9 Cognition and Language · 9.1 Cognition and language
9.1.2 Problem solving, decision making and creativity
Problem solving is thinking directed at reaching a goal past an obstacle, by algorithms (sure but slow) or heuristics (fast but fallible); decision making is choosing among options, often by mental short-cuts that cause predictable biases; creativity is producing ideas that are both new and appropriate, mainly through divergent thinking.
- APPSC Paper I
- Standard level
- 13 min read
- Free
Core facts
- Problem solving: goal-directed thinking to move from an initial state to a goal state when the way is blocked. It is not unique to humans: animals solve problems too (Thorndike's cats, Köhler's apes).
- Parts of a problem: initial state, goal state, the obstacles, and the operations (steps) allowed.
- Well-defined problem: clear start, goal and rules (a crossword, a maths sum). Ill-defined problem: goal or method unclear (writing a good essay, choosing a career).
- Steps of problem solving (textbook outline): identify / define the problem → represent it and gather information → generate possible solutions → evaluate and choose → carry out → evaluate the result (and go back if it fails). Polya's four steps of 1945 are in MAB-EI-03.
- Trial and error: trying responses until one works; E.L. Thorndike (puzzle-box cats, 1898).
- Insight: sudden grasp of the whole solution after re-seeing the problem (the "aha" experience); Wolfgang Köhler, chimpanzee Sultan joining sticks and stacking boxes to reach bananas (The Mentality of Apes, German 1917; English 1925). Köhler was a Gestalt psychologist.
- Algorithm: a step-by-step procedure that always gives the correct solution if followed (a formula, trying every combination of a lock) but may be slow.
- Heuristic: a rule of thumb or short-cut; quick and usually works, but does not guarantee a solution.
- Common heuristics: means-end analysis (reduce the gap between present state and goal step by step, through subgoals: Allen Newell and Herbert Simon, General Problem Solver, late 1950s), working backward (start from the goal), analogy (use the solution of a similar problem), hill climbing (always take the step that seems to get closer).
- Obstacles to problem solving: mental set, functional fixedness, lack of motivation, confirmation bias, poor representation of the problem, emotional stress.
- Mental set: the tendency to keep using a method that worked before. It speeds up solving of similar problems but blocks new, simpler solutions. Classic study: Abraham Luchins, water-jar problems (1942).
- Functional fixedness: seeing an object only in its usual function. Classic studies: Karl Duncker's candle problem (the box of tacks can be a candle holder; published 1945 in English) and Norman Maier's two-string problem (1931; a pair of pliers used as a pendulum weight).
- Decision making: choosing one course of action from alternatives, after judging their costs, benefits and chances. Judgement: estimating likelihoods and drawing conclusions from evidence.
- Amos Tversky and Daniel Kahneman (1974): judgement heuristics:
- Availability: judging how frequent something is by how easily examples come to mind (fear of flying after a crash in the news).
- Representativeness: judging by how much something resembles a typical case, ignoring base rates.
- Anchoring and adjustment: starting from an initial value and adjusting too little.
- Framing effect (Tversky and Kahneman, 1981): the same choice is judged differently when worded as a gain ("90% survive") or a loss ("10% die"). Prospect theory (1979): losses weigh more than equal gains (loss aversion). Kahneman: Nobel Prize in Economics, 2002.
- Satisficing and bounded rationality: Herbert Simon (see MAB-EI-03).
- Creativity: the ability to produce ideas or products that are novel (original) and appropriate (useful, fitting the purpose). Both are needed; novelty alone is mere oddity.
- Creative thinking is part of everyday life, not only of art and science: it shows in teaching, conversation, helping others, asking questions, cooking, solving family problems.
- Convergent vs divergent thinking (J.P. Guilford): convergent = one correct answer; divergent = many possible answers; creativity draws mainly on divergent thinking.
- Features of creative (divergent) thinking: fluency (number of ideas), flexibility (variety of kinds of ideas), originality (unusual ideas), elaboration (developing an idea in detail). Reproducibility is not one of them: reproducing what exists is the opposite of creating.
- Wallas (1926), four stages: preparation → incubation → illumination → verification. Details, tests of creativity (Torrance, Baqer Mehdi, Passi), brainstorming (Osborn), lateral thinking (de Bono) and Getzels and Jackson are in EDU-ID-03.
Explained
1. Algorithm vs heuristic
| Point | Algorithm | Heuristic |
|---|---|---|
| Nature | systematic, exhaustive rule | short-cut, rule of thumb |
| Result | correct answer guaranteed | answer likely, not guaranteed |
| Speed | slow when options are many | fast |
| Example | trying all 10,000 PINs of a 4-digit lock | trying birthdays first |
Most real-life problems are solved by heuristics because a full algorithm would take too long; computers use algorithms where speed allows.
2. Trial and error vs insight
| Point | Trial and error | Insight |
|---|---|---|
| Who | Thorndike (cats in puzzle box) | Köhler (chimpanzees) |
| Process | gradual, by stamping in the response that works | sudden reorganisation of the whole field |
| Learning curve | slowly falling time taken | sudden drop; solution kept and transferred |
| School | connectionism / behaviourism | Gestalt |
3. How mental set and functional fixedness block us. In Luchins's water-jar task, people who solved several problems with a long formula (B − A − 2C) kept using it even when a short one (A − C) would do; people without the practice series saw the short way at once. In Duncker's candle task, people given the tacks inside the box rarely thought of the box as a shelf; when the box was given empty, many more solved it. Both show that past experience can help or hinder: a set helps on similar problems and harms on different ones. Remedies: restate the problem, think of unusual uses, take a break (incubation), ask someone new.
4. Other obstacles. Lack of motivation (giving up early), confirmation bias (looking only for evidence that supports the first idea), fixation on irrelevant details, poor representation (a problem drawn as a diagram may become easy), anxiety and time pressure.
5. Steps and errors in decision making. A careful decision: list options → gather information on each → weigh consequences and probabilities → choose → review. In practice people rely on the judgement heuristics above, which produce biases: overconfidence, sunk-cost thinking (continuing because much has already been spent), the framing effect, hindsight bias ("I knew it all along"). Group decisions add groupthink (Janis; see MAB-EI-03) and group polarisation (groups move to a more extreme position than members held alone).
6. Creative thinking: the NCERT view. Creative thinking is not limited to a few geniuses; it varies by degree in everyone and can be trained. Its two hallmarks are novelty and appropriateness. It works with critical (convergent) thinking: divergent thinking generates many ideas, convergent thinking selects and checks the best. Barriers to creative thinking:
| Barrier | Example |
|---|---|
| Habitual | mental set, doing it "the way it's always done" |
| Perceptual | functional fixedness, seeing only one side |
| Motivational | low interest, fear of failure |
| Emotional | fear of ridicule, anxiety |
| Cultural | stress on conformity, only one right answer |
Ways to foster it: brainstorming (quantity of ideas, no criticism during the session), building a big list before judging, thinking of opposites and analogies, lateral thinking, keeping a notebook, taking time for incubation, and an environment of freedom and acceptance.
7. Creativity and intelligence. They are related but not the same. Intelligence tests stress convergent thinking; creativity tests stress divergent thinking. Research suggests a threshold: above-average intelligence (about IQ 120) is needed for high creativity, but above it the two are only weakly related. So a person can be highly intelligent but not very creative, and vice versa. (Getzels and Jackson's study: EDU-ID-03.)
Common traps
- ✗ "Heuristics always give the correct solution." ✓ Only an algorithm guarantees a correct solution; heuristics are short-cuts.
- ✗ "Problem solving is unique to human beings." ✓ Animals also solve problems (Thorndike's cats, Köhler's chimpanzees).
- ✗ "Mental set only hinders problem solving." ✓ It speeds up solving of similar problems; it hinders new ones.
- ✗ "Functional fixedness: Luchins; mental set: Duncker." ✓ Mental set: Luchins (water jars); functional fixedness: Duncker (candle) and Maier (two strings).
- ✗ "Insight learning: Thorndike." ✓ Köhler (Sultan); Thorndike = trial and error.
- ✗ "Availability heuristic = judging by resemblance to a type." ✓ Resemblance = representativeness; availability = ease of recall.
- ✗ "Creativity = novelty only." ✓ Novelty + appropriateness.
- ✗ "Reproducibility is a feature of creative thinking." ✓ The features are fluency, flexibility, originality, elaboration.
- ✗ "Creative thinking is seen only in art and science." ✓ It shows in everyday acts: teaching, conversation, helping others, asking questions.
- ✗ "Wallas: preparation, illumination, incubation, verification." ✓ Incubation before illumination.
Quick revision
- Problem solving = goal-directed thinking; initial state → goal state past obstacles; not unique to humans.
- Well-defined vs ill-defined problems; steps: define, represent, generate, evaluate, act, review.
- Thorndike: trial and error (1898); Köhler: insight, Sultan (Gestalt).
- Algorithm = always correct, slow; heuristic = rule of thumb, fast, no guarantee.
- Means-end analysis and subgoals: Newell and Simon; working backward; analogy.
- Mental set: Luchins water jars (1942); functional fixedness: Duncker candle, Maier two strings.
- Tversky and Kahneman (1974): availability, representativeness, anchoring; framing (1981); Kahneman Nobel 2002.
- Creativity = novel + appropriate; divergent thinking (Guilford): fluency, flexibility, originality, elaboration.
- Wallas 1926: preparation, incubation, illumination, verification.
- Creativity ≠ intelligence: threshold about IQ 120; tests and Getzels-Jackson in EDU-ID-03.
Go deeper: Deeper (beyond what APPSC Paper I usually asks)
Deeper Advanced
1. Problem space and representation. Newell and Simon described problem solving as a search through a problem space: all the states that can be reached by legal moves. Algorithms search the whole space; heuristics prune it. Classic puzzles used in research: the Tower of Hanoi (means-end analysis and subgoals), missionaries and cannibals (hill climbing fails when a step must move away from the goal), and the nine-dot problem (solvers wrongly assume lines must stay inside the square).
2. Two systems of thought. Kahneman's System 1 (fast, automatic, intuitive: the source of heuristics) and System 2 (slow, effortful, logical: checks System 1). Biases appear when System 2 does not step in (see MAB-EI-03).
3. Views of creativity. Guilford's Structure of Intellect put divergent production among the operations of intellect. Sternberg's investment theory: creative people "buy low and sell high" in ideas, and need intellectual skills, knowledge, thinking style, personality, motivation and a supportive environment. Amabile stressed intrinsic motivation: people are most creative when interested in the task for its own sake, and external rewards can reduce creativity. Csikszentmihalyi linked creative work to the state of flow.
4. Traits of creative people. Independence of judgement, tolerance of ambiguity, openness to experience, curiosity, willingness to take risks, persistence, a sense of humour. Creative products are judged by peers in the field, so creativity has a social side as well.
Practise this topic. Questions on Problem solving, decision making and creativity, with answers explained.
All Cognition and language notes · APPSC Paper I syllabus · APPSC Paper I Mock 1 with answers · Start free
Medha AI writes its own notes and checks them against the sources listed. Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.