1 Representing Problems
Learn how goals, available actions, and constraints shape problem representations, and how reconsidering assumptions can open new paths toward a solution.
When a situation becomes a problem
A problem exists when someone wants to reach a goal but cannot see an obvious way to get there. The gap between the current situation and the desired situation creates the need to solve it.
In cognitive psychology, a problem can be described through its starting situation, its desired outcome, and actions that might move the situation from one state to another. Some problems are relatively clear, while others require the solver to determine what the goal or acceptable methods should be.
The elements of a
A identifies the , , , and . Together, these elements define the : the possible states and paths a solver can consider. A solution is a path from the to an acceptable that respects the relevant .
A has a relatively explicit starting point, goal, and permitted actions; finding a route through a maze is one example. In an , the goal or acceptable methods may be uncertain. For example, deciding how to improve a team’s communication may first require defining what “improve” means.
Consider planning a study session. The might be that three chapters remain unread, and the might be being prepared to answer questions on all three chapters by Friday. could include reading, making notes, and self-testing. could include class, sleep, and a limited number of study hours. A vague goal such as “study more” makes it harder to judge which actions will help, while a specific goal makes progress easier to assess.
How goals and assumptions guide action
Goals and shape a by determining which differences matter and which actions seem relevant. A constraint may be externally imposed, such as a fixed deadline, or assumed by the solver, such as believing that studying must happen in one long block. Distinguishing actual limits from assumptions can reveal additional options.
The same situation can be represented in different ways, and each representation can direct attention toward different causes and strategies. For example, describing a student who is falling behind as having “not enough time” may suggest cutting activities or scheduling more carefully. Describing the situation as “unclear priorities” may instead suggest choosing which material matters most. Neither representation guarantees a solution.
Reconsidering a representation
The nine-dot problem asks solvers to connect nine dots arranged in a square using four straight, connected lines. Solvers often treat the square formed by the dots as a boundary, although the instructions do not require the lines to stay inside it. Questioning that assumed boundary expands the possible paths and makes a solution available. This is an example of .
When progress stalls, it can help to restate the goal, list the actual rules, check which rules are only assumptions, or draw the problem in another form. These steps do not remove genuine ; they help distinguish them from restrictions introduced by the solver’s current representation. An alternative representation may open a path to a solution, but changing the representation alone does not ensure that the solver will find or carry out the solution.