The ultimate goal of the Problem of the Week curriculum is to improve students' performance at solving problems correctly. I believe this happens over time and with practice. I also believe that the act of writing it out helps my students’ internalize their learning . The specific goals of problem solving in mathematics are to:
• Improve students’ willingness to try problems and improve their perseverance when solving problems.
• Improve students’ self-concepts with respect to the abilities to solve problems.
• Make students aware of the problem-solving strategies.
• Make students aware of the value of approaching problems in a systematic manner.
• Make students aware that many problems can be solved in more than one way.
• Improve students' abilities to select appropriate solution strategies.
• Improve students’ abilities to implement solution strategies accurately.
• Improve students’ abilities to get more correct answers to problems.
MATHEMATICAL PROBLEM DEFINED
A problem is a task for which:
• The person confronting it wants or needs to find a solution.
• The person has no readily available procedure for finding the solution.
• The person must make an attempt to find a solution.
FOUR PHASES IN SOLVING A PROBLEM
In solving any problems, it helps to have a working procedure. I teach the following
4-step procedure: Understand it, Plan it, Try It, and Look Back at it.
UNDERSTAND IT: Before you can solve a problem you must first understand it. Read and re-read the problem carefully to find all the clues and determine what the question is asking you to find. What is the unknown? What are the data? What type of problem is it?
PLAN IT: Once you understand the question and the clues, it's time to use your previous experience with similar problems to look for strategies and tools to answer the question. Do you know a related problem?
TRY IT: After deciding on a plan, you should try it and see what answer you find. Can you see clearly that the step is correct? But can you also prove that the step is correct? Is the answer reasonable? Are there other answers? Can you check the result? Can you derive the result differently?
LOOK BACK AT IT: Once you've tried it and found an answer, go back to the problem and see if you've really answered the question. What was interesting or hard about this problem? What was surprising? What did you learn from solving the problem? How might you approach the problem differently next time?
PROBLEM SOLVING STRATEGIES
1. Make a table
2. Make an organized list
3. Look for a pattern
4. Guess and check
5. Draw a picture or graph
6. Work backwards
7. Solve a simpler problem