problem solving
index To algebra

This problem sequence provides instruction
on how to start a problem solution.

Starting a problem solution is the simplest, least time consuming-part of solving a problem. Starting a problem solution consists of applying the following two steps.

STEP 1: Identify what the problem asks for.

Scan the problem looking for action words such as find, determine, show that, where, how.and similar words. What is asked for follows such words. What is asked for will precede a question mark if one is present.

Skip over any phrases beginning with constraining words such as if, assuming, given that and similar words.

Do not try to understand the problem. All you want to know at this step is what the problem asks for. This is the first Request in the problem solution.

STEP 2. Respond to the request in the simplest manner possible.

Respond to the Request by first asking yourself How Would I Find Out?
To answer the question, "How Would I Find Out?" first look in the problem statement. In word problems in elementary school, middle school, introductory/intermediate algebra and in real life problems, the answer to "How Would I Find Out?" is frequently in the problem statement. If the answer to "How Would I Find Out?" is not in the problem statement, one must find it in knowledge space.
Knowledge space consists of principles of the subject, dictionaries, encyclopedias, the internet, previous experience and common sense. In reading a problem solution steps in the solution that use words such as clearly, certainly, obviously, it can be shown that, we know that, from chapter xx, and scientist know, came from the knowledge space of the author of the problem solution. This type of step often confuses the reader since the reader may not have access to the elements of knowledge space the author used.
If more than one response is possible, choose the simplest response.
Problems which have several ways of answering the question, "How Would I Find Out?" provide an excellent opportunity to become skilled in problem solving.

In group problem solving, have the groups collectively identify valid responses to what is asked for. Then have different groups develop the problem solution starting with a particular response to what is asked for. When completed, the groups can compare the solutions and identify the most elegant solution. This will frequently be the one that started with the simplest response.

Once a problem is started the response will ask for additional information. One is then in the same position as in starting a problem. The new request is a subproblem of the problem. Dealing with this is done in the same way as starting a problem. STEP 1 is used to identify what the response asks for. With this identified, STEP 2 is used. Answering the question "How Would I Find Out?" is needed. The answer may be either in the problem statement or in knowledge space. In subject matter courses such as physics and chemistry the response is most commonly in knowledge space.

Repeated use of the two steps leads one through the solution of the problem.The Result can then be generated. The 3 R's of problem solving


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