1. { Problem Solving Dr. Melanie Maxwell & Dr. Stephen Sher Pythagoras Project Common Core SMP Event July 29 – August 2, 2013 Transitioning from Teacher Problem Solving to Student Problem Solving

2. Today you will be able to:  Extend your understanding of problem solving.  Identify and apply stages of the problem solving process  Identify and apply a variety of problem solving strategies.  Discuss and begin plan for implementing instruction to increase student’s problem skills and aptitude. Objectives

3. { How do we want students to view problem solving? Problem Solving Desired Reality

4. Common Core State Standards Mathematical Practices MP 1 Make sense of problems and persevere in solving them… Students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. CCSS SMP Goals

5. CCSS MP Goals Common Core State Standards Mathematical Practices  Shift the paradigm just knowing algorithms for isolated procedures flexible skills needed for real world problem solving (MP 4- Modeling)  Shift the paradigm from just knowing algorithms for isolated procedures towards flexible skills needed for real world problem solving (MP 4- Modeling)  Math to meet future problems

6. NRC Mathematical Proficiencies NCTM Process Standards (2000) NRC Mathematical Proficiencies NCTM Process Standards (2000) (Adding It Up, 2001) (Adding It Up, 2001) CCSS Mathematical Practices What is “necessary for anyone to learn mathematics successfully” http://www.carnegielearning.com/webinars

7. Problem Solving Reasoning and Proof Communication Connections Representations Build new knowledge Solve problems From a variety Of contexts Apply a variety of Strategies Monitor and Reflect on the Process NCTM Process Standards NCTM Process Standards Fundamental Aspect of math Make and investigate conjectures Develop and evaluate math. conjectures Select and use various types of reasoning and methods of proof Organize and consolidate thinking Communicate coherently and clearly to peers, and others Analyze and evaluate the thinking of others Use the language to express math. ideas precisely Use connections between math. ideas Math. ideas interconnect and build into a coherent whole Recognize and apply math. in contexts outside of math. Create and use representations to organize, record, and communicate math. ideas Select, apply, translate between math. representations to solve problems Model and interpret physical, social, and math phenomena

8. Making Sense -the first step in Problem Solving Representation Reasoning Communication Making Connections within and outside of mathematics

9. { Now! How do we bridge this gap?

10. “Problem” A puzzling, yet intriguing situation for which there is no immediate, apparent solution, yet there are multiple solution paths. (compiled definition) Depth of Knowledge (DOK) perspective  Interaction of task and learner  Varies by grade level, student, and concept Consider a continuum of definitions SimpleComplex Computation, including computation surrounded by words Coordinating a variety of concepts, processes, and tasks.

11. George Pólya Understand the Problem Devise a Plan Carry out the Plan Look Back Activity: Read Standard for Mathematical Practice 1 (SMP 1). Identify correlations between Pólya’s research and SMP 1. Problem Solving Process

12. Problem Solving Strategies Draw a Diagram Act It Out Make a Table or Chart Look for a Pattern Make a Graph Write an Equation Try, Check, Revise Make an Organized List Use Reasoning Work Backwards Solve a Simpler Problem

13. Task: Each team member will solve the problem using the PS strategy they pull from the bag. Reflect on the Focus Questions regarding the strategy or strategies you used. PS Strategies PS Strategies Activity I

14. From Inside Mathematics Snail Pace  Which snail moves more quickly than the others?  Explain how you figured this out.

15. Focus Questions (Metacognition)  How did you start this strategy?  What challenges did you have applying this strategy?  What are the advantages of your strategy for this problem?  What are the disadvantages of your strategy for this problem?  How does this strategy clarify the mathematics in this problem?  What did you need to understand to be able to apply your strategy?

16.  Discuss a focus question with insights from each team member. (No monopolizing the discussion.)  Pick a different focus question, repeat.  Write one sentence summarizing a personal or team “aha!”  Whole group whip around, biggest aha! Debriefing

17. EQ: How do I determine which strategy to use to start solving a problem? Do not solve the problems, just understand and plan. Do not solve the problems, just understand and plan.  Choose a problem.  Identify the strategies you could use to start the problem.  Explain what about the problem made you think to use each strategy.  Choose another problem and repeat the processes. Try to select a problem that would use different strategies.  Goal: Articulate why and how specific strategies help solve certain types of problems. PS Strategies PS Strategies Activity II

18. { How do we create opportunities for students to develop process and strategy skills? Teaching Problem Solving Skills

19.  Solve using _____ strategy then discuss focus questions.  Problem Classification  Explicit direct instruction of PS strategies. (How does it work?)  Consistent use of Think Aloud  Label processes and strategies students use  Discussing possible strategies (which ones, why, how will you start) before solving  Sample problems for students to reference, “It is like the monkey problem.” Ways to Build PS Skills

21. One Method – PS Wall

22. Climate is essential  Establish respectful & courteous talk, no exceptions  Everyone has a right to be heard and their ideas considered with respect  Everyone has the obligation to listen with respect  Respect for person does not mean you agree with them.  “I revised my thinking.”  “I don’t understand....”  “Please clarify ….” Building a PS Environment

23. Be less helpful, but be very supportive.  Teacher guides information, but is not the main source of information when problem solving  Idea sharing poster (thanks to KH)  Build students’ work time (5 min + 5 min +...) Remember the biomolecule of Problem Solving?  Questioning  Knowing mathematical objective  Choosing good tasks  Anticipating student solutions, yet being open to unanticipated solutions Building a PS Environment

24.  Problem solving is...  What do you plan to implement to begin moving from your current reality to a CC reality of students as engaged problem solvers?  What can you explore THIS year?  How will you begin the year? (KISS) Summary & Action Plan