A Problem With Problem Solving Teaching Thinking Without Teaching Knowledge

The Mathematics Educator
2007, Vol. 17, No. 2, 7–14
Jamin Carson 7
A Problem With Problem Solving:
Teaching Thinking Without Teaching Knowledge
Jamin Carson
Problem solving theory and practice suggest that thinking is more important to solving problems than
knowledge and that it is possible to teach thinking in situations where little or no knowledge of the
problem is needed. Such an assumption has led problem solving advocates to champion content-less
heuristics as the primary element of problem solving while relegating the knowledge base and the
application of concepts or transfer to secondary status. In the following theoretical analysis, it will be
argued that the knowledge base and transfer of knowledge—not the content-less heuristic—are the
most essential elements of problem solving.
Problem solving theory and practice suggest that
thinking is more important in solving problems than
knowledge and that it is possible to teach thinking in
situations where little or no knowledge of the problem
is needed. Such an assumption has led problem solving
advocates to champion content-less heuristics as the
primary element of problem solving while relegating
the knowledge base and the transfer or application of
conceptual knowledge to secondary status. Yet if one
analyzes the meaning of problem solving, the
knowledge base and the transfer of that knowledge are
the most essential elements in solving problems.
Theoretical Framework
Problem solving is only one type of a larger
category of thinking skills that teachers use to teach
students how to think. Other means of developing
thinking skills are problem-based learning, critical
thinking skills, creative thinking skills, decision
making, conceptualizing, and information processing
(Ellis, 2005). Although scholars and practitioners often
imply different meanings by each of these terms, most
thinking skills programs share the same basic elements:
(1) the definition of a problem, (2) the definition of
problem solving, (3) algorithms, (4) heuristics, (5) the
relationship between theory and practice, (6) teaching
creativity, (7) a knowledge base, and (8) the transfer or
the application of conceptual knowledge.
The Definition of a Problem
The first element of the theory of problem solving
is to know the meaning of the term problem. This
theoretical framework uses the definition of problem
presented by Stephen Krulik and Jesse Rudnick (1980)
in Problem Solving: A Handbook for Teachers. A
problem is “a situation, quantitative or otherwise, that
confronts an individual or group of individuals, that
requires resolution, and for which the individual sees
no apparent or obvious means or path to obtaining a
solution” (p. 3).
The Definition of Problem Solving
Krulik and Rudnick (1980) also define problem
solving as
the means by which an individual uses previously
acquired knowledge, skills, and understanding to
satisfy the demands of an unfamiliar situation. The
student must synthesize what he or she has learned,
and apply it to a new and different situation. (p. 4)
This definition is similar to the definition of the
eighth element of problem solving, transfer: “[w]hen
learning in one situation facilitates learning or
performance in another situation” (Ormrod, 1999, p.
348).
Problem Solving is Not an Algorithm
One of the primary elements of this framework is
that problem solving is not an algorithm. For example,
Krulik and Rudnick (1980) say,
The existence of a problem implies that the
individual is confronted by something he or she
does not recognize, and to which he or she cannot
merely apply a model. A problem will no longer be
considered a problem once it can easily be solved
by algorithms that have been previously learned.
(p. 3)
Dr. Jamin Carson is an assistant professor of curriculum and
instruction at East Carolina University. He teaches the theory
and practice of instruction as well as classroom management and
discipline. His primary research interest is the epistemology of
curriculum and instruction.

8 Problem Solving
Table 1
Types of Problem Solving
John Dewey (1933) George Polya (1988)
Stephen Krulik and
Jesse Rudnick (1980)
Confront Problem Understanding the Problem Read
Diagnose or Define Problem Devising a Plan Explore
Inventory Several Solutions Carrying Out the Plan Select a Strategy
Conjecture Consequences of
Solutions
Looking Back Solve
Steps in
Problem
Solving
Test Consequences Review and Extend
Additionally, advocates of problem solving imply
that algorithms are inferior models of thinking because
they do not require thought on a high level, nor do they
require deep understanding of the concept or problem.
Algorithms only require memory and routine
application. Further, they are not useful for solving
new problems (Krulik & Rudnick, 1980).
Problem Solving is a Heuristic
Advocates of problem solving argue that educators
need to teach a method of thought that does not pertain
to specific or pre-solved problems or to any specific
content or knowledge. A heuristic is this kind of
method. It is a process or a set of guidelines that a
person applies to various situations. Heuristics do not
guarantee success as an algorithm does (Krulik &
Rudnick, 1980; Ormrod, 1999), but what is lost in
effectiveness is gained in utility.
Three examples of a problem solving heuristic are
presented in Table 1. The first belongs to John Dewey,
who explicated a method of problem solving in How
We Think (1933). The second is George Polya’s, whose
method is mostly associated with problem solving in
mathematics. The last is a more contemporary version
developed by Krulik and Rudnick, in which they
explicate what should occur in each stage of problem
solving. I will explain the last one because it is the
more recently developed. However, the three are
fundamentally the same.
The following is an example of how the heuristic is
applied to a problem.
Problem: Twelve couples have been invited to a
party. The couples will be seated at a series of
small square tables, placed end to end so as to form
one large long table. How many of these small
tables are needed to seat all 24 people? (Krulik &
Rudnick, 1987, pp. 29–31)
The first step, Read, is when one identifies the
problem. The problem solver does this by noting key
words, asking oneself what is being asked in the
problem, or restating the problem in language that he
or she can understand more easily. The key words of
the problem are small square tables, twelve couples,
one large table, and 24 people.
The second step, Explore, is when one looks for
patterns or attempts to determine the concept or
principle at play within the problem. This is essentially
a higher form of step one in which the student
identifies what the problem is and represents it in a
way that is easier to understand. In this step, however,
the student is really asking, “What is this problem
like?” He or she is connecting the new problem to prior
knowledge. The student might draw a picture of what
the situation would look like for one table, two tables,
three tables, and so on. After drawing the tables, the
student would note patterns in a chart. (See below.)
The third step, Select a Strategy, is where one
draws a conclusion or makes a hypothesis about how to
solve the problem based on the what he or she found in
steps one and two. One experiments, looks for a
simpler problem, and then conjectures, guesses, forms
a tentative hypothesis, and assumes a solution.
The fourth step is Solve the Problem. Once the
method has been selected the student applies it to the
problem. In this instance, one could simply continue
the chart in step three until one reached 24 guests.

Jamin Carson 9
Step 2: Explore.
Draw a diagram to represent the problem.
Make a chart, record the data, and look for patterns.
Number of
tables
1 2 3 4 . . .
Number of
guests
4 6 8 10 . . .
Pattern: As we add a table, the number of guests that
can be seated increases by 2.
Step 3: Select a Strategy.
Number of
tables
1 2 3 4 5 6 7
Number of
guests
4 6 8 10 12 14 16
Form a tentative hypothesis. Since the pattern seems to
be holding true for 16 guests, we can continue to add 1
table for every additional guest until we reach 24.
Therefore, we add 4 additional tables for the additional
guests (16 + 8 = 24). Hypothesis: It will take 11 tables
to accommodate 24 guests.
Step 4: Solve the Problem
Number
of
tables
1 2 3 4 5 6 7 8 9 10 11
Number
of
guests
4 6 8 10 12 14 16 18 20 22 24
The final step, Review and Extend, is where the
student verifies his or her answer and looks for
variations in the method of solving the problem; e.g.,
t =
n "2
2
, where represents the number of tables. Or we
could ask for a formula to determine how many guests
we can seat given the number of tables. For example, n
= 2t + 2 or n = 2(t + 1).
Problem Solving Connects Theory and Practice
A perennial charge brought against education is
that it fails to prepare students for the real world. It
teaches theory but not practice. Problem solving
connects theory and practice. In a sense this element is
the same as the definitions of problem solving and
transfer, only it specifically relates to applying abstract
school knowledge to concrete real world experiences
(Krulik & Rudnick, 1980).
Problem Solving Teaches Creativity
Real world situations require creativity. However,
it has often been claimed that traditional classrooms or
teaching approaches do not focus on developing the
creative faculty of students. Advocates of problem
solving, by contrast, claim that problem solving
develops the students’ creative capacities (Frederiksen,
1984; Slavin, 1997).
Successful Problem Solvers Have a Complete and
Organized Knowledge Base
A knowledge base consists of all of the specific
knowledge a student has that he or she can use to solve
a given problem. For example, in order to solve
algebraic problems, one not only needs to know
information about numbers and how to add, subtract,
multiply, and divide, but one must also possess the
knowledge that goes beyond basic arithmetic. A
knowledge base is what must accompany the teaching
of a heuristic for successful problem solving to occur.
Problem Solving Teaches Transfer or How to Apply
Conceptual Knowledge
Transfer, or the application of conceptual
knowledge, is the connecting of two or more real-life
problems or situations together because they share the
same concept or principle. Transfer or the application
of conceptual knowledge helps students see similarities
and patterns among seemingly different problems that
are in fact the same, or similar, on the conceptual level.
Some research about problem solving claim that it
is more effective than traditional instruction (Lunyk-
Child, et al., 2001; Stepien, Gallagher, & Workman,
1993), that it results in better long-term retention than

Problem Solving
10
traditional instruction (Norman & Schmidt, 1992), and
that it promotes the development of effective thinking
skills (Gallagher, Stepien, & Rosenthal, 1994; Hmelo
& Ferrari, 1997).
On the other hand, in Research on Educational
Innovations, Arthur Ellis (2005) notes that the research
base on problem solving lacks definition, possesses
measurement validity problems and questionable
causality, and it fails to answer the claim that
successful problem solvers must have a wealth of
content-specific knowledge. Ellis further notes that
there is “no generally agreed-on set of definitions of
terms” (p. 109), that thinking skills are notoriously
difficult to measure, and that given these first two
problems, it is impossible to trace cause back to any
specific set of curricular instances. Ellis states,
[t]he idea that thinking skills are content specific
and cannot be taught generically must be seriously
entertained until it is discredited. We don’t think
that will happen. And if this is so, how does one
construct content-free tests to measure thinking
skills? (pp. 109–110)
The conclusions of Ellis and other research studies
I will cite later state that it would be impossible to
reinvent solutions to every problem that develops
without recourse to past knowledge. This recourse to
past knowledge is evidence, in itself, that one must not
completely construct reality. One must apply
knowledge that has already been formed by others and
understand that knowledge, or else not solve the
problem. It is this critique that I will invoke in the
following treatment of problem solving. What I hope to
show is that the heuristic for problem solving cannot be
successful if one holds strongly to the theoretical
framework in which it is often situated. Rather, one
must accept that already formed knowledge is essential
to problem solving. In fact, the meanings of problem
solving found in articles and textbooks often convey
this contradiction. On the one hand, it is argued that
problem solving is the antithesis of a content-centered
curriculum. On the other hand, a successful problem
solver must possess a strong knowledge base of
specific information, not merely a generalizeable
heuristic that can be applied across several different
situations.
The Problem With Problem Solving
The main problem with problem solving lies in the
fourth element listed above: problem solving is a
heuristic. Recall that a heuristic is a guideline that may
or may not yield success but, unlike an algorithm, it
does not depend on knowledge of the problem to be
successful. Heuristic is a method of thought that does
not pertain to any specific problems or content. The
element is problematic because it contradicts three
other elements within the theory: the definition of
problem solving, successful problem solving requires a
knowledge base, and problem solving enables learners
to transfer knowledge. Each of these three elements
implies that previously learned knowledge of the
problem is necessary to solving the problem, whereas
use of a heuristic assumes no knowledge is necessary.
I argue, like Peikoff (1985), that there is no way to
separate thinking or problem solving from knowledge.
Just like instruction and curriculum, these concepts
imply one another and cannot be discussed separately
for long. Likewise, to acquire knowledge, one must
think. This is not to say that students cannot construct
knowledge as they solve a given problem, only to say
that often the problems they are presented only require
them to apply existing knowledge. From this
perspective, it must be assumed that students do not
construct all of the knowledge in a given curriculum.
Yet problem solving as a heuristic is the most
cherished aspect of problem solving because it is
content-less. For example, in the preface to
Mathematical Discovery, George Polya (1962), one of
the foremost thinkers on problem solving says,
I wish to call heuristic the study that the present
work attempts, the study of means and methods of
problem solving. The term heuristic, which was
used by some philosophers in the past, is half-
forgotten and half-discredited nowadays, but I am
not afraid to use it.
In fact, most of the time the present work
offers a down-to-earth practical aspect of heuristic.
(p. vi)
Instructional textbooks sometimes play off this
process versus content dichotomy: a teacher can either
teach students to be critical thinkers and problem
solvers or she can teach students more content
knowledge. The authors of one textbook say,
Too often children are taught in school as though
the answers to all the important questions were in
textbooks. In reality, most of the problems faced by
individuals have no easy answers. There are no
reference books in which one can find the solution
to life’s perplexing problems. (Gunter, Estes, &
Schwab, 2003, pp. 128–129)
The dichotomy implies that thinking and knowledge
are mutually exclusive, when in fact critical thinking
and problem solving require a great deal of specific
content knowledge.

Jamin Carson 11
Problem solving and heuristics cannot be content-
less and still be effective. Critical thinking, problem
solving, and heuristics must include a knowledge base
(Fredricksen, 1984; Ormrod, 1999). Including the
knowledge base enables the principle cognitive
function of problem solving—the application of
conceptual knowledge, or transfer—to occur (Peikoff,
1985). However, the degree to which Dewey and Polya
actually believed that a heuristic could be completely
content-less and still be effective is not clear. Further,
many instructional textbooks actually stress the
importance of content knowledge in solving problems
(Henson, 2004; Kauchak & Eggen, 2007; Lang &
Evans, 2006).
The Elements of Problem Solving Revised
Each of the above elements of problem solving
will be reviewed again in light of the relationship
between thinking and knowledge and the research base
on problem solving. Element one, the definition of a
problem, implies that one must have some knowledge
of the problem to solve it. How can one solve a
problem without first knowing what the problem is? In
fact, identification of the problem is what is called for
in the first two steps, Read and Explore, of the
heuristic. In this step, the student first becomes aware
of the problem and then seeks to define what it is or
what the problem requires for its solution. Awareness
and definition comprise the knowledge that is essential
to solving the problem. Consider the effectiveness of
students relative to their respective experiences with a
given problem. The student more familiar with the
problem will probably be better able to solve it. In
contrast, the student new to the problem, who has only
studied the heuristic, would have to re-invent the
solution to the problem.
So the first two steps of the heuristic imply that
one needs a great deal of knowledge about the problem
to be an effective problem solver. In fact, if one wants
to solve the problem for the long term, one would want
to thoroughly study the problem until some kind of
principles were developed with regard to it. The final
outcome of such an inquiry, ironically, would yield the
construction of an algorithm.
The second element, the definition of problem
solving, also implies a connection between thinking
and knowledge. It says that problem solving is
essentially applying old knowledge to a new situation
(Krulik & Rudnick, 1987). However, if knowledge or a
problem is genuinely new, then the old knowledge
would not apply to it in any way. Ormrod (1999)
suggests that the so-called new situation is really the
same as the old in principle. For example, the principle
of addition a student would use to solve the problem 1
+ 2 = 3 is essentially the same principle one would
apply to 1 + x = 3. The form may be different but
ultimately the same principle is used to solve both
problems. If this is the case, then a more proper
element of problem solving would be number eight, the
transfer of knowledge or application of conceptual
knowledge.
The third and fourth elements algorithms and
heuristics are problematic. Krulik and Rudnick (1980)
distinguish between algorithms and heuristics. Unlike
employing an algorithm, using a heuristic requires the
problem solver to think on the highest level and fully
understand the problem. Krulik and Rudnick also
prefer heuristics to algorithms because the latter only
applies to specific situations, whereas a heuristic
applies to many as yet undiscovered problems.
However, an algorithm requires more than mere
memorization; it requires deep thinking too. First, in
order to apply an algorithm, the student must have
sufficient information about the problem to know
which algorithm to apply. This would only be possible
if the student possessed a conceptual understanding of
the subject matter. Further, even if a student could
somehow memorize when to apply certain algorithms,
it does not follow that he or she would also be able to
memorize how to apply it (Hu, 2006; Hundhausen &
Brown, 2008; Johanning, 2006; Rusch, 2005).
Second, algorithms and problem solving are
related to one another. Algorithms are the product of
successful problem solving and to be a successful
problem solver one often must have knowledge of
algorithms (Hu, 2006; Hundhausen & Brown, 2008;
Johanning, 2006; Rusch, 2005). Algorithms exist to
eliminate needless thought, and in this sense, they
actually are the end product of heuristics. The necessity
to teach heuristics exists, but heuristics and algorithms
should not be divided and set against one another.
Rather, teachers should explain their relationship and
how both are used in solving problems.
A secondary problem that results from this flawed
dichotomy between algorithms and heuristics is that
advocates of problem solving prefer heuristics because
algorithms only apply to specific situations, whereas
heuristics do not pertain to any specific knowledge. If
one reflects upon the steps of problem solving listed
above one will see that they require one to know the
problem to be successful at solving it..
Consider the sample problem above to which the
heuristic was applied. If one knows the heuristic
process and possesses no background knowledge of

Problem Solving
12
similar problems, one would not be able to solve the
problem. For example, in the first step of the heuristic
one is supposed to Read the problem, identify the
problem, and list key facts of the problem. Without a
great deal of specific content knowledge how will the
student know what the teacher means by “problem,”
“key facts,” and so on? The teacher will probably have
to engage the student in several problems. Without
extensive knowledge of facts, how does the student
know what mathematical facts are, and how they apply
to word problems, for example?
In the second step, Explore, the problem solver
looks for a pattern or identifies the principle or
concept. Again, how can one identify the pattern,
principle, or concept without already possessing
several stored patterns, principles, and concepts?
Indeed, to a student with very little mathematical
knowledge, this problem would be extremely difficult
to solve. The heuristic would be of little help.
The heuristic says to draw a diagram, presumably
to make the problem more concrete and therefore more
accessible to the student, but without already knowing
what the concept the problem exhibits this would very
difficult, if not impossible. Using the chart with the
data as an example, it would require previous
knowledge in mathematics to be able to construct it. It
seems that the heuristic in this problem is in reality just
another algorithm that the teacher will have to teach as
directly and as repetitively until the students learn how
and when to apply it, which is the very opposite of
what advocates of problem solving want. The same is
also true of step five, Review and Extend. Presumably
if a student could represent this problem in algebraic
form, he or she should also be able to solve the same
problem without recourse to drawing diagrams,
recording data, etc. One could simply solve the
problem right after step one.
The sample problem illustrates what scientists have
discovered about novices and experts. In studies that
examined expert and novice chess players, researchers
found that their respective memories were no different
in relation to random arrangements of chess pieces.
When the pieces were arranged in ways that would
make sense in a chess game, the experts’ memories
were much better. The theory is that an expert chess
player is not a better problem solver, he or she just has
a more extensive knowledge base than a novice player.
He or she is past the rudimentary hypothesis testing
stage of learning, past the problem solving heuristic
stage and is now simply applying algorithms to
already-solved problems (Ross, 2006). The same could
be said for students applying a heuristic to the above
problem. The only ones who could solve it would be
those who use an algorithm. Even if a teacher taught
the heuristic to students, he or she would essentially be
teaching an algorithm.
Advocates of problem solving are not solely to
blame for the misconception between thinking and
knowledge and between heuristics and algorithms. The
misconception is likely due to teachers that have over-
used algorithms and never shown students how they
are formed, that they come from heuristics, and that
one should have a conceptual understanding of when
they should be used, not merely a memorized
understanding of them.
The fundamentally flawed dichotomy within
problem solving probably stems from thinking in terms
of “either-ors.” One side defines appropriate education
as teaching algorithms by having students memorize
when to use them but not why. The other side, by
contrast, emphasizes that thinking for understanding is
preferable to simply memorized knowledge. Perhaps
what has happened in the shift from the former to the
latter practices is the instructional emphasis has shifted
from content to thinking so much that the knowledge
base has been wiped out in the process. Ironically,
eliminating knowledge from the equation also
eliminates the effectiveness of problem solving.
The dichotomy between knowledge and thinking
has also affected elements five and six. Number five
states that problem solving connects theory and
practice. At the core of this element is yet another
flawed dichotomy. Many educators hold that education
should prepare students for the real world by focusing
less on theory and more on practice. However, dividing
the two into separate cognitive domains that are
mutually exclusive is not possible. Thinking is actually
the integration of theory and practice, the abstract and
the concrete, the conceptual and the particular.
Theories are actually only general principles based on
several practical instances. Likewise, abstract concepts
are only general ideas based on several concrete
particulars. Dividing the two is not possible because
each implies the other (Lang & Evans, 2006).
Effective instruction combines both theory and
practice in specific ways. When effective teachers
introduce a new concept, they first present a
perceptual, concrete example of it to the student. By
presenting several concrete examples to the student,
the concept is better understood because this is in fact
the sequence of how humans form concepts (Bruner,
Goodnow, & Austin, 1956; Cone 1969; Ormrod, 1999;
Peikoff, 1993). They begin with two or more concrete
particulars and abstract from them the essential

Jamin Carson 13
defining characteristics into a concept. For example,
after experiencing several actual tables a human
eventually abstracts the concept a piece of furniture
with legs and a top (Lang & Evans, 2006).
On the other hand, learning is not complete if one
can only match the concept with the particular example
of it that the teacher has supplied. A successful student
is one who can match the concept to the as yet unseen
examples or present an example that the teacher has
not presented. Using the table as an example, the
student would be able to generate an example of a new
table that the teacher has not exhibited or discussed.
This is an example of principle eight, the transfer of
knowledge or applying conceptual knowledge.
The dichotomy between theory and practice also
seems to stem from the dichotomous relationship
between the teaching for content-knowledge and
teaching for thinking. The former is typically
characterized as teaching concepts out of context,
without a particular concrete example to experience
through the five senses. The latter, however, is often
characterized as being too concrete. Effective
instruction integrates both the concrete and abstract but
in a specific sequence. First, new learning requires
specific real problems. Second, from these concrete
problems, the learner forms an abstract principle or
concept. Finally, the student then attempts to apply that
conceptual knowledge to a new, never before
experienced problem (Bruner, Goodnow, & Austin,
1956; Cone, 1969; Ormrod, 1999; Peikoff, 1993).
The theory vs. practice debate is related to problem
solving because problem solving is often marketed as
the integration of theory and practice. I argue,
however, it leaves out too much theory in its effort to
be practical. That is, it leaves out the application of
conceptual knowledge and its requisite knowledge
base.
Element six, problem solving teaches creativity, is
also problematic. To create is to generate the new, so
one must ask how someone can teach another to
generate something new. Are there specific processes
within a human mind that lead to creative output that
can also be taught? The answer would depend at least
in part on the definition of create. When an artist
creates, he or she is actually re-creating reality
according to his or her philosophical viewpoint, but
much, if not all, of what is included in the creation is
not a creation at all but an integration or an arranging
of already existing things or ideas. So in one sense, no
one creates; one only integrates or applies previously
learned knowledge. No idea is entirely new; it relates
to other ideas or things. The theory of relativity, for
example, changed the foundational assumptions of
physics, but it was developed in concert with ideas that
already existed. There may be no such thing as pure
creativity, making something from nothing. What
seems like creativity is more properly transfer or the
application of concepts, recognizing that what appears
like two different things are really the same thing in
principle.
On the other hand, it is possible to provide an
environment that is conducive to creativity. Many
problem-solving theorists have argued correctly for the
inclusion of such an atmosphere in classrooms (Christy
& Lima, 2007; Krulik & Rudnick, 1980; Slavin, 1997;
Sriraman, 2001). I only object to the claim that
problem solving teaches creativity defined as creating
the new. It can, however, teach creativity defined as
the application of previously learned principles to new
situations.
Element seven, problem solving requires a
knowledge base, although not problematic is only
neglected within the theory of problem solving. This is
ironic given how important it is. Jeanne Ormrod (1999)
says, “Successful (expert) problem solvers have a more
complete and better organized knowledge base for the
problems they solve” (p. 370). She also relates how
one research inquiry that studied the practice of
problem solving in a high school physics class
observed that the high achievers had “better organized
information about concepts related to electricity” (p.
370). Not only was it better organized, the students
were also aware of “the particular relationships that
different concepts had with one another” (Cochran,
1988, p. 101). Norman (1980) also says,
I do not believe we yet know enough to make
strong statements about what ought to be or ought
not to be included in a course on general problem
solving methods. Although there are some general
methods that could be of use…I suspect that in
most real situations it is…specific knowledge that
is most important. (p. 101)
Finally, element eight, problem solving is the
application of concepts or transfer, is also not
problematic; it too is only neglected within the theory
of problem solving. Norman Frederiksen (1984) says,
for example, “the ability to formulate abstract concepts
is an ability that underlies the acquisition of
knowledge. [Teaching how to conceptualize] accounts
for generality or transfer to new situations” (p. 379).
According to this passage, it is the application of
conceptual knowledge and not the heuristic alone that
as Frederiksen says, “accounts for generality or

Problem Solving
14
transfer,” (p. 379) which the advocates of problem
solving so desire.
Conclusion
Problem solving would be more effective if the
knowledge base and the application of that knowledge
were the primary principles of the theory and practice.
Currently, it seems that a content-less heuristic is the
primary principle, which, as I have argued, is
problematic because it dichotomizes thinking and
knowledge into two mutually exclusive domains. In
fact, in the course of solving any problem one will find
themselves learning of all things not a heuristic, but an
algorithm. In other words, teachers must not only teach
students the heuristic and set their students free upon
the problems of everyday life. Rather, teachers must, in
addition to teaching students sound thinking skills,
teach them what knowledge in the past has been
successful at solving the problems and why.
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