“Although a sizable body of knowledge is prerequisite to expert skill, that knowledge must be indexed by large numbers of patterns that, on recognition, guide the expert in a fraction of a second to relevant parts of the knowledge store. The knowledge forms complex schemata that can guide a problem’s interpretation and solution, and that constitute a large part of what we call physical intuition.” ~ American psychologist Jill Larkin et al
Problem-solving – goal-oriented reasoning – is the mind’s most meaningful occupation. All organisms solve problems. Some, such as corvids and octopi, are able to effectively think through the problem-solving cycle and render their first attempt successful. Others with less acumen, such as humans, rely more upon trial and error.
There are numerous steps to solving a problem. Several of those steps may be iterative, particularly planning.
Problem-solving is an exercise in planning. Good planning requires diligence. Shortcuts in the early steps are a surefire formula for iteration after attempted execution.
Identifying a problem can itself be a problem. Misdiagnosing the problem leads one astray from the get-go. Trying to define a problem may result in iterating back to identifying exactly what the problem is.
Once a problem is defined, a solution is sought. The first step is to identify the goals that may suffice as a solution. This involves identifying constraints – what is not going to be attempted.
Once goals are set strategies are devised to effect a solution. Considering approaches can lead to a reevaluation of the goals, which may be overambitious and pared back.
Step-by-step procedures – algorithms – can help solve certain kinds of problems. Otherwise, people often fall back on heuristics: rough rules of thumb learned from experience.
3 heuristic approaches often prove helpful in solving problems: working backwards, apt analogy, and dissection. Working backwards is helpful when the goal is clearly specified, such as mazes, or certain math problems. Complex problems sometimes yield to a strategic analogy: finding similarities between the current problem and one previously encountered. Big problems are best faced by dissection: breaking them down. Slicing a sizable situation into sub-goals, which are then tackled one at a time, is often the only way to accomplish large projects.
People sometimes get stuck because they latch onto an ineffective strategy and won’t let go. This can arise from a mental set: the tendency to approach a new problem the same way as a similar one encountered before. Problem-solving by analogy only goes so far.
Another inflexibility arises with functional fixedness: viewing familiar objects as having only specific uses. Failing to see that a coin may (at times) substitute for a flathead screwdriver is an example of functional fixedness.
Sometimes problems become intractable only because of self-imposed limitations. One cannot hope to achieve what is believed impossible for oneself.
“Humans are thinkers who readily jump to conclusions, based on limited knowledge and biased by motives, emotions, and perceptions.” ~ Philip Zimbardo et al
Devising a strategy, collating information, and evaluating alternatives comprises a feedback loop that may even reach back to defining the problem. The well-skilled spend more time in these early stages – getting the big picture right – than novices, who worry more about details.
Choosing a course of action among alternatives is the first step in execution. Resources are then allocated. A failure to have sufficient resources to execute a plan iterates back to selecting an option, or even further, to the early planning stages, even goal setting.
An attempt is made to meet the goal. Progress is monitored. The effort may be adjusted, including reallocating resources.
Once the work is finished, the results are evaluated for how well the goals were met. Falling short may require patchwork, or worse, send one back to the drawing board.
“The Einstellung (set) effect occurs when the first idea that comes to mind, triggered by familiar features of a problem, prevents a better solution being found. It affects both people facing novel problems and experts within their field of expertise.” ~ Bosnian psychologist Merim Bilalic et al
The mind tends to set itself into a familiar frame. The Einstellung effect happens when looking at a new situation or problem in the same way as those encountered in the past, though a fresh look is required. Einstellung is German for mind-set, setting, or attitude.
The Einstellung effect occurs as the data which comprises the situation is selectively categorized as it has been before. Relevant data which do not fit predetermined categories may be excluded. This easy categorization sets the schema in which a problem is considered.
People frequently face probability problems which are commonly presented as percentages (e.g., 10%). A more intuitive format is natural frequency (e.g., 1 in 10).
“Even though natural frequencies are much easier to understand, people are more familiar with probabilities represented by percentages because of their education.” ~ German mathematician Stefan Krauss et al
The human mind is not inclined to work with percentages. (Natural frequency is of countable fractions (1 of 4) whereas percentage (25%) is an abstraction which the mind grapples with to make concrete.) But, because this Einstellung is instilled, the mind translates a problem which may be more easily solved using natural frequencies into probabilities, making the problem harder to solve.
Functional fixedness is a related cognitive bias of looking at objects as being usable only in a certain way. 5-year-olds don’t suffer functional fixedness, but the syndrome has crept in by age 7.
“The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify into every corner of our minds.” ~ English economist John Maynard Keynes