Transcript Understanding the Shifts in the Common Core State Standards

Understanding the Shifts
in the Common Core State
Standards
A Focus on Mathematics
Wednesday, October 19th, 2011
2:00 pm – 3:30 pm
Doug Sovde, Senior Adviser, PARCC Instructional Supports
and Educator Engagement, Achieve
Beth Cocuzza, Student Achievement Partners, LLC






Shift One: Focus
Shift Two:
Coherence
Shift Three: Deep
Understanding
Shift Four: Fluency
Shift Five:
Application
Shift Six: Intensity
The Six Shifts in Mathematics



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
Shift One: Focus

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.
Shift Two: Coherence

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.
The Importance of Focus
Traditional U.S. Approach
K
Number and
Operations
Measurement
and Geometry
Algebra and
Functions
Statistics and
Probability
12
CCSS K-8 Domain Structure
Domain
Grades
Major 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
Operations—Base Ten
K-5
•Place value understanding
•Develop base-ten algorithms using place value and properties of operations
•Computation competencies (fluency, estimation)
Number and
Operations—Fractions
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 System
6-8
•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
Functions
8
•Extend and formalize understanding of quantitative relationships from Grades 3-7
•Lay groundwork for work with functions in High School
Measurement and Data
K-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
Geometry
K-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
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
Focusing attention within Number and
Operations
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.

The Importance of Coherence
Making connections at a single grade
Multiplication and
Division
Properties of
Operations
Area
Coherence example: Grade 3
“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)
Coherence example: Progression
across grades
Content Emphases by Cluster
Grade Four
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

Shift Three: Deep Understanding

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
Shift Four: Fluency
Grade
Required Fluency
K
Add/subtract within 5
1
Add/subtract within 10
2
3
Add/subtract within 20
Add/subtract within 100
Multiply/divide within 100
Add/subtract within 1000
4
Add/subtract within 1,000,000
5
Multi-digit multiplication
6
7
Multi-digit division
Multi-digit decimal operations
Solve px + q = r, p(x + q) = r
Required Fluencies



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
Shift Five: Application

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.
Shift Six: Intensity

Place Value
◦ Standards Progression
◦ Seeing the Six Shifts

Fractions
◦ Standards Progression
◦ Seeing the Six Shifts
The Shifts in Action—Two
Examples
Place Value Problems for Deep
Understanding

Place Value
◦ Standards Progression
◦ Seeing the Six Shifts

Fractions
◦ Standards Progression
◦ Seeing the Six Shifts
The Shifts in Action—Two
Examples
Example: Fractions
4.NF
Fractions Problems for Deep
Understanding
Questions?