2.2.6 Overview of Problem Solving

by Jim Morgan (Civil Engineering, Texas A&M University) and
Barbara Williams (Biological & Agricultural Engineering, University of Idaho)

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Problem solving is a process whereby a “best” outcome is determined for some situation, subject to certain constraints. Many models for problem solving exist, differing in their emphasis and in the sequence of steps employed. The steps in some of the models are more difficult to employ than others, making them less accessible to less experienced practitioners. There are two distinct types of problem solving: analytical and open-ended. Analytical problem solving yields one correct answer and therefore tends to be more discipline-specific, whereas open-ended or creative problem solving can lead to multiple solutions and therefore draws on a wide variety of cognitive, affective, and social skills. One can see important differences in the levels of skill development and skill integration required among these domains by noting the behaviors of novice and expert problem solvers.
 

Table 1  Affective and Social Questions in Problem Solving

Divergent Questions Convergent Questions What can I/we do better? Which problems do we have influence to change? What information do you/we need to know? What concerns can be grouped together? Why haven’t you/we already solved this? Which problem do we want to work on? What are some ways to do this differently? Which ideas really appeal to you/us? What are the key decision points? Which idea is most relevant? What are sources of assistance/resistance? What steps need to be taken by whom and when?

Importance of Problem Solving

Many employers have long regarded problem solving, critical thinking, and the ability to work on teams as critical workforce competencies (SCANS, 1991). Despite the importance of problem solving, many educational analysts and industry representatives report that students leave higher education with an underdeveloped ability to solve open-ended problems (CAHE, 2005). In part, this arises because instructors of undergraduate courses prefer students to construct knowledge through single-answer analytical problem solving before they address more complicated open-ended problems that require higher levels of knowledge (2.2.2 Elevating Knowledge from Level 1 to Level 3). Both analytical and open-ended problem-solving methods are more effective when they have process steps that are well-defined and are carried out in a systematic fashion, when there are specific strategies that prompt the practitioner to effectively carry out the steps, and when these strategies invite practitioners to take stock of strengths and weaknesses in aspects of the problem-solving process (2.3.7 Learning Processes through the Use of Methodologies).

What Constitutes a Problem?

When most students, and many faculty members, think of problem solving, they imagine a homework exercise with a single correct answer. Working out homework exercises can be considered problem solving to the extent that this activity reinforces the use of standard equations and cultivates specific problem-solving skills such as pattern recognition. However, open-ended problem solving presents a higher level of challenge because it requires the problem solver to respond to situations which are completely new to him or her (2.2.3 Developing Working Expertise (Level 4 Knowledge)). The following definition by Woods captures this essence. “The problems that we focus on to solve are ones where there is no immediately apparent procedure, idea, or routine to follow; if one has an idea how to solve ‘the problem,’ then this problem is simply an exercise. What we call a problem is a real challenge; it is a situation where we really have to struggle to define it, figure out what it means, and resolve it”.

Open-ended or creative problem-solving involves resolution of a discrepancy between one’s expectations and the reality of one’s situation; of a gap between participant expectations (future state) and participant preparation (current state). Newell and Simon stress the importance of this gap in their definition of problem solving; to them it is “a situation where a person desires to resolve a gap between a goal state and an initial state. Some blockage in the gap prevents the person from immediately seeing a course of action. If there is no blockage, then the situation is an exercise, not a problem” (Newell & Simon, 1972). Where analytical problem-solving tends to invoke cognitive skills primarily, open-ended problem-solving involves significant social and affective dimensions.

The affective and social dimensions resulting from having to address an ill-defined gap or blockage are presented in Parnes’ (1992) survey of creative problem solving. Activities such as objective finding, fact finding, problem finding, idea finding, solution finding, and acceptance finding are framed in terms of divergent and convergent questions that connect with individual and group values. Sample questions are posed in Table 1.

Table 2  Selected Methods for Problem Solving

Inspiration Method	Polya Method	Woods Method	Myrvaagnes Method
Preparation Incubation Inspiration Verification	Define plan Plan Carry out plan Look back	Define problem Think about problem Devise plan Carry out plan Look back	Define the problem Identify key issues Collect/assess information Identify assumptions Break problem into parts Model Sub-problems Integrate Solutions Test/validate Generalize the Solution Communicate the Solution

Methods for Problem Solving

Many problem-solving methods are found in the literature (Woods, 2000). Four methods of varying complexity are summarized in Table 2. The inspiration method is described by Rubenstein (1975) and is attributed to Descartes. It consists of 4 steps as shown; the essential step (inspiration) is often depicted as a light bulb blinking on. Unfortunately this is how many students view the solution of open-ended problems: that only a genius can solve them. The other three methods have less ambiguous steps that are more easily conceptualized and practiced.

While the methods of Polya, Woods, and Myrvaggnes regard the first step in identifying a problem to be defining it, this is often not obvious. A problem solver may have only glimpses of symptoms and a request to “fix it.” For example, when a medical doctor performs a diagnosis, he or she observes the symptoms, reviews possible causes of these symptoms, and looks for other evidence that points toward the same possible cause until the problem appears. Even when the problem to be solved is clear, one must practice to develop skills needed to determine the usefulness of the available information, realize what information is not given, subdivide the problem, model alternative solutions, test the viability of solutions, and generalize results. As a problem solver becomes more experienced, the titles of each step in the method are sufficient to keep the process of solving the problem progressing. For novices, however, more scaffolding is needed for each step.

The benefit of Polya’s “plan” step, the “carry out plan” step, and the implied iteration in the “look back” step is supported by the fact that “many a guess has turned out to be wrong but is nevertheless useful in leading to a better one.” The “think about it” step in the Woods method (Stice, 1987) involves asking three critical-thinking questions that help to direct learning that is required to solve the problem, and actions that should be part of the plan:

What are the attributes of the problem?

What area of knowledge is involved?

What information should be collected?

Myrvaagnes (1999) further dissects the “think about it” step to include identifying key issues, assessing information, identifying assumptions, and subdividing the problem. His steps to “model sub-problems” and “integrate solutions” further explicate the “carry out plan” step. Similarly, his “test/validate” step, “generalize the solution” step, and “communicate the solution” step further inform assessment-minded thinking in the “look back” step (4.1.9 SII Method for Assessment Reporting).

What is often surprising to those observing a problem solver is the fact that obtaining the solution is not the last step. Ordinarily the relief at obtaining a solution would be cause for celebration, especially when the problem involves a new situation. However, the first solution identified is often not the best solution. For a solution to be defended as sound, it is important to validate the solution, look back, generalize, and document the solution for review by a wider audience.

Problem-Solving Skills

Problem solving is a complex performance that is built from a diverse set of cognitive and affective skills (2.5.3 Distinguishing Between Problem Solving, Design, and Research). Table 3 highlights learning skills drawn from the Cognitive Domain (2.3.4) associated with problem solving.

Woods (2000) recognizes the importance of what he calls “attitudes” that can promote or inhibit problem solving. As shown in Table 4, these are Affective Domain (2.3.6) skills that fall under self-development, emotional management, valuing self, and valuing others. To the extent that problem solving occurs in an interpersonal environment, a variety of Social Domain (2.3.5) skills, such as those outlined in Table 5, are also critical in problem solving.

Differences Between Novices and Experts

Stice (1987) and Woods (2000) suggest that successful problem solvers possess some or all of the following characteristics listed in the first column of Table 6. However, there are significant differences in the ways novices and experts manifest these characteristics.

Novices and experts differ significantly in their initial approaches to problem solving. When faced with a problem, the novice gets right to work, and is motivated not to waste time on mistakes or blind alleys. To an observer, the novice appears to be working hard. Ironically, the expert does not appear to be doing much, or making much, if any, progress. The expert rereads the problem multiple times, draws pictures and sketches, invests time building a knowledge base surrounding the problem, and explores parallel solution paths. At some point, the expert may produce a solution that appears to come out of nowhere. The two other most significant differences between the novice and expert are in their use of reflective thinking and their level of confidence in their ability to ultimately find an acceptable solution.

Concluding Thoughts

Rarely do expert problem solvers stop to share their process for problem solving. This leads many to believe that problem solving is trivial, and others to believe it is innate and magical. By making explicit the methodologies one uses, along with the diverse array of cognitive, affective, and social skills that are invoked in creating a solution, one can give others the opportunity to see the process of problem solving more clearly and more deeply. The Methodology for Creating Methodologies (2.4.16) offers advice for capturing this type of expert knowledge and promoting reflective thinking for those who are learning the process.

References

Commission on Accountability in Higher Education. (2005). Accountability for better results: A national imperative for higher education. Boulder, CO: State Higher Education Executive Officers.

Myrvaagnes, E., with Brooks, P., Carroll, S., Smith, P. D., & Wolf, P. (1999). Foundations of problem solving. Lisle, IL: Pacific Crest.

Newell, A., & Simon, H. A. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.

Parnes, S. (1992). Source book for creative problem solving: A fifty-year digest of proven innovation processes. Buffalo, NY: Creative Education Foundation.

Polya, G. How to solve it (2^nd ed.). NJ: Princeton University Press.

Rubinstein, M. F. (1975). Patterns of problem solving. Englewood Cliffs, NJ: Prentice-Hall.

Secretary’s Commission on Achieving Necessary Skills (SCANS). (1991). What work requires of schools: A SCANS report for America 2000. Washington, DC: Department of Labor.

Stice, J. (1987). Developing critical thinking and problem-solving abilities: New directions for teaching and learning #30. San Francisco: Jossey-Bass.

Woods, D. R. (2000). An evidence-based strategy for problem solving. Journal of Engineering Education, 89, 443-459.

 

Table 3  Problem-Solving Skills in the Cognitive Domain

 

Table 4  Problem-Solving Skills in the Affective Domain

 

Table 5  Problem-Solving Skills in the Social Domain

 

Table 6  Differences Between Novice and Expert Problem-Solvers