Computational Problem Solving Background

Problem solving is the science of converting a problem statement into a form that is easy to understand and solve. Problem solving is a skill needed in many fields of mathematics, science and engineering. It is particularly important in computer science. One element of successful problem solving is to determine the basic relationships in the problem and express them as algebraic formulas. Sometimes the relationships are straight forward, other times, they are more complex. The chart method of problem solving developed for elementary algebra and used at this site is easy to use and understand. It directly supports problem solving on a computer and is amenable to processing plural data.

Most presentations of story problem charting techniques are organized by the topics in the algebra texts, such as ratios, areas, triangles, etc. However, this site presents the story problems based on the complexity of the solution. There are four classes of complexity based on two formula families. Within each formula family the complexity of the formula, the number of entries in the chart, the length of the solution and the number of charts may vary. The first two classes of problems are based on the two formula families - rate and relational formulas. The third class combines formulas from the first two classes. The data for problems in Class I(rate), Class II (relational or "more than") and Class III (combined relational and rate problems) can be organized into one chart. The problems in Class IV require two or more charts to organize the data.

All problems at this site are solved using the same basic steps. Chart generation is a very important part of problem solving and is discussed in detail. The steps involved in problem solving are presented in a standard solution sequence.