieve Beth Cocuzza, Student Achievement
Partners, LLC
Slide 2
The Six Shifts in Mathematics Shift One: Focus Shift Two:
Coherence Shift Three: Deep Understanding Shift Four: Fluency Shift
Five: Application Shift Six: Intensity
Slide 3
Shift One: Focus Significantly narrow and deepen the scope and
content of how time and energy is spent in the math classroom Focus
deeply on only the concepts that are prioritized in the standards
so that students reach strong foundational knowledge and deep
conceptual understanding Students are able to transfer mathematical
skills and understanding across concepts and grades
Slide 4
Shift Two: Coherence Carefully connect the learning within and
across grades so that students can build new understanding onto
foundations built in previous years. Begin to count on deep
conceptual understanding of core content and build on it. Each
standard is not a new event, but an extension of previous
learning.
Slide 5
The Importance of Focus The current U.S. curriculum is a mile
wide and an inch deep. Focus allows each student to think,
practice, and integrate each new idea into a growing knowledge
structure.
Slide 6
K 12 Number and Operations Measurement and Geometry Algebra and
Functions Statistics and Probability Traditional U.S. Approach
Slide 7
DomainGradesMajor Work/Major Concerns (not a complete list)
Counting and Cardinality K Know number names and the count sequence
Count to tell the number of objects Compare numbers Operations and
Algebraic Thinking K-5 Concrete use of the basic operations (word
problems) Mathematical meaning and formal properties of the basic
operations Prepare students to work with expressions and equations
in middle school Number and OperationsBase Ten K-5 Place value
understanding Develop base-ten algorithms using place value and
properties of operations Computation competencies (fluency,
estimation) Number and OperationsFractions 3-5 Enlarge concept of
number beyond whole numbers, to include fractions Use understanding
of basic operations to extend arithmetic to fractions Lay
groundwork for solving equations in middle school The Number
System6-8 Build concepts of positive and negative numbers Work with
the rational numbers as a system governed by properties of
operations Begin work with irrational numbers Expressions and
Equations 6-8 Understand expressions as objects (not as
instructions to compute) Transform expressions using properties of
operations Solve linear equations Use variables and equations as
techniques to solve word problems Ratios and Proportional
Relationships 6-7 Consolidate multiplicative reasoning Lay
groundwork for functions in Grade 8 Solve a wide variety of
problems with ratios, rates, percents Functions8 Extend and
formalize understanding of quantitative relationships from Grades
3-7 Lay groundwork for work with functions in High School
Measurement and DataK-5 Emphasize the common nature of all
measurement as iterating by a unit Build understanding of linear
spacing of numbers and support learning of the number line Develop
geometric measures Work with data to prepare for Statistics and
Probability in middle school GeometryK-8 Ascend through
progressively higher levels of logical reasoning about shapes
Reason spatially with shapes, leading to logical reasoning about
transformations Connect geometry to number, operations, and
measurement via notion of partitioning Statistics and Probability
6-8 Introduce concepts of central tendency, variability, and
distribution Connect randomness with statistical inference Lay
foundations for High School Statistics and Probability CCSS K-8
Domain Structure
Slide 8
Focusing attention within Number and Operations Operations and
Algebraic Thinking Expressions and Equations Algebra Number and
Operations Base Ten The Number System Number and Operations
Fractions K12345678High School
Slide 9
The Importance of Coherence Coherence provides the opportunity
to make connections between mathematical ideas. Coherence occurs
both within a grade and across grades. Coherence is necessary
because mathematics instruction is not just a checklist of topics
to cover, but a set of interrelated and powerful ideas.
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Coherence example: Grade 3 Making connections at a single grade
Properties of Operations Area Multiplication and Division
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Coherence example: Progression across grades 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)
Slide 12
Content Emphases by Cluster Grade Four
Slide 13
Shift Three: Deep 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 Students demonstrate deep
conceptual understanding of core math concepts by applying them to
new situations
Slide 14
Shift Four: Fluency Students are expected to have speed and
accuracy with simple calculations 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
Slide 15
Required Fluencies GradeRequired Fluency KAdd/subtract within 5
1Add/subtract within 10 2 Add/subtract within 20 Add/subtract
within 100 3 Multiply/divide within 100 Add/subtract within 1000
4Add/subtract within 1,000,000 5Multi-digit multiplication 6
Multi-digit division Multi-digit decimal operations 7Solve px + q =
r, p(x + q) = r
Slide 16
Shift Five: Application Use math and choose the appropriate
concept for application even when not prompted to do so Provide
opportunities at all grade levels for students to apply math
concepts in real world situations Teachers in content areas outside
of math, particularly science, ensure that students are using math
at all grade levels to make meaning of and access content
Slide 17
Shift Six: Intensity The standards call equally for conceptual
understanding, procedural skill and fluency, and application of
mathematics. Meeting these standards requires intensity in the
classroom. Practice is intense: fluency is built and assessed
through timed exercises. Solitary thinking and classroom discussion
are intense, centered on thought-provoking problems that build
conceptual understanding. Applications are challenging and
meaningful. The amount of time and energy spent practicing and
understanding learning environments is driven by the specific
mathematical concept and therefore, varies throughout the given
school year.
Slide 18
The Shifts in ActionTwo Examples Place Value Standards
Progression Seeing the Six Shifts Fractions Standards Progression
Seeing the Six Shifts
Slide 19
Place Value Problems for Deep Understanding
Slide 20
The Shifts in ActionTwo Examples Place Value Standards
Progression Seeing the Six Shifts Fractions Standards Progression
Seeing the Six Shifts