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Exploring Coherence in the2011 MA Curriculum Framework for

Mathematics

Exploration Activity:Tracing Domain

and Cluster Progressions

April 2011

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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

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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

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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.

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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.]

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Topic Placement in Top Achieving Countries

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Topic Placement in the U.S.

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International ComparisonWhole Group Discussion

•In what ways do the curricula of the top-achieving countries exhibit coherence?

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Look Familiar?Domain Progression in the New Standards

PK-8 Domains Progression

Domains PK K 1 2 3 4 5 6 7 8

Counting and Cardinality MA                  

Operations and Algebraic Thinking MA                  

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                    

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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)

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Format of the Standards

StandardStandard2.NBT.1 (code)2.NBT.1 (code)

Domain Domain Grade Level

Grade Level

2.NBT (code)

2.NBT (code)

ClusterCluster

Cluster

Heading

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Activity 1: DomainsIndividual 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

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Activity 1: DomainsSmall 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

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Activity 2: Cluster HeadingsIndividual 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

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Activity 2: Grade 4 Example

Domains and Clusters PK K 1 2 3 4 5 6 7 8

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 x            

Work with addition and subtraction equations.     x              

Work with equal groups of objects to gain foundations for multiplication.       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        

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Activity 2: Cluster HeadingsSmall 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

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Main Activity 3: StandardsIndividual 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

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Main Activity 3: StandardsGrade Level Share Out

• How do the standards clarify the progression of concepts within your grade level and/or across grades?

Time estimate: 10 minutes

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Wrap-UpWhole 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

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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/