Problem Solving

Kim Sloane


Much of human activity is problem solving. The research into this activity ranges from looking at problems large and small, from problems solved in seconds to extended multi-step processes that may occur over long periods of time. Extensive research has also been conducted in the field of creativity. All problem solving is in some way creative. Creativity has also been divided and subdivided into categories and subsets. One distinction is likewise between large and small, between “Big C” and “Little C,” distinguishing the world-altering, paradigm-shifting discoveries from the everyday insights that get us through the day.

Putting the two terms together, “creative” and “problem solving,” opens the door to a vast body of literature and research. A quick look at Google Scholar reveals the following hits for articles on problem solving and some of the subcategories: problem solving: 650,000; analogy and problem solving: 1,840,000; creative problem solving: 3,970,000; visualization and problem solving: 2,060,000 (not to be confused with “creative visualization,” which makes up some of this number); metacognition and problem solving: 248,000. Something similar would occur with a search for “creative,” which gets 5,850,000.

Pratt Institute has chosen “creative problem solving” as one of its All-Institute Learning Goals.  Others are Justice, Environmental Sustainability, Global Citizenship, Resilience, Versatile Communication, and Disciplinary Fluency. Creative problem solving is an appropriate goal for the Institute, as problem solving is at the heart of art and design practice. Pratt supplies a definition:
Creative Problem Solving: Creative problem solving is dialogic, co-creative, and iterative as students pose questions, identify problems and opportunities, and design transformative strategies. Through critical, resourceful, and reflective processes, students consider diverse perspectives to make informed decisions. Students envision, implement, and reassess meaningful solutions that are grounded in humanistic concerns related to society and the environment. (2021)
I think it would serve the Institute well to investigate this goal more deeply and ask how it specifically relates to an art and design education and how we might explicitly incorporate problem solving in curricular design and classroom practice.

This paper is an attempt to begin this investigation. The paper is divided into parts to clarify the complex of overlaps and conflations and the density of the subject matter. First, the paper will discuss existing processes of design and problem solving. I will then present the research I have undertaken in the domain of problem solving itself offering some definitions and terminology as well as a taxonomy. Additionally I will focus on problem-solving tools and capacities that dominate the extensive literature on the subject while highlighting capacities that are applicable to a school of art and design. Lastly, I offer a conclusion and recommendations for classroom interventions to produce a class of problem solvers who know they are problem solvers.

Existing Processes

In the literature of problem solving, one immediately encounters discussion and research on process and processes. Two processes dominate and have been widely distributed, practiced, and marketed by a range of educational, business, and military organizations. They are related, but distinct. One is Design Processes, variously formulated, and the second is called “Creative Problem Solving” or CPS. In both cases, the processes have been broken down to stages and sequences of activities or practices that lead to a solution. I will treat these briefly, as they are important in the study of problem solving. They both have advocates and detractors. However, rather than discuss the value of the processes, I want to concentrate on the elements, concepts, and practices that underpin and constitute the stages of these processes and ultimately lead to their success.

First, a quick look at the design process. The design process is close to and part of the problem-solving process. The design process is also related to some creative-thinking paradigms and has been articulated by a range of people in many places. One sequence of activities made popular by the Stanford Design School is “Empathy, Define, Ideate, Prototype, Test” (Hasso Plattner Institute of Design at Stanford, n.d.). Harvard Business School uses “Clarify, Ideate, Develop, Implement” (Harvard Business School, n.d.). Both schools teach these processes in workshops or online courses. The concept of “design thinking” underpins these processes (Brown, 2008). IBM simplifies the process to a repeating loop of “Observe, Reflect, Make” (Elmansy, 2016).

When capitalized, “Creative Problem Solving” (CPS) denotes a specific “framework and approach” that has “emerged from an extensive tradition of research, theory, and practice over four decades” (Treffinger et al., 1994, p. 223). It is referred to as CPS and has been studied, tested, and taught. Alex Osborn, founder of the Creative Education Foundation, first developed CPS in the 1940s. Osborn also coined the term and developed the practice of brainstorming. Osborn worked with Sid Parnes to create the Osborn-Parnes Creative Problem-Solving Process (Treffinger, 2006).

The CPS process cites four conditions and four stages:

Four Conditions
  • Balance divergent and convergent thinking
  • Ask problems as questions
  • Defer or suspend judgment
  • Focus on “Yes, and” rather than “No, but”

Four Stages
  • Understanding the Challenge
  • Generating ideas
  • Focusing Ideas
  • Preparing for Action; or Clarify, Ideate, Develop, Implement

There are many subcategories, practices, and variations of both design processes and CPS that one can find on various websites dedicated to these ideas (Boyles, 2022). The advent of artificial intelligence (AI) has accelerated this research, as we seek to find ways to program machines to solve our problems.

The Problem of the Problem

So, various processes have been proposed and practiced, taught, and researched in the hope of helping to find processes to arrive at solutions to problems. I would like to look at the level below, not at steps or sequences of process, but at the questions and activities that these steps should include. It is good to propose iteration as a stage of a process, but it seems better to investigate those activities and cognitive domains that will promote promising, original, varied, and valuable iterations. One can ask what is the problem to be solved, but one might first ask what is a problem? Are there kinds of problems? Do different kinds require different approaches to a solution? Does problem solving differ from creativity or is it the same process? Is the term creative problem solving simply a redundancy?

All problem-solving involves the problem of the problem (Getzels, 1982).

To begin, here are some definitions of problems:
  • “When behavior is blocked because a desired end is not at once attainable a problem arises”” (Maier, 1933, p. 144).
  • “A problem exists when a living creature has a goal but does not know how it is to be reached” (Dunker, 1945, p. 1).
  • A problem is “a question raised for inquiry, consideration, discussion, investigation or solution” (Merriam-Webster, 2024).

And yes, there are different categories and kinds of problems. Here is a taxonomy of problems:

  • Overarching: Categories of Problems

    • Presented—the problem is a known problem with a known formulation and a known method of solution (Getzels, 1982, p. 41).
    • Discovered—The problem already exists but is not proposed by another; it may or may not have a known formulation or method of solution (Getzels, 1982, p. 41).
    • Created—“the problem does not exist until someone invents or creates it” (Getzels, 1982, p. 41).
  • Kinds of Problems (could be in any of the above categories)

    • Well-Defined (or Well-Structured) Problem: a problem space understood, and a solution space understood;
    • Ill-Defined (or Ill-Structured) Problem: a problem whose understanding is not readily represented as a problem space (Getzels, 1982);
    • Multi-Step Problem: a sequence of correct steps; tasks with no single step as key; solution depends on taking a number of correct steps;
    • Insight Problem: not a multi-step process; a single insight will solve the problem;
    • Knowledge-Lean Problem: very little knowledge is needed to solve;
    • Knowledge-Rich Problem: task with special knowledge or training needed to solve;
    • Wicked Problem: “social or cultural problem that is difficult or impossible to solve” or measure; no definite formulation; no template; often a symptom of another problem (Kolko, 2012, p. 10).

In my research on the processes, I did not encounter any mention of distinction among kinds of problems apart from John Kolko’s book Wicked Problems (2012). It seems important to get to this level to understand how to proceed toward a solution. It is good to know, for instance, that most design problems are considered ill-defined or ill-structured. They are likely not presented but will be either discovered or created. The important question is, then, after one has identified the nature of the problem, what tools are needed, what capacities should be drawn upon for this particular situation? It is not so much the sequence or stages that matter, but one should be attentive to engaging the cognitive domains and capacities that will engender original solutions.

Problem-Solving Tools and Capacities

Five important capacities for Problem Solving have emerged from my research and have relevance to visually based fields of art and design.

The capacities that I have identified are:
  • Metacognition
  • Creativity
  • Divergent/convergent thinking
  • Visualization
  • Analogy

All these capacities intertwine and overlap. Metacognition is the combination of overarching capacities, of which the rest are subsets.


Metacognition is the awareness of one’s thinking process. One might expand this to the awareness of one’s learning process and making process. Metacognition is linked with all our concerns, from creativity to problem solving.

Norbert Jaušovec (1994) conducted studies on the relationship between metacognition and problem solving:

The study was designed to investigate the influence of metacognition on problem-solving performance. The cumulative results indicate that metacognition is an important factor in problem-solving performance, equally important in solving closed and more creative, open-ended problems. (p. 27)
Introducing a writing component to studio classes is an intervention that is simple and, as stated, has potential to be a very effective way to develop metacognition. Written reflection, however, needs direction, prompts, and feedback to be truly formative. Creating awareness of process, making concepts and outcomes explicit, promoting planning, monitoring, and self-assessment are all positive strategies to promote metacognition (Sloane, 2022, p. 44).


Creativity is, of course, its own great subject of inquiry and is inextricably linked with problem solving. Earlier writing, at the beginning of the twentieth century, saw creative thinking as virtually the same as problem solving. Creativity has been defined in many ways, but most definitions in design are close to that given by Sawyer (2006) and Sternberg and O’Hara (1999): “bringing into being something that is both novel and useful” (as cited in Hargrove & Rice, 2015, p. 160).

Creativity was once considered to be a capacity possessed by only a few. Now it is believed to be inherent in everyone, and that we can inspire, develop, and teach creative abilities. Making the stages explicit and available to students will also stimulate and develop metacognition, which in turn stimulates creative thinking:

Creative thinking can be defined as a meta-cognitive process—of generating novel or useful associations that better solve a problem, produce a plan, or result in a pattern, structure, or product not clearly present before. Designers can improve creativity by focusing on metacognitive thinking in the classroom. (Hargrove, 2013, p. 492)

Divergent / Convergent Thinking

Creativity, the creative-thinking process, and problem solving are linked to convergent and divergent thinking. Divergent thinking, or DT—often referred to as lateral thinking—is the process of creating multiple, unique ideas or solutions to a problem (American Psychological Association, 2018).

Divergent thinking is a cognitive development. It is related to—and a piece of the larger goal of—metacognition. Metacognition and creativity are linked. All are linked to problem solving:

A student’s cognitive development has a profound effect on their ability to both think divergently and reflect on their own thought process. In addition, educational strategies intended to develop these skills, and a student’s creativity, vary in accordance with cognitive level. (Hargrove & Rice, 2015, p. 160)
As educators, we can introduce methods of divergent thinking and practice, and we can make clear the distinctions between DT and convergent thinking. This practice is clearly an important part of the creative and problem-solving process.


Like divergent thinking, visualization is a critical capacity in problem solving that we can promote in the curriculum and classroom. Visualization is the formation and representation of a mental image. Mental imagery plays a central role in cognition and has been widely researched. Mental imagery, manipulation of images, and spatial reasoning have all been linked to problem solving.

Visualization is an important component in problem solving through the identification and manipulation of problem elements in all possible configurations. It is important to develop the ability to rotate elements and imagine a range of spatial orientations as well as various relationships of parts to the whole. It should be noted that the Pratt Foundation course formerly called “Drawing” became “Visualization/Representation” because the skills and abilities cited above are critical for artists and designers. One of the outcomes of the course is: Gain in their ability to perform tasks involving the reconfiguration and mental rotation of forms, in 3-D spatial visualization and spatial reasoning.

Analogy, Analogical Reasoning, and Subprocesses

Analogy underpins our understanding of nearly everything. Analogy is a correspondence between two things, typically based on structure. When we encounter an unfamiliar situation or encounter a problem, we use analogy to make sense of it. Retrieval, mapping, evaluation, and abstraction are some of the parts that result in analogical reasoning. Retrieval is the process of being reminded of a past situation from long-term memory. The process of transferring the known structure—what is retrieved—onto the unknown is called mapping. Evaluating an analogy involves at least three kinds of judgment: structural soundness, factual correctness, and relevance. In analogical abstraction, the common structure that represents the interpretation of an analogy is extracted and stored. This kind of schema abstraction helps to promote transfer to new examples. The process will repeat many times until a suitable or satisfying match is made. In imagistic processes involved in problem solving such as we have described, images are formed that were never before perceived: the designer, the inventor, and the discoverer work to represent something new, a brainchild that has never previously been stored in memory and can therefore not be retrieved. This is exciting, and is the thrill of analogy.

Drawing is an analogical process. We seek to create a structure on the page that maps to a structure either observed or felt. We look for a similar set of relations. These relations may not result in resemblance or so-called accuracy, but may be of a much more mysterious, novel, and personal origin.


The components of the problem-finding, problem-solving process are multifaceted and complex. Each one is its own rabbit hole, and, as noted, the research is vast. 

It is understood that strategies do not guarantee creative success. Indeed, so-called “expert” performance, or over-reliance on formulaic practice, has been shown, in some cases, to inhibit creativity. Design thinking and process has been roundly critiqued in many places as an effort to package and commercialize, to water down and oversimplify, what is a very complicated activity (Kolko, 2017; Vinsel, 2018). However, this is usually a critique of the practice of a process, not of concepts and capacities. Any investigation into the process should be an effort to understand the facets, the parts, and the elements at play. We should know that they may be practiced in any sequence, may be picked up and discarded, and that each individual and each problem will be unique. We can see that it is a complex, not a linear, system, and that it is about the interactivity of elements, not a pre-ordered formula. The key to all process is active practice—awareness and promotion of achieving metacognition toward “Discovery-Oriented Behavior.”


What we can do in the classroom/curriculum:

1)    We should develop metacognition through directed and prompted reflection and critique. This can happen through well-crafted assignments with clear criteria and guided reflection. Making is reflection in action (Schön, 1983). Reorient toward the cognitive.

2)    We should encourage Discovery-Oriented Behavior by organizing assignments with the opportunity or necessity to problem find, formulate, and discover.

i)  Require activity before the actual “beginning” of the making process. Having students rearrange a still life before or during the drawing process is a simple example of this (even moving their drawing bench qualifies as a start).

ii) This can and should include an induced moment for design thinking: have them make many “representations” before they “begin” (ideations and then iterations are representations).

iii) Show as many manipulations of elements as possible. Show them at the discovery stage and the solving stage. Then the process may build to deeper and more varied forms of inquiry. If the student has discovered the problem, they have the best shot at solving it. At the end of the semester, perhaps they create their own problem to solve. Frame it as such in the assignment.
3) Understand different categories and kinds of problems and how and why they may require different strategies of solution.

4) Understand visualization and the reasons it facilitates problem solving. This is not an automatic outcome of drawing; rather, it needs to be explicitly practiced and the desired outcome understood by students. The “exploded” view is an example of this, as it is drawing rotations.

5)  Understand the power of analogy and how it relates to making. Drawing, figure drawing in particular, is productive here. Drawing is an analogical exercise: one creates a structure on the page that is analogous to a structure in the world, real or imagined. Figure drawing is about sets of relationships on the page that map to sets of relationships in the world. It need not have to do with resemblance, so innovative structures may be created based on any number of ways of seeing.

6) Everything must be explicit. Metacognition is the key to the whole enterprise. Writing with well-designed prompts that use the vocabulary of cognitive domains and the terminology of art and design is the first, but not the only, step. Make problem solvers who know they are problem solving.


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