CCSS Verbs of Math: Habits of a Mathematical Thinker

1. CCSS Verbs of Math: Habits of a Mathematical Thinker July 30 - 31, 2013

2. Our Presenters • Sean Timmons • Project Coordinator, STEM • Carolyn Viss • Project Coordinator, Mathematics

3. Goals and Outcomes • Establish familiarity with the Common Core Standards for Mathematical Practice (SMP) • Distill key elements of each SMP • Analyse assessment items through the lens of the SMP • Identify SMP in an instructional segment • Refine an existing lesson or task to more fully align with one or more SMP

4. Two Types of Math Standards • Vary by grade level and conceptual category • Describe what students should know, understand, and be able to do at that grade level • Same eight standards common to all grade levels K-12 • Capture: • Mathematical processes • Habits of mind and thinking skills specific to math Math Content Standards Standards for Math Practice

5. Focusing on our Materials • Let's take a moment to walk through our Common Core spirals for mathematics. • Where are the Standards for Mathematical Practices located? • Let's also locate the Standards for Mathematical Practices grade-level overview and mark its location.

6. Standards for Mathematical PracticeSean Timmons

7. Standards for Mathematical Practice • Place an emphasis on student demonstrations of learning that describes their thought process. • Require students to develop the disposition to acquire a deep, flexible, and enduring understanding of mathematics. What is the focus for the practices? adapted from Briars & Mitchell (2010) Getting Started with the Common Core State Standards

8. Let's look at the eight standards. • 1. Make sense of problems and persevere in solving them. • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 6. Attend to precision. • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning. Standards for Mathematical Practice:

9. The Verbs in Mathematics The practice standards describe actions that: • require students to think differently about mathematics. • ask students to solve problems and apply mathematics. • are crucial to developing an enduring understanding of mathematics.

10. The Verbs in Mathematics • Let's look at an example: • Standard for MP6: Attend to precision • Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

11. Taking a Closer Look • Let's take a look at the Standards for Mathematical Practices. • After carefully examining the Standards for Mathematical Practices, summarize your standard or your thoughts.

12. Working Together • In groups of two, take a moment to share your thoughts and understanding about the practices. • Summarize your thoughts and understanding about the practices in the "Pair" section. • Together, develop a common understanding about your Standard for Mathematical Practices and record it in the "Share" section.

13. Developing a Collective Understanding Create a poster for your standard. Please be prepared to present a 1-2 minute presentation to the group.

14. Why are the math practices important? The Hunt Institute and Council of Chief State School Officers (CCSSO)

15. Reflection and Discussion • Take a moment to think about the Standards for Mathematical Practice. • How will math teaching and learning change in your classroom or at your site? • Take a moment to discuss the implications of this change with your table group.

16. Analysing the Assessment, Identify the SMPs in Instruction, and Refining Existing ActivitiesCarolyn Viss

17. Will this be on the test? Find X

18. Smarter Balanced Assessment Consortium SBAC • Consider some sample tasks and look for alignment to Standards for Mathematical Practice • www.smarterbalanced.org

19. Grade 3, CCSS3.NF.3a smarterbalanced.org sample equiv fractions

20. Grade 6: CCSS 6.SP.3 smarterbalanced.org sample sandbags

21. Grade 6: CCSS 6.SP.3 Scoring Rubric

22. Grade 6 Performance Task Taking a field trip smarterbalanced.org sample field trip

23. SMP in the Classroom As you reflect on the types of tasks students will be required to do, consider the implications for classroom instruction. • What are the teacher's actions? • What are the students' actions?

24. Dip into the Classroom Identify Standards for Mathematical Practice in a lesson • SMP 2 Reason abstractly and quantitatively • SMP 3 Construct viable arguments and critique the reasoning of others • SMP 6 Attend to precision InsideMathematics.org Stephanie Letson, 2nd Grade

25. Dip into the Classroom • Identify Standards for Mathematical Practice in a lesson • Dave Younkin, 4th grade, Public School 234 NY

26. Dip into the Classroom Consider a math task or activity that: • exemplifies one or more of the standards for mathematical practice • your students will be tackling in the next weeks How might you modify the task to more fully align with the SMP?

27. ...not to reinvent the wheel

28. Task Analysis

29. Reflection on Shifts • Reflect on shifts you see in the transition from 1997 Standards to CCSS. • Create a seven word bumper sticker summarizing the shift you see in mathematics as we transition into the Common Core

30. Contact Information • Carolyn Viss • cviss@stancoe.org • Sean Timmons • stimmons@stancoe.org