An illustration of the basic structure of problem solving. The algebraic operations
of substitution and simplification are done error free using
SureMath - the math software for 21st century problem solving.
The starting equation RESPONDS directly to what is
ASKED FOR and REQUESTS additional information.
The next step RESPONDS to the request.
Supplying the RESPONSE to the requesting equation
produces a RESULT.
The REQUEST-RESPONSE-RESULT structure will solve any problem.
The RESPONSE is shown indented, which indicates that the response is a subproblem of the main problem. This is the same type of logical organization that is familiar in forming a table of contents, an index, an organizational chart, computer programming and many other common methods of presenting information.
An organized presentation of a problem solution enhances communication between the problem solver and himself as well as with users of the solution.
Solving word problems is a simple, straightforward process. It is the communcation of the solution effectively to one's self and others which is challenging. Mathematics provides a language through which the communication can be done.
It is widely asserted that problem solving and using mathematics require quite different logical processes than are used in other endeavors. This fallacy is the principle cause of the preceived difficulty of mathematics and problem solving. This false perception is a cultural thing.