Problem Solving: Insights, Challenges, and Approaches
By Elena G. Makri, Editor
Nova Science Publishers
One framework into the world is problem-solving. How do people (and employees) solve their problems may speak about their knowledge, skills, and abilities / attitudes as well as their character. Ditto with organizations and workplaces. So, too, with nation states (with their cultural constraints, political ones, economic ones, technological ones, and others). A plotline may be seen as a series of challenges for the protagonists and the lesser characters. Culturally, people groups solve problems and pass on their knowledge to future ones. The idea of problem-solving as a way to see the world works from the micro- to the meso- to the macro- scales.
Dr. Elena G. Makri, Editor of Problem Solving: Insights, Challenges, and Approaches, is comprised of works that show different approaches to solving problems at all scales. In particular are those that require collaboration among people with various skill sets. How are problems identified and defined? What are useful metrics for assessing a problem or situation? What is relevant to problem solving? What are creative ways to arrive at practical and efficient solutions? What are ways to understand the implications of particular actions towards a solution? What are ways to test the efficacy of solutions? What are ways to solve problems into the longer term than the mere present alone? What are “hard” or “complex” problems? What are the problem landscapes (“problem scapes”) of particular industries or sectors or spaces? What about partial solutions?
The book opens with inspiring quotes by present-day influencers who share insights about problem solving. Problems may be seen in a positive light as a builder of the human spirit (M. Scott Peck), as a way to make social progress (Martin Luther King, Jr.), and as an expression of humanity even in the presence of thinking machines (B.F. Skinner) others (Makri, 2022, p. iv). Jocko Willink’s quote observes the importance of owning problems in order to solve them. Real-world inventor Dean Kamen observes: “Every once in a while, a new technology, an old problem, and a big idea turn into an innovation” (p. iv). Deepak Chopra observes the human characteristics that benefit performance in problem solving: “The highest levels of performance come to people who are centered, intuitive, creative, and reflective—people who know to see a problem as an opportunity” (p. iv).
Figure 1. Problem Solving (abstract with geometric shapes)
Problem solvers cannot be cowed by the challenges; they have to have knowledge and skills and methods to solve problems. They also have to collaborate well. They have to have the strength of convictions if they are on to something. The text is an “intersectoral theoretical, research and technological advancements that shape the critical domains problem-solving is and might be conceptualized, exercised and developed” (Makri, 2022, p. xi).
Using “A Directed Change of Variety” for Creative Problem-Solving
Igor Zadesenets’ “The View of Development as a Directed Change of Variety Gives Clues for Creative Problem-Solving” (Ch. 1) takes problem solving abstract. This work draws from the practices of cybernetics and information theory, in its assertion that people would benefit by developing “a directed change of variety.” This work highlights how thinking of a problem can change the possible approaches and outcomes. People often experience mental blocks when they try to find solutions for insight problems in part because human minds work along “trivial” mental routes (Smith, 1995, as cited in Zadesenets, 2022, p. 4). People tend to misfocus on the wrong details, not noticing the important details for actual and effective problem solving. They fixate on the wrong aspects. They misuse their own prior experiences, which are costly references for trial-and-error problem solving.
This independent researcher posits a particular type of problem, that of, for example, keeping a situation under control, and managing state transitions from one state to another. He writes:
Let us say, to make sure that events (state transitions) from list A happen, but events from list B do not, which is a classical control task. Once we have solved such a problem, we can reproduce the solution over and over again. This is precisely how we create and develop techniques and technologies. (Zadesenets, 2022, p. 3)
If factors of a problem context may be sufficiently abstracted, they may be set up in equations (such as from cybernetics, such as from information theory), and once solutions are identified, they may be applied again and again to analogical situations. Then, the challenge is to find analogical situations, structurally similar problems, and then to apply the solutions.
Figure 2. Puzzle Pieces
There has been research on the codification of problem solving techniques, based on examples (from inductive reasoning, specific to general) and from principles (from deductive reasoning, general to specific). It is in the moving between those approaches that new insights may be acquired. There are prior studies examining the innovations in patents, for example. A seminal work involves G.S. Altshuller’s TRIZ tool for technical problem solving (https://en.wikipedia.org/wiki/TRIZ). The learning may be captured in symbols—language, mathematics, and other forms of symbology.
Control of variety appears to be a generalization of a level high enough to cover most of the directions of development in the area of controls. At the same time, this concept is specific enough to allow detailed interpretation. This gives the basis for the development of a universal system of clues by systematizing, enriching, simplifying, and to some degree, scientifically justifying existing techniques. (Zadesenets, 2022, p. 4)
The various arising challenges may involve solutions that draw from parts of prior solutions. Such efforts involve attempts to shore up forces for order, to counter entropy, randomness, disorder, and even chaos. Abstracting out problems and solutions enables humanity to not just codify experience but to learn from observations, such as from nature and evolution (and other systems). A greater variety of source information may be integrated into a possible solution.
Figure 3: Rising Spiral Depiction (by CrAIyon)
The researcher writes:
The work of evolution combines the retention of successful attempt results and the elimination of errors. Usually, winner species have certain advantages, thanks to greater variety, for example, more developed organs or more sophisticated behavior. This leads to a complication of the ecosystem. The process is developing in an upward spiral. Similar process can be observed in technology and society.
At the same time, simplification of a tool and elimination of its uncontrolled behavior requires the elimination of redundant information.
The way to improve tools is to control their variety. This concept seems to the author a promising candidate for a generalized model or universal analogy for solving problems. (Zadesenets, 2022, p. 8)
The proposed model, called “Control of Variety,” begins by looking at a problem with a high level of generalization first (sort of a high level of blur) (Zadesenets, 2022, p. 8). The idea is to not prematurely specify the aspects of a problem but to start at a higher level of generalization. The researcher describes the approach:
The cybernetic approach seems promising here. In our case, it comprises establishing the ratio of the number and probabilities of events from different groups (targets, disturbances, control events), and defining generalized parameters that influence this ratio. Interpretation of these relationships can tell a lot about the paths of evolution of ‘controls.’ This interpretation provides general solutions that can serve as clues. The specification of types of events (or states) depending on specific conditions is still necessary to solve specific problems. Thus, we must ascend from a specific situation to a generalized model, find a general solution, and interpret it for a specific case. (Zadesenets, 2022, p. 8)
Where diversification of solutions can be a competitive advantage, focusing in on the most effective approaches can control for that variety and enable easier standardization and adoption. This work touches on SCAMPER, Systematic Inventive Thinking (SIT), Theory of Inventive Problem Solving (TRIZ), and Lean Manufacturing, as inspirations. To fully appreciate this chapter, readers would do well to read more deeply in terms of the models, theories, and related data. This work suggests that there is a necessary level of complexity beyond which simplifications may not be possible, and this may be the optimal point at which to delimit diversification.
This model enables identifying the “kind of changes, actions, states” allowable in a context that may make particular problems easier to solve (Zadesenets, 2022, p. 25).
An Immersive Learning Game-Based Experience to Enhance Problem Solving
Eleni G. Makri’s “Serious Games in Higher Education: A Multimodal Problem-Solving Immersive Learning Experience” (Ch. 2) champions the game modality for developing problem solving skills in various contexts. The main focus here is on the Maritime Spatial Planning (MSP) Challenge 2050 gameplay workshop (p. 38). This two-day gaming event involved 18 postgraduate students from “maritime spatial planning, water resource management” studies, with the support of Programmers and then with a maritime spatial planning expert moderating the event. The game attracted teams from different countries. The teams had access to various gameplay resources, including maritime spatial planning datasets.
The research focused on learning from how the various participants in the competition dealt with the challenges of the event. The researcher writes:
The Canadian gamers reported that they found (it) difficult to define the goals of the game due to cognitive load (i.e., large amount of information and data provided to them). However, they declared that they developed ways to mitigate this challenge by incorporating planning, removing unnecessary information on the screen and allocating balanced task completion between teams. (Makri, 2022, p. 39)
The research involved captured recorded audio and video of the group player interactions, which revealed some team power dynamics. The game itself simulated some of the chaotic pressures of a real-world emergency scenario, with a need to respond based on empirics and available resources. Multi-stakeholder serious games may help learners become more aware of important issues and “practice…content and procedure” (Makri, 2022, p. 41).
Figure 4. Puzzle Pieces 2
Another serious game described involves student players who are “mayors” of islands and need to make decisions for the wellbeing of citizens while protecting the larger ecosystem and environment. Makri (2022) writes:
The students must manage the economy of the island to achieve the most sustainable balance. On this island, users have access to different sources of non-renewable energy, such as oil, natural gas, and uranium. They also have renewable energy sources, including water, the sun, and the wind. Moreover, since they live on an island, they must properly manage the available space. (p. 44)
Some constructive practices in such games involve feedback (“instant, helpful and practical”) provided to players perhaps in between rounds (p. 46), debriefing of the game, and other cognitive supports for learning.
Problem-Solving in Project Management
Adrian Hepworth’s “Problem-Solving: Practice and Theory in the Project Management Office—A Cognitive Approach” (Ch. 3) begins with an observation of the high-impacts of leader decisions. The researcher writes:
Erroneous decisions traced back to the approaches used appear to fail from poor information collected to support the decision or the mental routine used to decipher the information and make the decision. (p. 55)
The research in this chapter focuses on project management in the oil and gas industries. The goal was to test an intervention for a “mental decision model that would improve project performance and decision-making processes in both the project management office and the field and influence critical and conscientious thinking” (p. 55). This study is based on action research:
The research findings were espoused through the learning set participant’s reflections crossing three action cycles. Each learning cycle progressed with new insights and evolved the main categories. I show the analysis revealed the critical concepts for forming a mental model framework: Situation, Conscience, Experience, Listening, Confidence, and Sensemaking. The mental model framework was found to influence practical approaches to forming justified decisions. (Hepworth, 2022, p. 56)
The research methods use mixed methods, qualitative and grounded theory. The research is based on “two action learning sets from Iraq and Azerbaijan and thirty worldwide interviews” (p. 56). Ultimately, the mental model framework “was found to influence practical approaches to forming justified decisions” (p. 56). The definitions of the main elements—Situation, Conscience, Experience, Listening, Confidence, and Sensemaking—are defined clearly and intuitively. The researcher writes:
All participants described the approaches to problem-solving as using previous Experiences as the key factor and Conscience as a cautioner to wellbeing, safety, and risk considerations. Sensemaking was expressed as putting together collected knowledge that subconsciously creates cognitive scenarios. Participants described Situation understood as a process for defining the problem in a clear statement. Confidence was expressed as competence and using similar previous experiences to shape a current problem by actively sharing ideas and moving towards a remedy. Participants described Listening as fundamental to gaining insight into problems, reflecting on views and triggers. (Hepworth, 2022, p. 78)
Leaders of projects play critical roles in project success and failure.
Pedagogical Problem Solving
Teachers bring complex skillsets to solving problems in teaching and learning, in Insuk Han’s “The Cooperation Mechanism of Teacher Professional Identity and Metacognition in Pedagogical Problem-Solving: Implications for Teacher Education” (Ch. 4). How much effort teachers bring to their daily problem solving depends on their commitment to their “professional identity” (PI) since such work is identity-congruent and critical for becoming expert professional problem solvers in the pedagogical space. This work posits:
…identity often leads a person to activate metacognition for his/her production of reasonable cognitions, emotions, and actions in his/her particular contexts. In other words, PI seems to motivate teachers to use metacognition for their professional practice. (Han, 2022, p. 122)
Metacognition plays an important role in problem solving: “While solving problems, people a) encode the nature of the problems and make representations of its elements, b) select or form strategies for the attainment of the goal, and c) identify and overcome obstacles that impede progress” (Anderson, 198, Davidson & Sternberg, 1998, as cited in Han, 2002, p. 124). For language teachers engaging in pedagogical problem-solving, they work the problem in four phases: “a) comprehension of the problem by problem recognition and definition (problem representation), b) construction of a strategy (solution representation), c) contextualization of the strategy by implementation, and d) evaluation of the effectiveness of the strategy and formation of new meanings” (Han, 2022, p. 125).
Figure 5. Problem-Solving (in Deep Dream Generator)
This theoretical study suggests the importance of teaching as a calling perhaps more than a money-earning endeavor.
Problem Solving to Develop Basic Skills in Adults
D. Pérez-Jorge, V. Escobar-González, D. González-Dorta, and L. Fariña Hernádez’s “Problem-Solving as a Strategy for the Development of Basic Skills in the Adult Population” (Ch. 5) explores an adult training program for workforce preparedness. Fifteen adult learners participated in the study. They came with “a diversity of styles, rhythms, and learning abilities” (p. 145). The participants ranged in age from 21 to 61 years old, and a majority lacked formal education beyond primary school although a few did have high school diplomas. Formal assessments were done to measure their general intelligence, logical reasoning, verbal abilities, numerical abilities, and visuospatial reasoning (Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 154).
Their work revealed some gaps:
The data obtained indicate that these students have very different mental aptitudes, and that adult education models, based on current criteria, are not adequate because they do not respect individual abilities, which consequently generates inadequate performance and learning difficulties in students with this profile. (Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 145)
The research was conducted to test Polya’s problem-solving method, which asserts that there are four phrases of problem solving: understanding the problem and objectives, thinking about which strategy to use, applying the selected strategy, and answering or checking the solution to the problem for correctness (Polya, 1965, as cited in Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 150). Polya’s approach also focused on “modeling, trial-and-error, and information organization” (p. 153).
There was also exploration of the benefit of learning logical-mathematical reasoning as a tool for engaging the world. One approach is to convert information into a math structure to enable manipulation of the elements to a solution (Mayer, 1986, as cited in Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 151). Another is to propose hypotheses and test them and “giving it a mathematical structure, transforming it into a diagram adapted to the problem” (Mayer, 1986, as cited in Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 151).
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The Map of Mathematics
The adult training program focused on basic elementary mathematical operations, proportions; algebraic language; calculating lengths, areas, volumes; calculating angles; monetary units; statistical information; probabilities, and others. (Pérez-Jorge, Escobar-González, González-Dorta, & Fariña Hernádez, 2022, p. 152) The training program also focused on communicating in Spanish orally and in writing. The adult learners also worked on issues such as “the improvement of motivation, social skills, and basic professional competencies” (p. 152). They also worked on metacognition.
The research team found benefits to logical reasoning after the teaching of the problem-solving method, but they also asserted that the variance among the learning group was problematic for the teaching and learning.
Comparing Perfectionistic and Non-Perfectionistic Adolescents in Social Problem Solving
How do characteristics of learners affect how they perform in learning contexts? L. Kasik, Z. Gál, and Z. Nagy’s “Social Problem-Solving and Anxiety in Perfectionist and Non-Perfectionist Adolescents” (Ch. 6) explores this dynamic, particularly in terms of learner anxiety and performance. This chapter explores “the relationship between social problem-solving and anxiety in adaptive, maladaptive, and non-perfectionists” among 11 – 12 year olds in the 6th grade and 16 – 17 year-olds in the 10th grade (p. 165). A number of established assessment instruments—for perfectionism, for social problem solving, for state-trait anxiety in children, and others, were used. They write:
Scores on the APSR factors indicated that nearly one-third of both 6th and 10th graders were perfectionists. In both age groups, two-thirds of perfectionists showed patterns of adaptive perfectionism, while the other third was maladaptive. (Kasik, Gál, & Nagy, 2022, p. 165)
A striving for perfection is not inherently negative or positive, but how that perfectionism is handled by the children matters. They write:
In line with previous research, maladaptive perfectionists at both ages were characterized by negative orientation towards their social problems, and the problem-solving style they most often utilized was avoidance. They were also concerned about making mistakes, felt heightened anxiety because of the perceived criticism coming from their parents, and had unrealistically high expectations towards themselves. Trait anxiety was also most prevalent among maladaptive perfectionists, especially for the older age group. Our results also point out the need for institutional education to address students with maladaptive perfectionism more conscientiously, as it is closely linked to social problem-solving even in early adolescence. Based on our findings, it is assumable that maladaptive perfectionism, combined with the feelings of anxiety it aggravates, leads to diminished efficacy and worse well-being. Kasik, Gál, & Nagy, 2022, p. 166)
Parental pressures were found to be detrimental to some of the learners. The researchers also found nuanced insights:
For non-perfectionists, high standards (ASPR) had a strong positive correlation with concern over mistakes (FMPS). High standards also had a weak positive relationship with negative orientation (SPSI-R). Among non-perfectionist 10th graders, trait anxiety showed a strong positive correlation with parental criticism (FMPS) and a strong negative correlation with positive orientation (SPSI-R).
In the case of adaptive perfectionists, also at both ages, the high standards (ASPR) factor had a positive moderate-strong correlation with avoidance (SPSI-R). For the 16-17-year-olds, there was also a moderate to strong correlation with doubts about actions (FMPS) and negative orientation (SPSI-R). (Kasik, Gál, & Nagy, 2022, p. 180)
There were findings differentiating between those with “state” vs. “trait” anxieties. For learners to thrive, customized teaching and learning may be a benefit, based on astute and conscientious teaching (and parenting).
Dr. Elena G. Makri, editor of Problem Solving: Insights, Challenges, and Approaches (2022), is affiliated with the University College Dublin and Insight SFI Research Centre for Data Analytics.
“TRIZ.” (2023, Feb. 22). Wikipedia. Retrieved Feb. 28, 2023, from https://en.wikipedia.org/wiki/TRIZ.
About the Author
Shalin Hai-Jew works as an instructional designer / researcher at Kansas State University. Her email is email@example.com.