The University of Akron

Planning the solutions to mathematical chemistry and physics problems in a systematic way enables students to more frequently solve the problems correctly.

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Systematic Approaches in Problem Solving

Research Findings:
Most of the studies on mathematical problem solving in the sciences have examined processes students use to solve chemistry and physics problems. Mathematical problem solving in biology focuses on genetics, and research on using a systematic approach in solving these types of problems is lacking. Polya in the 1940s suggested the four-step approach described below, which researchers have modified over the years.

In the classroom:
Expert problem solvers take a considerable length of time planning and analyzing a given problem before using mathematics for its solution. Novice problem solvers appear to use cues in the problem to search their memory for a formula or algorithm that they can use to solve the problem. Unfortunately, if superfluous information is given in a problem, this frequently causes them to use an incorrect formula.

Even though it is recognized that students use different types of strategies in solving problem, novice problem solvers can improve their problems solving skills if they do so in an organized way. Such a systematic approach includes: 1) understanding the problem; 2) devised a plan; 3) carrying out the plan; and 4) looking back. In order to understand the problems, students must identify what information is given in the problem, and what is sought. Sometimes drawing a picture (such as a force diagram in physics or a picture of what is happening on the molecular level in chemistry) aids in understanding the problem. Using this information, students then formulate plans for the problem solution. Helping students categorize problems into specific types enhances the planning stage. The final step, looking back, involves checking the mathematics used, the execution of the plan, and the reasonableness of the answer.

These steps are not necessarily sequential in nature. For example, during the planning stage it may be necessary to revert to the understanding phase to recall additional information needed or to eliminate superfluous information. The steps do not come naturally to students, and need to be illustrated and practiced when students are taught to solve problems. In addition, because using a systematic approach requires more time than simply using a formula, care must be taken to assign fewer, but more varied, problems for practice, and to allow more time for problem solving on tests.