Successful problem solvers are methodical, or systematic, in their problem solving. They are as concerned with the techniques they are using as they are with obtaining the right answer. These techniques may involve reorganizing a problem into simpler terms, breaking a problem into steps, making a plan about how to proceed, determining the best way to solve a problem, pulling out key ideas, etc.
Being systematic in problem solving requires students to:
- be alert to details
- preview or predict the outcomes of their actions
- sustain their effort and be goal directed
- look at the problem in different ways before choosing the best way to solve it (inhibiting first responses when necessary)
- pace themselves and self-monitor their answers at each step
Systematic problem solving often involves "step-wisdom," knowing that the best way to solve a particular problem may be to break it up into a series of logical steps, rather than to try to solve it all at once.
A systematic approach to problem solving also involves higher order thinking skills, including thinking strategically, recognizing when a problem calls for a well-thought out solution rather than an automatic response, determining the appropriate steps when breaking down a problem, ordering the steps correctly, and monitoring progress during and after problem solving.
Here are some strategies to help students become systematic in their math problem solving.
- Help students develop "step-wisdom," the ability to know when math problems need to be broken into steps to be solved, rather than done all at once. Work with the entire class to break down sample problems. First, model a step-wise approach. Let students observe how you approach problems (verbalize your steps, explain how you think through each step, etc.). Then, have students do the step breakdown, identifying what needs to be done first, what action or operation should follow next, etc.
- When assigning math activities and projects, give these assignments one step at a time to encourage students to work in stages.
- Provide students with a set of questions they can ask themselves to "jump start" their problem solving, e.g. "What does this question remind me of?", "What am I being asked to do or find?", "What are the important facts or numbers?", etc.
- Provide students with a general strategy which can be used in many problem solving situations, for example, present the following four problem solving steps (Poyla, 1945): (1) Understand the problem, (2) Make a plan for solving the problem based on the information given, (3) Carry out the plan (4) Look back at the solution.
- Teach students about strategies they can use for organizing a word problem before attempting calculations, for example, making a graphic chart that shows the important information, using a personalized checklist of steps, etc.
- Isolate specific steps in problem solving, and have students focus on one step at a time. For example, provide word problem activities in which students identify only what the question is asking them to find, which information is necessary to answer the question, which operations should be used in the problem, or whether or not the answer provided to a word problem makes sense.
- Explain to students that good problem solvers rarely skip steps when problem solving, although it might seem that they do. Instead, problem solvers learn to do steps mentally (in their heads) instead of writing them down or talking about them. Suggest that with experience, students may learn to do this, too.