Problem Solving Dr Melanie Maxwell Dr Stephen Sher

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

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

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

CCSS SMP Goals 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 MP Goals Common Core State Standards Mathematical Practices 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

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

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

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

How do we bridge this gap? { Now!

“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 Simple Computation, including computation surrounded by words Complex Coordinating a variety of concepts, processes, and tasks.

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

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

PS Strategies Activity I 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.

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

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?

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

EQ: How do I determine which strategy to use to start solving a problem? Do not solve the problems, just understand 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 Activity II

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

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

One Method – PS Wall

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

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 +. . . ) 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

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