CHAPTERS

Problem Solving and Critical Thinking

Historical Perspectives on Problem Solving

Critical Thinking

Summary

Suggested Readings

Every day, we encounter hundreds of problems that range in difficulty from deciding what cereal to eat for breakfast to planning long-term career goals. Because we face so many types of problems, it is often difficult to say with certainty what a problem i ~

or to know h ow to categorize them. In addition, the sheer range o f problems we encounter makes it very difficult to approach problem solving systemat icall y. Word problems in algebra, for example, seem to have little in commo n with the choices and decisions we face when buying a car.

Loosely, a problem exists when our present state differs from a desired state (Bransford & Stein , 198·-i ). Thinking of problem S<.llving in this vVa\ can he helpful for se\·e r;ll reasons. First , it emphasi/.es the con ti nual process of problem so lving. in which we move from ;m initial state to a more cll':lrly defined end st:tte . Second. thinki ng about problem solving as a procl'ss nf change from one sute to another helps us underst:md tktt virtually every problem we L'ncou11ter ca n he soln: d h\· using the same general str:Hcg\ despite <IPJ):Irent surLtce differences

Even though most :1d ul ts possess some form of gencr:tl prohlcm-.st lh-ing st r;lt­l'g\·, it i.s not the case that :til prohkms arL· similar to one ;mother. lbthcr. l'xperts :tgree that problems differ \\ith respec t to h\1\\· much structure tlw \· pro\·i<ie tilL' prohiL·m sol\'(:r (ll:tye.o.; , 191-ln) . An ill-defined problem h:1s lll<JrL' th :m Oll L' :tCCL' j)t:thlc solution :md no uni\-c-rs;tlh- agrcL·d-on str:ncg\· for reaching it (Ki tc lll'ner. Jl)x_-; i Worldwide ecologictl problems, such as gloh:tl wanning :md o;:o1W <iestructit m . pn )-

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F(t.;ll re 8-1 Specificity of problem A problem evaluation matrix.

Well -defined

Specificity of solution

Well-defined

Ill-defined

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vide good examples of ill-defined problems because scientists disagree al u n causes and possible solutions to these problems. A well-defined problem h , one correc t solution and a guaranteed method for finding it. Solving a qu:uJ ~­equ::nion in algebra class by using the quadratic fo rmula is a good example of ~t

defined problem because a unique solution :md a guaranteed means of obtainJo . always exist.

One useful way to clarify problems is to consider the specificity of the pr k:~:

and the specificity of its solution simultaneously by using some form of graph! 1\1 . resentation. Figure 8-1 illustrates what a problem evaluation matrix might look likt. when each dimension is divided into quadrants. Quadrant 1, in which the Pmblt..'l!. and the solution are both well defined , is typical of the mino r problem, \\t:

e ncounter in our daily lives and, to a certain extent, in the classroom. Using the qua­dr:uic formula to solve equations falls nicely into this category, as do other exampl~ o f everyday problem solving, such as finding a classmate's phone number in the tele­phone book or opening a savings account. But consider other problems. Writing a long essay fo r a midterm exam more accurately reflects the kind of activiry that occurs in Quadrant 2, in which the problem is well defined but its solution Is 001

'(e.g. , State whether vou agree with the federal government's decision to bur) nuclear -;vaste in your state and defend your position). Even more troublesome art the problems that appear in Quadrant 4, in which neither the problem nor the hr tion is well defined. Many of the truly difficult decisions we face individually or col­lectively fall somewhere in this category. Because these problems rarely have uni\-er­sally agreed-on solutions, solving them takes cooperation and compromi e on everyone 's part.

HISTORICAL PERSPECTIVES ON PROBLEM SOLVING

Thorndike, Dewey, and the Gestalt Psychologists

Interest in problem solving among psychologists and educators developed early in the twentie th centurv. One of the earliest views was proposed by E. L. Thorndike (1911) , who conducted a series of experiments in which he observed cats as rhe)' attempted to escape from carefully constructed wooden crates by pressing a lever

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