Exploring Coherence in the 2011 MA Curriculum Framework for Mathematics

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Exploring Coherence in the 2011 MA Curriculum Framework for Mathematics

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Exploring Coherence in the 2011 MA Curriculum Framework for Mathematics

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ExploringCoherence in the2011 MA Curriculum Framework for Mathematics

Exploration Activity:

Tracing Domain and Cluster Progressions

April 2011

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

- 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

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.

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.]

Topic Placement in

Top Achieving Countries

Topic Placement in

the U.S.

International Comparison

Whole Group Discussion

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

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

What can we tell about the coherence of the 2011 Curriculum Framework by looking at the:

Domains? (10 minutes)

Cluster headings? (15 minutes)

Standards? (15 minutes)

Grade Level

2.NBT (code)

Domain

Standard

2.NBT.1 (code)

C

l

u

s

t

e

r

H

e

a

d

i

n

g

Cluster

Format of the Standards

Time estimate: 5 minutes

- 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

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

Time estimate: 5 minutes

- 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

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

What do the cluster headings tell you about the progression of concepts within your grade level and/or across grades?

Time estimate: 10 minutes

Time estimate: 5 minutes

- 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

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

Time estimate: 10 minutes

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

- 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/