1. Common Core State Standards in Mathematics
For Cluster 2 Network Leaders and Teams
Prepared and presented by Louise Antoine, Kerry Cunningham, Linda Curtis-Bey, George Georgilakis, Carol Mosesson-Teig, Rose Shteynberg, Suzanne Werner
9/21/10

2. What are Standards?
Standards define what students should understand and be able to do.
Standards must be a promise to students of the mathematics they can take with them.

3. CCSS Mathematical Practices
The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics.

4. CCSS Mathematical Practices
The Common Core proposes a set of Mathematical Practices that all teachers should develop with their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics and informed by the Strands of Proficiency from Adding it Up from the National Research Council.

5. CCSS Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.

6. Common Core Format
K-8
Grade
Domain
Cluster
Standards
(There are no Pre-K Standards)
High School Conceptual Category Domain Cluster Standards

7. Grade Level Overview

8. Grade Level Overview
Cross- Cutting Themes
Critical Area

9. Format of K-8 Standards
Standard
Cluster
Standard
Cluster

10. Format of High School Standards
Domain
Standard
Cluster

11. Common Core - Domain
Overarching “big ideas” that connect topics across the grades
Descriptions of the mathematical content to be learned, elaborated through clusters and standards

12. Common Core - Standards
Content statements
Progressions of increasing complexity from grade to grade

13. High School Conceptual Categories
The big ideas that connect mathematics across high school
A progression of increasing complexity
Description of the mathematical content to be learned, elaborated through domains, clusters, and standards

14. High School Conceptual Categories
Number & Quantity
Algebra
Functions
Modeling
Geometry
Statistics & Probability

15. High School Pathways
The CCSS Model Pathways are NOT required. The two sequences are examples, not mandates
Two models that organize the CCSS into coherent, rigorous courses
Four years of mathematics:
One course in each of the first two years
Followed by two options for year 3 and a variety of relevant courses for year 4
Course descriptions
Define what is covered in a course
Not prescriptions for the curriculum or pedagogy

16. High School Pathways
Pathway A: Consists of two algebra courses and a geometry course, with some data, probability, and statistics infused throughout each (traditional)
Pathway B: Typically seen internationally, consisting of a sequence of 3 courses, each of which treats aspects of algebra; geometry; and data, probability, and statistics.

17. Answer Getting vs. Learning Mathematics
United States How can I teach my kids to get the answer to this problem? Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management. Japan How can I use this problem to teach mathematics they don’t already know?

18. How might a fourth grader solve these problems?=
-100
145-98=
- 98

19. Students Ideas About Math D. Schifter and M. Riddle
Read pages 28, 29, 30.
STOP at Dig into Content
Go back to Mathematical Practices in the Standards
Find evidence for students’ use of some of the Practices described in the CCSS document.

20. Domain Trace: Number and Operations in Base Ten: Grade 2
Use place value understanding and properties of operations to add and subtract 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

21. Domain Trace Number and Operations in Base Ten Grade 3
Use place value understanding and properties of operations to perform multi- digit arithmetic.
2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

22. Trail Mix Problem
At your tables, begin solving the problem on your own.
Discuss and share solutions and strategies at your table.
Choose one solution to share. Put it on chart paper.

23. Take a BREAK

24. Sharing Strategies
Listen
Connect
Compare

25. Looking at Student Work: Trail Mix Problem
Look at samples of student work
Analyze for evidence of understanding through the CCSS Mathematical Practices

26. A word from our sponsor…

27. LUNCH

28. Using Video to Examine Teacher Practice

29. Framework for Viewing What does the teacher do to foster learning?
What is the impact on student learning?

30. What Are Mathematical Tasks?
Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students’ attention on a particular mathematical idea.

31. Why Focus on Mathematical Tasks?
Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it;
Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information;

32. Why Focus on Mathematical Tasks?
The level and kind of thinking required by mathematical instructional tasks influences what students learn; and
Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

33. “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000
“The level and kind of thinking in which students engage determines what they will learn.” Hiebert et al., 1997

34. The Cognitive Level of Tasks
Lower-Level Tasks
Memorization
Procedures without connections
Higher-Level Tasks
Procedures with connections
Doing mathematics

35. Task Analysis Guide
Read over the Task Analysis Guide and highlight important words, phrases or ideas for each level.
Discuss at your table.
What type of task was the Trail Mix problem? Why?

36. Adapt-a-Task Activity
Choose a standard from the 4th Grade or from the 8th Grade CCSS in Mathematics.
As a group, write a low-level demand task on a large post-it note.
Discuss why the task is low-level demand using the Task Analysis Guide.

37. Adapt-a-Task Three Stay-One Stray
Designate one person as the Traveler. The Traveler takes the group’s low-level demand task and moves to the next table. The rest of the group stays.
The Traveler explains why the task is a low- level demand task to the new group.

38. Adapt-a-Task
The new group creates a high-level demand task from the low-level demand task using the Task Analysis Guide and the CCSS Standards for Mathematical Practices and writes their new task on chart paper.
Facilitator Walk
Facilitators move the charted tasks from table to table.

39. Facilitator Walk (continued)
Table groups evaluate the cognitive level of each task presented by the facilitator using the criteria from the Task Analysis Guide and writes the demand level (M, PwoC, PwC, DM) on a post-it note.
The facilitator moves from table to table adding the post-it notes from each group to their charts.
The facilitators discuss feedback on the tasks with the whole group.

40. Reflection Review of the CCSS in Mathematics
Article - Students Ideas About Math
Trail Mix Problem
Looking at Student Work
Using Video to Examine Teacher Practice
Adapt-a-Task (Low and High Level Tasks)

41. A Sample Plan for Year 1
Explore and integrate at least one Mathematical Practice, into your students’ repertoire of doing mathematics.
Integrate a Mathematical Practice into an existing unit of study in your curriculum map.
Explore and collect mathematical tasks that will support students’ use of the CCSS Mathematical Practices.
Collect student work and integrate looking at student work into your school’s inquiry team work.
Use classroom talk to support the CCSS Mathematical Practices.
Develop one Domain strand trace covering the grade spans of your school (e.g. K-5, K-8, 6-8, 6-12, etc)