1 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades The National Council of Supervisors of Mathematics The Common Core State Standards Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades

2 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Module Evaluation Facilitator: At the end of this Powerpoint, you will find a link to an anonymous brief e- survey that will help us understand how the module is being used and how well it worked in your setting. We hope you will help us grow and improve our NCSM resources!

3 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Common Core State Standards Mathematics Standards for Content Standards for Practice

4 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Today’s Goals: To explore the mathematical standards for Content and Practice To consider how the Common Core State Standards (CCSS) are likely to impact your mathematics program and plan next steps In particular, participants will Examine how robust problem solving tasks develop students’ fluency with the Standards for Mathematical Practice

5 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Standards for Mathematical Practice “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” (CCSS, 2010)

6 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Standards for Mathematical Practice 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.

7 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Structuring the Practices

8 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Standards for Mathematical Practice 1. Individually review the Standards for Mathematical Practice. 2.Choose a partner at your table and discuss a new insight you had into the Standards for Mathematical Practice. 3.Then discuss the following question. What implications might the Standards for Mathematical Practice have on your classroom?

9 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Part and Whole Task Level B Maggie and Lexie were making funny shapes out of flat clay. They decided to play a game. Maggie would make a flat clay shape and Lexie would have to divide the clay shape fairly by cutting it into two pieces. The pieces would have to be the same size (amount of clay). CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003

10 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Part and Whole Task Level B Using this figure as an example of Maggie’s clay shapes, show where Lexie could make the cut to create two pieces that have the same amount of clay. Explain how you know your solutions are correct and complete. CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003

11 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Part and Whole Task 1.Individually, work on each of the shapes. 2.Then work with a partner to compare your work. Look to see if you can find all the lines that will bisect each shape. Make sure your explanation is mathematically complete, concise, and correct! 3.Consider each of the following questions, and be prepared to share your thinking with the group: a)What mathematics content is needed to complete the task? b)Which problem solving related practices are needed to complete the task?

12 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem Solving from NCTM’s Principles and Standards for School Mathematics “Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings.” NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author. (p. 52)

13 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem Solving from NCTM’s Principles and Standards for School Mathematics “Students should have frequent opportunities to formulate, grapple with and solve complex problems that require a significant amount of effort and should be encouraged to reflect on their thinking.” NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author. (p. 52)

14 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem Solving In Your Classroom What opportunities do your students currently have to grapple with non-routine complex tasks... and to... …. reflect on their thinking and consolidate new mathematical ideas and problem solving solutions?

15 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem of the Month (POM!) POM! is a strategy for engaging students in problem solving. It reaches across a range of grade levels in a school or district, using a series of mathematically related, leveled, non-routine and challenging tasks. Here is how it works: Students in grade x and grade x + 1 work on the first of a series of leveled tasks. Then students in grade x + 1 show students in the next grade, x + 2, what they were able to do with the first task. Together they try to expand/enhance their solutions. Next, they move on to the next level of task and the process is repeated.

16 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades for-teachers/problems-of-the-monthhttp:// for-teachers/problems-of-the-month Problem of the Month! Brian Cooper Vallemar School Grades 7 and 8

17 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem of the Month Working with a partner, review the tasks from Level A through Level E of the “Part and Whole POM!” Identify the nature of the mathematics (content and practice) that students are likely to access as they complete these tasks. What opportunities do these tasks offer students to develop skill with the Standards for Mathematical Practice?

18 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades The Nature of Tasks Used in the Classroom … Tasks as they appear in curricular materials Student learning Will Impact Student Learning!

19 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades But, what teachers do with the tasks matters, too! Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) The Mathematical Tasks Framework Tasks as they appear in curricular materials Student learning Tasks as they appear in curricular materials Student learning Tasks as set up by teachers Tasks as enacted by teachers and students

20 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Student Activity Logs ools-for-teachers/problems-of-the-monthhttp:// ools-for-teachers/problems-of-the-month Problem of Month! Vallemar School Grades 4 - 8

21 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Problem of the Month! How might the POM! and the Summary Activities support the development of the Standards for Mathematical Practice for a broad range of students? What opportunities and challenges for teachers working to implement the CCSS does a Problem of the Month! activity suggest to you?

22 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Teaching with Challenging Tasks ools-for-teachers/problems-of-the-monthhttp:// ools-for-teachers/problems-of-the-month Problem of Month! Ford Long Mathematics Coach Vallemar School Grades 4 - 8

23 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Planning to Support Students’ Opportunity to Learn 1. Review the index of POM task sets, then use the Inside Mathematics website to review the Problem of the Month task sets. dex.php/tools-for- teachers/problems-of-the-month 2. Depending on time, select a task set and design a lesson that offers opportunities for students to develop key content and problem solving related practices.

24 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Next Steps and Resources Review the implications you listed earlier and discuss with your table group one or two next steps you might take as a district, school, and teacher.

25 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Today’s Goals: To explore the mathematical standards for Content and Practice To consider how the Common Core State Standards (CCSS) are likely to impact your mathematics program and plan next steps In particular, participants will: Examine how robust problem solving tasks develop students’ fluency with the Standards for Mathematical Practice

26 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades End of Day Reflections 1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain. 2.Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.

27 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Join us in thanking the Noyce Foundation for their generous grant to NCSM that made this series possible!

28 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Project Contributors Geraldine Devine, Oakland Schools, Waterford, MI Aimee L. Evans, Arch Ford ESC, Plumerville, AR David Foster, Silicon Valley Mathematics Initiative, San José State University, San José, California Dana L. Gosen, Ph.D., Oakland Schools, Waterford, MI Linda K. Griffith, Ph.D., University of Central Arkansas Cynthia A. Miller, Ph.D., Arkansas State University Valerie L. Mills, Oakland Schools, Waterford, MI Susan Jo Russell, Ed.D., TERC, Cambridge, MA Deborah Schifter, Ph.D., Education Development Center, Waltham, MA Nanette Seago, WestEd, San Francisco, California Hope Bjerke, Editing Consultant, Redding, CA

29 National Council of Supervisors of Mathematics Illustrating the Standards for Mathematical Practice: Problem Solving Across the Grades Help Us Grow! The link below will connect you to a anonymous brief e- survey that will help us understand how the module is being used and how well it worked in your setting. Please help us improve the module by completing a short ten question survey at: