Nature and Scope

The notion which holds that solutions depend on how they are represented in the human mind is one of the most enduring contributions of psychology to modern study of problem-solving. Representation involves the way or way people think about, perceive, visualize, and conceptualize the problem and methods of its resolution. This entails that depending on the nature of a problem and its representation, not all people would solve one problem in the same way. Equally, it is important to understand and appreciate the exact nature of a problem itself prior to seeking the desired solution. There are several categorizations of the nature of problems. One theory proposes a two-theme category: adversary and non-adversary. Adversary problems involve two or more people competing, such as in the game of chess or football; and non-adversary problems are intricate or complex and most people fall in this category of problem presentation [7].

The other theory proposes a categorization in which problems are defined in accordance to their nature and scope of representation [10]. On the one hand, structured problems are well defined and predictable. A person can follow a step-by-step procedure to solve them, and there is usually a correct answer or solution to the presenting problem. The initial information becomes part of the problem statement. Alternatively, a person needs to apply multiple strategies or combination mix to achieve the goal, and there is usually a correct answer or solution to the presenting problem provided the relevant information is gathered in the process. On the other hand, unstructured problems are mostly ill-defined and vague with unclear goals. The person needs to apply multiple perspectives and strategies and may yield many correct answers or solutions due to their complexity, intricacy and magnitude. Most people experience this latter category of situational factors, essentially because the problems are illdefined, unclear and require substantial domain knowledge and intuition to their resolution and sustenance [11].

Problem-solving involves the steps, actions and strategies a person implements to get from the initial state, which is the onset of a problem, to the desired goal which is the resolution of a problem. The solution to a given problem represents sequential actions that emanate from the initial state, along the branches of a problem-tree, to achieve the desired goal [7]. The modern concept of problem-solving has shifted to represent a complex mental activity consisting of a variety of cognitive skills and actions [10]. It represents higher order thinking skills and actions such as abstraction, visualization, association, comprehension, manipulation, generalization, analysis and reasoning. This underscores the complexity of problem-solving, because it involves mental activity with a variety of cognitive skills in its interpretation, achievement and sustenance.

There are many models used to describe problem-solving by different proponents. This discourse advocates for a three-step process (Figure 1). The process is complementary and influences each step to yield preferred solutions after application of relevant strategies and interventions. The three steps are: problem space, problem state, and strategies. The problem space represents the nature and scope of a presenting problem. Its presence is characterized by varying states in prognosis from onset of the problem to its resolution, and application of appropriate strategies. Generally, people solve the presenting problem by searching in the problem space which oscillates between the three steps of problem-solving. The rules and actions that help people in their searching in the problem space are known as guides or operators. It is an accepted truism that the problem space can be very large to the extent of overwhelming limited capacity of the working memory. Given the limitations of information storage and retrieval, how do people manage to search in the problem space of an intricate nature when chances of forgetting are high; and how do they choose appropriate guides. For most problems, people possess domain knowledge that helps in deciding what to do. Experience and resilience play a reasonable part too. For novel problems, the selection of guides focusses at cognitive shortcuts or common heuristics.

The second step, known as the problem state, is descriptive and applicable in many respects and consists of three states. The first stage in this process is called the initial state that stimulates the connections prevailing at the outset of a problem. It is the problem state which is crucial in that it describes the presenting problem and possible avenues of its resolution. This step is strengthened by the third step, strategies, which are to be applied in solving the presenting problem. The initial state represents basic information, experiences, reactions, assessments, and options that would help to contextualize the nature and scope of any given problem. Depending on the nature and scope of a problem and its representation, the application of strategies involves gathering new or additional information and formal consultation so as to enhance the knowledge base about the presenting problem, including recall of how a similar problem was solved in the past and the appropriate strategies applied at that time or in those circumstances and conditions.

From the initial state then comes the intermediate state. This is a process in which strategies are defined in the context of what actions, decisions, and remedies are to be undertaken or implemented to narrow gaps between the initial state and the goal state. Depending on the nature and scope of a problem and its representation, the intermediate state involves development of sub-goals, review of alternative options, generating an action plan, implementation and appraisal. It also includes reviewing or revisiting the strategies and actions to consolidate the implementation and remedial processes. The goal state is final; and it represents solutions to the presenting problem and choice of strategies to be applied. This state presents the problem in a solvable condition and appropriate strategies used in solving it. The solutions restore the original desirable and non-problem state to allow normal functioning and operation of the unit. This integrates reporting and feedback on the worthiness and effectiveness of all strategies that were applied to solve the presenting problem. It acts as a blueprint for future reference and resilience should similar problem situations arise.

Inadvertently, how a problem is stated can affect its difficulty, resolution and management. For instance, two problems with the same space can vary greatly in their presentation and maintenance. In such a situation, it would require further conceptualization and analysis of the structure of a problem to enhance understanding of its dynamism and complexity. Ambiguity and vagueness in the problem statement or perception may result in the generation of a wrong and less effective solution or option. It is desirable to fully understand the problem in terms of its content and context prior to searching for possible solutions. The most cardinal approach to problem-solving would be the need to be aware of the actual issues to be solved, the basic ways of resolving them, and the preferred outcome.

Cardinal Focus

The strategies of problem-solving are related to integral elements of decisions, choices, opinions, and actions that a person takes or applies in solving a presenting problem at any stage in the implementation process. Strategies stem from appraising a problem situation and selecting achievable goals. Some strategies are more effective and produce immediate results than others. Apparently, no strategy can always suit every problem situation, conditions and circumstances; and some strategies could be altered when there are changes to the goal state and its implementation process [7]. Besides, there is no prior reason to assume that people will use the same kind of strategy in different kinds of situations all the time and circumstance [12]. It is factual that information is basic to understanding the nature and scope of problems, as well as the application of appropriate strategies to solve them.

There are many strategies that people use in the problemsolving process that could be aptly integrated in traditional counselling provision. Hereunder is a summary of some of the most applied strategies [7,9,10]. First, trial-and-error. This is the most applied strategy in problem-solving. It involves the identification and application of different actions and options aimed at solving a presenting problem to which there seems to be no logical solution. For instance, when a car breaks down, the driver or mechanic would apply this strategy in trying to identify the problem initially after which the cause is found and ameliorated. This might lead to the solution of the presenting problem. Second, heuristics. This is the application of standard guidelines and procedures for selecting actions that are likely to lead to a solution, more of “rule of thumb” strategies to solve presenting problems. These might be referred to as cognitive shortcuts such as trade-off, perceptual similarity, and means-end analysis in this process because of their efficacy and efficiency compared to other strategies. The major aim of any heuristic is to reduce a problem to manageable proportions by increasing the selectivity of actions and their relevance in the implementation and evaluation processes. Third, insight. This is basically a sudden vision of how all parts fit together, or how to represent the problem differently. The insight could come at the end of a directed process or seemingly out of the blue, or indeed, after a traditional counselling interaction. Insight is an important element in problem-solving. Fourth, creativity. This involves innovative thinking, generating novel ideas, and making new connections between existing ideas and fresh thinking. It helps in the development of new knowledge and understanding. More subtle problem situations might require ingenuity and creativity in their resolution. Fifth, coping mechanisms. This involves the deliberate actions a person takes or applies to manage problems of a psychological nature. It is most helpful to direct actions to remove or alter threatening circumstances such as alcoholism because of loss of a loved one. Besides, it is prudent to direct actions or thoughts to control undesirable feelings such as anger and hostility because of, for instance, loss of a job placement. Adapting helpful coping strategies leads to the resolution of some problem situations and conditions.

And lastly, consultation. This situation prevails through the conscription of experts or more senior members of staff to assist in the problem-solving field. The experts possess knowledge and experience in their field of specialization, they take time to analyze issues, and they are likely to find solutions to the problems presented before them. The focus of this strategy is on addressing psychosocial dysfunction that adversely affects people during their life and living. Psychosocial aspects have a significant role to play in the wider spectrum of social welfare and human relation services offered to needy people at the various levels of contact. This must be diligently applied in varying circumstances. It is apparent that the nature and complexity of some problems may pose insurmountable obstacles to their resolution. The most notable of these in the context of this discussion are variable. For instance, how the problem is understood or stated and its implementation process, its complexity or simplicity of the procedures, its interpretation and application. Besides, personal issues such as failure to achieve the desired goals, withdrawal arising from feelings of inadequacy or incompetency or ignorance and focus on one aspect of behaviour that may adversely affect the final outcome might be considered. This has no adaptive value or continuity, and it can lead to frustration if not handled carefully. Some actions may be prolonged without positive results. A mind set developed in perception of these entities may predispose past experiences and resilience in solving the presenting problem.

In everyday living, some people fail to apply a shorter version of solving a presenting problem because they perceive it according to their sociocultural norm. They become set into a pattern of thought by activating stored schema of how to solve that type of presenting problem. This relates closely to negative attitudes that prevent some people from processing new information to solve a presenting problem based on resilience. Attitudes are learned throughout the lifespan; and they are part of the socialization process. Some attitudes are so central to other people to the extent that they become resistant to change or alteration. The permanency of attitudes clearly bears some implications for change and continuity. The perceptual paradox arising from people that are largely influenced by the selectivity in attributions, defense mechanisms, stereotyping, distortions and errors may also play a part in creating misconceptions. It should be appreciated that people perceive and interpret any presenting problem differently which might contribute to some of them selecting information that is supportive of their points of view. They may choose not to acknowledge contrary information that might lead to solving the presenting problem. Other people may ascribe positive or negative characteristics to another person based on a general categorization and perceived similarities. Further, some people may perceive specific characteristics of the problem that keeps them from arriving at a solution; or they may view this from a wider picture and focus on familiar aspects of an object which might work against solving the problem. The perception of a person may be based more on certain expected characteristics than on the recognition of that person as a separate entity. This is basically personal. Subjective interpretations of what is perceived may yield differences in perception in which some people see different things and attach different meanings to the same stimuli, hence the apparent misunderstandings that might become a hindrance to solving the presenting problem. The selectivity of information can be distorted resulting in erroneous perception that might work against finding amicable solutions to settle the problem.

Conclusion

This article argues that problem-solving depends on how it is represented in the human mind. Representation involves the way or way people think about, perceive, visualize, and conceptualize the problem and methods of how to solve it. There are many models used to describe the problem-solving process by different proponents and protagonists, but this discussion illustrates one of the most practical ways of viewing this subject in contemporary society. Strategy is an integral element in problem-solving. It involves the decisions, choices, opinions and actions that a person takes or applies to solve a presenting problem at any stage in the process. Some strategies are more effective and produce immediate results than others. Apparently, no strategy can always suit every problem situation, conditions and circumstances.

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