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Here us nother problem that an experienced problem solver can do in the head but the novice needs
to be clear about the steps that are done. Novices emulate the incomplete written presentations of the in the head solutions
and thus cannot handle problems that exceed the capacity of the short term memory.
An enviroment in which reliable problem solving can be learned and used is available in
SureMath - the math software for 21st century problem solving.

Depreciation problem

The solution is started by responding directly to what is ASKED FOR, namely, the value at the end of two years.

Once this is written, it is seen that the depreciation at the end of one year is ASKED FOR. The response to this request is indented, since it is a subproblem which will supply information to the starting equation.

The starting equation is transformed by substitution, or operation, to yield the next state of the solution. Reliable problem solving involves repeated use of changing one state, through applying the production(s) requested by that state, into a new state of the solution.

One solution state -> Production -> New solution state

There often is more than one solution path for a problem. All such paths are equally valid. There is no such thing as the best way or the correct way. Each path provides different insights and may use different mathematical tools.

By solving a problem through different paths one comes to understand the problem, the concepts and analytical tools.

It is useful to return to the display of the solution and compare the transparent solution (blue background) with the textbook solution (yellow background). Much of the process that went into writing the textbook solution remained in the writer's mind. In the transparent solution the processes the writer used are displayed.

It is not at all surprising that students use algorithmic approaches. They are vigorously trained in algorithmic, number manipulation, methods.

The answer book solution provides a very good example. There is no rational justification for the 20% = 1/5 being the first statement in the solution.

Equations Talk!

This problem solution was developed using SureMath,
the problem solving software for the 21st century.

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Copyright 1995. Howard C. McAllister