A Logical Problem Solving Strategy

1 Teaching Problem SolvingPage 19A Logical Problem Solving StrategyIntroductionAt one level, Problem Solving is just that, Solving problems. Presented with a Problem youtry to solve it. If you have seen the Problem beforeand you already know its solution, you can solvethe Problem by recall. Much of the time, however,you have never experienced this situation before (ifyou had, you would not call it a Problem ). Solvingreal problems involves making a Logical chain ofdecisions which lead from an unclear situation to asolution. Solving physics problems is not verydifferent from Solving any kind of Problem .

2 In yourprofessional life, you will encounter new andcomplex problems (after all, if your employersknew how to solve these problems, why wouldthey pay you?). The skillful Problem solver is ableto invent good solutions for these new problemsituations. But how does the skillful Problem solvercreate a solution to a new Problem ? And how doyou learn to be a more skillful Problem solver?A Logical Problem - Solving StrategyThe Problem - Solving Strategy presented here isbased on research done in a variety of disciplinessuch as physics, medical diagnosis, engineering,project design and computer programming.

3 Thereare many similarities in the way experts in thesedisciples solve problems. The most importantresult is that experts follow a general Strategy forsolving all complex problems. That is, expertssolve real problems in several steps. Gettingstarted is the most difficult step. In the first andmost important step, you must accurately visualizethe situation, identify the actual Problem , andidentify information relevant to the Problem . Atfirst you must deal primarily with the qualitativeaspects of the situation. You must interpret theproblem in light of your own knowledge andexperience.

4 This enables you to decide whatinformation is important, what information can beignored, and what additional information may beneeded, even though it was not explicitly this step drawing a useful picture of the problemsituation is crucial to getting started correctly. Apicture is worth a thousand words (if it is the rightpicture).In the second step, you must represent theproblem in terms of formal concepts andprinciples, whether these are concepts ofengineering design, concepts of medicine, orconcepts of physics. These formal concepts andprinciples use the accumulated knowledge of yourfield and thus enable you to simplify a complexproblem to its essential parts.

5 Frequently, yourfield has developed a formalized way to diagramthe situation which helps show how the conceptsare usually applied to a Problem . Third, you mustuse your representation of the Problem to plan asolution. Planning results in an outline of the logicalsteps required to obtain a solution. In many casesthe Logical steps are conveniently expressed asmathematics. Fourth, you must determine asolution by actually executing the Logical stepsoutlined in your plan. Finally, you must evaluatehow well the solution resolves the original general Strategy can be summarized interms of five steps.

6 :(1)Comprehend the Problem .(2)Represent the Problem in formal terms.(3)Plan a solution.(4)Execute the plan.(5)Interpret and evaluate the Strategy begins with the qualitative aspects of aproblem and progresses toward the quantitativeaspects of a Problem . Each step uses informationTeaching Problem SolvingPage 20gathered in the previous step to translate theproblem into more quantitative terms and to clarifythe decisions which you must make. These stepsshould make sense to you. You have probablyused a similar Strategy , without thinking about it,when you have solved problems Importance of WritingSolving a Problem requires that you constantlymake decisions.

7 This is very difficult to do if youmust also remember many pieces of informationand the relationships between those pieces ofinformation. Soon you overload your brain whichhas only a small number of short term memorylocations. You could forget important parts of theproblem or the steps in a mathematical chain of decisions you construct may evenhave Logical flaws. Drawing pictures and diagramsand writing your procedures using words, symbols,and mathematics makes the paper a part of yourextended memory. Your brain is then free to dealwith the decision-making process.

8 The singlebiggest mistake of novice Problem solvers is notwriting down enough in a form which is organizedto be a useful aid to their memory. If you have hadthe experience of understanding how to solve aproblem when someone shows you how but getting lost when you try to do a similar problemyourself, the effective use of writing could be yourprimary Physics-Specific StrategyEach profession has its own specializedknowledge and patterns of thought. Theknowledge and thought processes that you use ineach of the steps will depend on the discipline inwhich you operate.

9 Taking into account thespecific nature of physics, we choose to label andinterpret the five steps of the general problemsolving Strategy as the Problem : In this step you develop aqualitative description of the Problem . First,visualize the events described in the problemusing a sketch. Write down a simple statementof what you want to find out. Write down thephysics ideas which might be useful in theproblem and describe the approach you willuse. When you finish this step, you shouldnever have to refer to the Problem the Physics: In this step you useyour qualitative understanding of the Problem toprepare for a quantitative solution.

10 First,simplify the Problem situation by describing itwith a diagram in terms of simple physicalobjects and essential physical what you want to find by namingspecific mathematical quantities. Using thephysics ideas assembled in step 1, write downequations which specify how these physicalquantities are related according to the principlesof physics or mathematics. The results of thisstep contains all of the relevant information soyou should not need to refer to step 1 the Solution: In this step you translate thephysics description into a set of equationswhich represent the Problem mathematically byusing the equations assembled in step 2.