1. 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 ca tegori ze them. In additio n , th e sheer ran ge o f problem s we
encounter makes it very difficult to approach problem solving system at icall y. Word
problems in algebra, for example, seem to have little in commo n with the ch o ices
and decisions we face w hen buying a car.
Loosely, a probl em exists when o ur 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 nu al 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 proble m solving as a procl'ss nf change from one sut e to another
helps us underst:md tktt virtually every problem we L'n cou11ter ca n he soln: d h·
using the sam e general str:Hcg despite < IPJ):Irent surLtce differe nces
Eve n though most :1d ul ts possess some form of gencr:tl prohlcm-. t lh-ing st r;lt-
s
l'g·, it i. not the case that :til prohkms arL· similar to on e ;mother. lbthcr. l'xperts
s
:tgree that probl ems differ ith respec t to h1· much struc ture tl w · pro·i<ie tilL'
prohiL·m sol'(:r (ll:tye.o.; , 191-ln) . An ill-defined problem h:1 lll<JrL' th :m Oll L' :tCCL' j)t:thlc
s
solution :md no uni-c-rs;tlh- agrcL·d-on str:ncg· for rea chin g it ( Ki tc lll' ner. Jl)x_-; i
Worldwide ecologictl problems, such as gloh:tl wanning :md o;:o1W <iestructit m . pn )-
IH5

2. IH-1 Parr Tltrcl" Fllst e ring Cognitive Grllwrh
. rer s
F(t.;ll re 8-1 Specificity of problem oring tr
A problem evaluation matrix. fully pre~
-
Well -defined lll·defil'16d
1:rgcly of
pn >blcm
Specificity
Well-defined
I~ Q"'dmot1 OuadrantJ :t rime :t
Th<>rn(m
of solution
Ill-defined L Quadrant2 Quadrant 4
in mud•
functiun
In C<
sdllUS, ~
Dewey's
vide good examples of ill-defined problems because scientists disagree al u n Step 1, P
causes and possible solutions to these problems. A well-defined problem h , of a prol
one correc t solution and a guaranteed method for finding it. Solving a qu:uJ ~­ nature of
equ::nion in algebra class by using the quadratic fo rmula is a good example of ~t developr.
defined problem because a unique solution :m d a guaranteed means o f obtainJo . testing tf.
always exist. the best,
One useful way to clarify problems is to consider the specificity of the pr k:~: and weal
and the specificity of its solution simultaneously by using some form of graph! 1 . 1 A th
resentation. Figure 8-1 illustrates what a problem evaluation matrix might look likt. Chapter
when each dimension is divided into quadrants. Quadrant 1, in which the Pmblt..'l!. those of
and the solution are both well defined , is typical of the min o r proble m, t: Kohler (
e ncounter in our daily lives and, to a certain extent, in the classroom. Using the qua- The mo
dr:uic formula to solve equations falls nicely into this category, as do other exampl~ placed i1
o f everyday problem solving, such as finding a classmate's phone number in the tele- reac h . K
phone book or opening a savings account. But consider other problems. Writing a that COL
long essay fo r a midterm exam more acc urately reflects the kind of activiry that rectly g1
occurs in Quadrant 2, in which the problem is well defined but its solution Is 001 unsucn
'(e.g. , State whether vou agree with the federal government's decision to bur) ceeded
nuclear -;vaste in your state and defend your position). Even more troublesome art behavio
the problems that appear in Quadrant 4, in which neither the problem nor the hr tan did
tio n is well defined. Many of the truly difficult decisions we face individually or col- Thornd
lectively fall somewhere in this category. Because these problems rarely have uni-er- ing the
sally agreed-on so lutions, solving them takes coo peration and compromi e on prompt
everyone's part. Ki'lhler'
time an
nature
solving
HISTORICAL PERSPECTIVES ON PROBLEM SOLVING An•
tional
Thorndike, Dewey, and the Gestalt Psychologists objects
Interest in proble m solving among psychologists and educators developed early in ple wit
the twentie th centurv. One o f the earliest views was proposed by E. L. Thorndike at tach
(1911) , who conducted a series o f experiments in which he observed cats as rhe)' attachi
attempted to escape from carefully constructed wooden crates by pressing a lever form f