Common Core High School Mathematics: Transforming Instructional Practice for a New Era

1. Common Core High School Mathematics:Transforming Instructional Practice for a New Era School Year Session 2: October 2, 2013 Tasks that Promote and Assess Thinking 1.1

2. Agenda • Homework Discussion • Principles of Task Modification • Break • Assessment Based on Task Selection • District Planning Time • Homework and closing remarks 1.2

3. Homework Discussion Activity 1: • Sit with others teaching the same content as you this semester. • One person places his or her selected tasks face up on the table • Other group members study them individually, in silence, for 1 minute • Discuss the levels of cognitive demand of each task • Repeat, until everyone has presented their tasks 1.3

4. Learning Intentions & Success Criteria Learning Intentions: We are learning to identify the principles of task modification, and of assessment based on task selection Success Criteria: We will be successful when we can select and modify a task to meet the shifts of the Common Core, and build an assessment framework for that task based on the principles by which it was selected.

5. Principles of Task Modification Activity 2: Consider the set of five tasks, A-E, and their modifications in your group. For each modification: • Identify the mathematical goal for the task • Identify the level of cognitive demand and reasons for that categorization • Identify the ways in which the task has changed 1.5 For the original task: Identify the mathematical goal for the task Identify the level of cognitive demand and reasons for that categorization Identify any promising features

11. Principles of Task Modification Activity 2: • Ask students to create real world stories for “naked number” problems • Use an additional representation and make connections between two (or more) representations • Solve an “algebrafied” version of the task • Use a task “out of sequence” before students have memorized a rule or have practiced a procedure that can be routinely applied • Eliminate components of the task that provide too much scaffolding • Provide more opportunities for students to conjecture, think and reason 1.11

12. Break

13. Assessment Based on Task Selection Activity 3: • Two consortia of states have accepted the assessment challenge: • The Standards of Mathematical Practice are STANDARDS that the participating states have signed on to implement. • Placing attention and focus only on content standards is insufficient! 1.13

14. Smarter Balanced Assessment Consortium (SBAC) • 27 states representing 43% of K-12 students • 21 governing, 6 advisory states • Washington state is fiscal agent

15. A Balanced Assessment System

16. Assessment Based on Task Selection Activity 3: Smarter Balanced Assessment Consortium (SBAC) claims about student performance in each of the following categories: Claim 1: Concepts and Procedures Claim 2: Problem Solving Claim 3: Communicating and Reasoning Claim 4: Modeling and Data Analysis We will look at each of these in turn – with a realization of overlap – particularly in classroom application. 1.16

17. Assessment Based on Task Selection Activity 3: • SBAC Claim 1: Concepts and Procedures • Students can • explain and apply mathematical concepts • interpret and carry out mathematical procedures with precision and fluency 1.17

18. Assessment Based on Task Selection Activity 3: • SBAC Claim 2: Problem Solving • Students can • solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies • Note: this is closely related to MP1 1.18

19. Assessment Based on Task Selection Activity 3: • Evidence sought in Claim 2: • Seek evidence of student performing expected routines, etc. 1.19

20. Assessment Based on Task Selection Activity 3: • SBAC Claim 3: Communicating and Reasoning • Students can • clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. • Note: this is an almost verbatim statement of MP3 1.21

21. Assessment Based on Task Selection Activity 3: • SBAC Claim 4: Modeling and Data Analysis • Students can • analyze complex, real-world scenarios • construct and use mathematical models to interpret & solve problems • Note: this is strongly related to MP4 1.22

22. Assessment Based on Task Selection Activity 3: • Evidence sought in Claims 3 & 4: • Student artifacts show students recognize that the task is intended to assess their strategy development • Students demonstrate construction of a sequence of mathematical reasoning, with justifications • Students self-assess their initiative and effort in establishing a strategy, and monitor its effectiveness 1.23

23. Assessment Based on Task Selection Activity 3: • In small groups, rotate through the stations around the room. At each station: • Decide which SBAC claim the task(s) at that station are designed to assess • Write your answer on a post-it note and attach it behind the task(s) 1.24

24. Assessment Based on Task Selection Activity 3: 1.25

25. Assessment Based on Task Selection Activity 3: 1.26

26. Assessment Based on Task Selection Activity 3: 1.27

27. Assessment Based on Task Selection Activity 3: 1.28

28. Assessment Based on Task Selection Activity 3: Analyze the “Shopping Carts” and “Supermarket Cart” tasks through the lens of the SBAC claims. How might each of these tasks be used to provide evidence for one or more of the claims? How are the two tasks similar? How do they differ? 1.29

31. Assessment Based on Task Selection Activity 3: Analyze the higher level task you brought for this week’s homework, through the lens of the SBAC claims. How might that task be used to provide evidence for one or more of the claims? 1.32

32. Learning Intentions & Success Criteria Learning Intentions: We are learning to identify the principles of task modification, and of assessment based on task selection Success Criteria: We will be successful when we can select and modify a task to meet the shifts of the Common Core, and build an assessment framework for that task based on the principles by which it was selected.

33. District Planning Time Activity 4: • Reorganize into your district teams. With them: • Continue your discussion from last time around your chosen focal Standards for Mathematical Practice. • Select one or two of the SMP that you would like to focus your reform efforts on across your district team this year. • As you discuss, consider what you might collect as evidence of student mathematical engagement in your focal SMPs. 1.34

34. Homework & Closing Remarks Activity 5: • Homework: • Read the article Responding to Students’ Work on a Rich Task by Emily Kuper and Patrick Kimani. • As part of your last homework, you selected two tasks (one low-level and one high-level) that you had used in one of your classes. Modify each of these tasks using the principles you discussed this evening, in order to raise the cognitive demand of each of them. (If you have already taught the 2 tasks you brought this week, you should choose 2 new tasks to modify.) Bring your original and your modified tasks to our next session (October 16). • Select a lesson or unit that you will develop and implement as your major project this semester. This should be something you will teach between November 20 and December 4. 1.35