Exploring Coherence in the 2011 MA Curriculum Framework for Mathematics

1. ExploringCoherence in the2011 MA Curriculum Framework for Mathematics Exploration Activity: Tracing Domain and Cluster Progressions April 2011

2. 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

3. 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

4. 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.

5. 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.]

6. Topic Placement in Top Achieving Countries

7. Topic Placement in the U.S.

8. International Comparison Whole Group Discussion • In what ways do the curricula of the top-achieving countries exhibit coherence?

9. 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 Look Familiar?Domain Progression in the New Standards

10. Activity Summary 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)

11. 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

12. Activity 1: DomainsIndividual Work 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

13. 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

14. Activity 2: Cluster HeadingsIndividual Work 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

15. 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 Activity 2: Grade 4 Example

16. 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

17. Main Activity 3: StandardsIndividual Work 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

18. 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

19. 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

20. 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/