Exploring Coherence in the
2011 MA Curriculum Framework for Mathematics
Exploration Activity:
Tracing Domain
and Cluster Progressions
April 2011
1
Desired Outcomes
After this activity participants will:
• Be familiar with the domains, clusters, and standards
organization of the new standards
• Explore the connection of concepts within a grade and
the progression of concepts between grades
• Understand how the domains and clusters help organize
and bring coherence to the grade level standards
2
Supporting changes in practice
• The new standards support improved
curriculum and instruction due to increased:
– FOCUS, via critical areas at each grade level
– COHERENCE, through carefully developed
connections within and across grades
– CLARITY, with precisely worded standards
that cannot be treated as a checklist
– RIGOR, including a focus on College and
Career Readiness and Standards for
Mathematical Practice throughout Pre-K-12
3
A Coherent Curriculum
• Is organized around the big ideas of
mathematics
• Clearly shows how standards are connected
within each grade
• Builds concepts through logical progressions
across grades that reflect the discipline itself.
4
Warm-Up: An International Perspective
• The mathematics curriculum of top achieving countries
on international assessments looks different than the
U.S. in terms of topic placement
[The charts in the next 3 slides are taken from:
Schmidt, W.H., Houang, R., & Cougan, L. (2002). A coherent curriculum:
The case of Mathematics. American educator, 26(2), 10-26, 47-48.]
5
Topic Placement in
Top Achieving Countries
6
Topic Placement in
the U.S.
7
International Comparison
Whole Group Discussion
•In what ways do the curricula of the top-achieving
countries exhibit coherence?
8
Look Familiar?
Domain Progression in the New Standards
PK-8 Domains Progression
Domains
PK
Counting and Cardinality
MA
Operations and Algebraic Thinking
MA
K
1
2
3
4
5
6
7
8
Number and Operations in Base Ten
Number and Operations - Fractions
Ratios and Proportional Relationships
The Number System
MA
Expressions and Equations
Functions
Measurement and Data
MA
Geometry
MA
Statistics and Probability
9
Activity Summary
What can we tell about the coherence of
the 2011 Curriculum Framework by looking
at the:
1. Domains? (10 minutes)
2. Cluster headings? (15 minutes)
3. Standards? (15 minutes)
10
Format of the Standards
Domain
C
l H
u e
s a
t d
e i
r n
Standard
2.NBT.1 (code)
g
Cluster
11
Activity 1: Domains
Individual Work
• On your activity record sheet:
– Note for each domain at your grade level
whether it is a BEGINNING POINT, BUILDING
POINT, OR END POINT
– Record any insights you have about the big
ideas for your grade level, based on the
domain headings
Time estimate: 5 minutes
12
Activity 1: Domains
Small Group Share Out
• From the domain headings and their status in
your grade level (beginning, building, or end
point), what do you know about the progression
of concepts within and across grades?
Time estimate: 5 minutes
13
Activity 2: Cluster Headings
Individual Work
•
Choose one domain as your focus domain
•
Using the PK-8 Domains and Clusters Progression Chart:
– Highlight the cluster headings of your focus domain at
your grade level
•
On your activity recording sheet:
– Note the conceptual progressions within and across
grades and any questions that you have that may be
answered by examining the standards
Time estimate: 5 minutes
14
Activity 2: Grade 4 Example
Domains and Clusters
PK
K
1
2
3
4
5
Operations and Algebraic Thinking
MA
x
x
x
x
x
x
Understand addition as putting together and adding to, and understand subtraction as
taking apart and taking from.
MA
x
Represent and solve problems involving addition and subtraction.
x
x
Understand and apply properties of operations and the relationship between addition and
subtraction.
x
Add and subtract within 20.
x
Work with addition and subtraction equations.
x
Work with equal groups of objects to gain foundations for multiplication.
6
7
8
x
x
Represent and solve problems involving multiplication and division.
x
Understand properties of multiplication and the relationship between multiplication and
division.
x
Multiply and divide within 100.
x
Solve problems involving the four operations, and identify and explain patterns in
arithmetic.
x
Use the four operations with whole numbers to solve problems.
x
Gain familiarity with factors and multiples.
x
15
Activity 2: Cluster Headings
Small Group Share Out
• What do the cluster headings tell you about the
progression of concepts within your grade level
and/or across grades?
Time estimate: 10 minutes
16
Main Activity 3: Standards
Individual Work
• On your activity recording sheet:
– Examine the standards in the 2011 MA
Curriculum Framework for Mathematics to
investigate the questions and progressions
that you noted in Main Activity 2
Time estimate: 5 minutes
17
Main Activity 3: Standards
Grade Level Share Out
• How do the standards clarify the progression of
concepts within your grade level and/or across
grades?
Time estimate: 10 minutes
18
Wrap-Up
Whole Group Discussion
• In what ways do the new standards exhibit
increased coherence compared to the former
standards?
• How do you foresee domains and clusters
impacting your work in the classroom.
Time estimate: 10 minutes
19
Feedback and Information
• To provide feedback on this activity as a
facilitator or participant, or to find more
activities and resources, go to the ESE’s
Curriculum and Instruction page at:
http://www.doe.mass.edu/candi/commoncore/
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