1. The Inquiry Process Model developed by George Polya (1887-1985) Stage 1: Understand the problem. a) make sure you understand all the words and phrases in the problem; b) identify the important information and the unimportant information; c) determine if any information is missing; d) write the problem in your own words; e) state the question that must be answered to solve the problem.

2. Stage 2: Make a Plan. a) identify possible strategies that apply to the problem; b) decide which main strategy you are going to try. Most problems will involve more than one strategy but there is usually one that is more dominant than the others.

3. Stage 3: Carry Out the Plan. a) work through the problem until you get an answer using the selected strategy; b) record your work as you progress so that you can see at a glance what you have completed; c) if necessary, select a new strategy to be able to continue solving the problem.

4. Stage 4: Look Back. a) reread the problem and check the solution to see that it meets the conditions stated in the problem and that it answers the question; b) ask yourself if the solution you’ve arrived at is logical and reasonable.

5. Characteristics of Good Problems A good problem: requires a student to connect new ideas to previously learned ones; can be solved in many ways; piques a student’s curiosity.

6. Some Reasons for Teaching Through Problem Solving The math makes more sense as it allows students to build connections between what the math is, why it is needed, and how it is applied. Problem solving builds perseverance as students learn that not being able to answer a question instantly does not mean it can’t be done.

7. Reasons (cont’) It introduces the student to the idea that creativity and choice has its place in Mathematics in the same way as it does in other disciplines such as Art and Music. Good problems allow students the opportunity to practice the use of concepts and skills that are often taught in isolation.