# Lecture 13: Cognition: Thinking and Problem-Solving
## Introductory Psychology
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## Learning Objectives
By the end of this lecture, students will be able to:
1. Define cognition and describe how concepts and categories organize thinking
2. Distinguish between algorithms and heuristics as problem-solving strategies
3. Identify common barriers to effective problem-solving
4. Explain the major heuristics and biases in judgment and decision-making
5. Describe the role of creativity and its components
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## Lecture Content
### I. Concepts and Categories
Cognition encompasses the mental activities associated with thinking, knowing, remembering, and communicating. One of the most fundamental cognitive operations is the formation of concepts — mental categories used to group objects, events, and ideas that share common features. Concepts allow us to organize and simplify the enormous complexity of the world and enable us to generalize knowledge to new instances.
We often judge whether something belongs to a category by comparing it to a prototype, the most typical or representative example of that concept. A robin, for instance, is a more prototypical "bird" than a penguin, and it is classified as a bird more quickly. An alternative account, the exemplar model, suggests that we store individual examples and compare new items to these stored instances rather than to a single abstract prototype. Concepts are organized hierarchically, from superordinate categories (animal) to basic-level categories (dog) to subordinate categories (golden retriever). The basic level tends to be the most commonly used and informationally rich.
### II. Problem-Solving Strategies
Problem-solving involves moving from a current state to a desired goal state when the path between them is not immediately obvious. Algorithms are step-by-step procedures that guarantee a correct solution if followed to completion, but they can be extremely time-consuming — trying every possible letter combination to solve an anagram, for example. Heuristics are mental shortcuts or rules of thumb that speed up problem-solving without guaranteeing a correct answer. Means-ends analysis works by reducing the difference between the current state and the goal state one step at a time. Working backward starts from the goal and moves toward the starting point. Hill climbing involves always moving in the direction of the goal, though this approach can get stuck at local maxima. Analogy involves recognizing structural similarity between a current problem and a previously solved one and transferring the solution, as demonstrated by Gick and Holyoak in 1980.
Trial and error — simply trying different solutions until one works — is inefficient but sometimes the only available option. Insight, the sudden "aha!" moment in which a solution appears all at once, involves restructuring one's representation of the problem. Unlike incremental approaches, insight cannot be reached through gradual steps and appears to engage the anterior superior temporal gyrus in the right hemisphere.
### III. Barriers to Problem-Solving
Fixation is the inability to see a problem from a fresh perspective. One common form is the mental set, the tendency to use strategies that have worked in the past even when they are no longer effective. In Luchins' water jar problem, participants who had practiced solving problems with a complex formula persisted with that formula even when a much simpler solution was available. Functional fixedness is the tendency to think of objects only in terms of their conventional functions. In Duncker's candle problem, participants struggled to use a box of tacks as a shelf for a candle because they saw the box only as a container for tacks. Overcoming functional fixedness requires reimagining the possible uses of everyday objects.
Unnecessary constraints arise when problem-solvers assume restrictions that do not actually exist. In the nine-dot problem, people assume they cannot draw lines beyond the boundary of the dot grid, preventing them from finding the solution. Confirmation bias in problem-solving leads people to seek evidence that confirms their current hypothesis rather than testing alternatives, as demonstrated in Wason's 2-4-6 task, where participants tested rules consistent with their hypothesis instead of trying to disconfirm it.
Three panels illustrating barriers to problem-solving. Panel A: Duncker's candle problem — a table with a candle, a box of thumbtacks, and matches on the left (the problem); on the right, the solution shows the box emptied and tacked to the wall as a platform for the candle, with an arrow labeled "overcoming functional fixedness." Panel B: The nine-dot problem — a 3x3 grid of dots with the instruction to connect all nine dots with four straight lines without lifting the pen; the solution shows lines extending beyond the perceived boundary of the dots. Panel C: Luchins' water jar problem showing the complex formula (B - A - 2C) that creates a mental set, and a simpler direct solution (A - C) that participants missed.
### IV. Judgment and Decision-Making
Humans are not perfectly rational decision-makers. Instead, we rely on cognitive heuristics that, while often useful, can introduce systematic biases. The representativeness heuristic, identified by Tversky and Kahneman, involves judging the likelihood of something based on how well it matches a prototype or stereotype. This heuristic leads to base rate neglect — ignoring statistical probabilities in favor of representativeness (assuming a shy, organized person is a librarian rather than a salesperson, despite salespeople being far more numerous). It also produces the conjunction fallacy, in which people judge the combination of two events as more likely than either event alone. In the famous "Linda problem," participants rated Linda as more likely to be "a bank teller who is also a feminist" than simply "a bank teller," even though the conjunction of two events can never be more probable than either event alone. The gambler's fallacy — believing that past random events influence future ones — is another consequence of representativeness thinking.
The availability heuristic involves estimating the likelihood of events based on how easily examples come to mind. Judgments are influenced by recency, vividness, emotional impact, and media coverage, which is why people tend to overestimate the risk of airplane crashes (which are vivid and heavily covered) while underestimating the far greater risk of car accidents.
Anchoring and adjustment bias occurs when an initial piece of information — even an arbitrary one — disproportionately influences subsequent judgments. In a classic demonstration, spinning a wheel before estimating the number of African countries in the United Nations significantly shifted participants' estimates toward the randomly generated anchor. Framing effects demonstrate that how a problem is worded influences the decisions people make. Kahneman and Tversky's prospect theory showed that people are risk-averse when outcomes are framed as gains and risk-seeking when the same outcomes are framed as losses: "200 of 600 people will be saved" and "400 of 600 people will die" describe the same situation but reliably produce different choices.
Additional biases include overconfidence bias (the tendency to overestimate the accuracy of our knowledge), belief perseverance (maintaining beliefs even after the supporting evidence has been discredited), and the sunk cost fallacy (continuing an endeavor because of resources already invested rather than evaluating future prospects).
A four-panel infographic on cognitive biases. Panel A: Availability heuristic — two news headlines, one about a shark attack (vivid, rare) and one about heart disease (common, less vivid), with a probability bar showing the actual risk is reversed from what people estimate. Panel B: Representativeness heuristic — the "Linda problem" with a Venn diagram showing that the set "bank teller" must be larger than the subset "bank teller AND feminist." Panel C: Anchoring — two groups of people, one given a high anchor number and one given a low anchor number, with their subsequent estimates clustered near their respective anchors. Panel D: Framing — two identical medical scenarios framed as "lives saved" vs. "lives lost," with pie charts showing the different choices people make under each frame.
### V. Creativity
Creativity is the ability to produce ideas that are both novel (original) and valuable (useful or meaningful). Divergent thinking involves generating many possible solutions in an open-ended, free-flowing manner and is measured by fluency, flexibility, and originality — as in the Torrance Tests of Creative Thinking. Convergent thinking, by contrast, involves narrowing possibilities down to a single best solution.
Sternberg and Lubart identified several components of creativity. Expertise provides the well-developed knowledge base from which creative ideas emerge. Imaginative thinking is the ability to see problems in new ways and make novel connections. A venturesome personality involves tolerance for ambiguity and a willingness to take risks. Intrinsic motivation — being driven by interest and satisfaction rather than external rewards — fuels persistent creative effort. And a creative environment provides the supportive, stimulating context that encourages unconventional ideas.
The incubation effect refers to the observation that stepping away from a problem can lead to creative breakthroughs, possibly because unconscious processing continues during the break. Brainstorming, or generating ideas without immediate evaluation, has mixed evidence regarding its effectiveness compared to individual ideation. The relationship between intelligence and creativity follows a threshold pattern: a moderate level of intelligence (roughly IQ 120) appears necessary for creativity, but beyond that threshold, personality and motivation matter more than additional IQ points.
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