Problem Solving Process
In my experience, when I talk about problem solving, many of my colleagues think I am speaking of word problems. I take a minute to explain to them the difference; word problems are math exercises that embed numeric equations into a variety of questions, and problem solving involves implicitly teaching students strategies to solve a variety of problems. Yes, word problems are an important part of problem solving and students do need to that can be useful to follow in order to become successful when they begin the problem solving process. They were most famously formulated by George Polya.4
In my classroom, I have found that Polya’s heuristics5 are appropriate and useful tools for my students in order for them to begin to understand a problem and what is being asked from the problem. These tools can be: draw a picture, look for patterns, make a chart or graph, guess and check, work backwards, make a list, choose an operation. Each strategy is introduced along with several problems that lend themselves to that specific strategy. I also provide my students with a graphic organizer to help them organize and make sense of the problems. I am not a big fan of teaching key words because there are always many, many problems that do not fit the key word rules, and it short circuits the thinking process involved in understanding the problem. I think this also teaches students to focus on a set of words and not to think holistically of the problem. This approach is both inadequate and misleading.
Polya’s ideas include: Understand the Question: students need to read the questions carefully and develop an understanding of what the question is asking. This, by far, is the most important step. Students need to understand the question. Many misconceptions and errors began when students answer a different question than what was being asked.
Choose a Plan: as students begin to work with the problem, they need to decide which strategy will best aid them.
Try your Plan: this is the place in the problem solving process that students put their ideas into action. They are thinking about each step as they proceed and continue or make changes if necessary.
Check your Answer: Once students come to a solution they need to ensure their response is accurate. They should ask themselves some questions to guide their thinking. Did you answer the question that was asked? Does your answer make sense? Did you remember to use the correct units? Then they should redo the problem another way and try to get the same answer and check your math work for small errors
After the solution has been determined students should then, Reflect: Think about what you have done and what you have learned. After a reasonable number of problems have been dealt with, this is also an opportunity to deepen understanding by thinking about how this problem relates to previous problems. Also, students should ask themselves if there is anything they are still confused about.
Comments: