Thinking & Problem-Solving (College Board AP® Psychology): Revision Note

What is thinking?

• Thinking is the mental manipulation of information

  • Thinking involves forming representations of the world and using them to reason, plan, and make decisions

• The basic building blocks of thought are concepts and images

  • Concept: a mental category used to group objects, people, events, or ideas that share common features

    • E.g. the concept of "chair" allows us to recognize an enormous variety of objects as chairs without having to learn each one individually

  • A prototype is the most typical or ideal example of a concept, which is the mental image that first comes to mind when you think of a category

    • E.g. for most people in Western cultures, a robin is a closer prototype for "bird" than a penguin, even though both are birds

    • Prototypes vary between individuals and cultures depending on experience

  • Image: a mental picture or sensory representation - images can be visual, auditory, tactile, or olfactory

    • E.g. imagining what your childhood home looks like, or imagining the taste of hot chocolate

Schemas, assimilation, and accommodation

• A schema is an organized mental framework built up through experience that shapes how we interpret new information

  • Schemas act as cognitive shortcuts - they allow us to process new situations quickly by fitting them into existing frameworks

    • E.g. you have a schema for "restaurant" that includes menus, servers, and paying at the end. When you enter a new restaurant, this schema guides your behavior automatically

• People form and modify schemas through two processes:

  • Assimilation: taking in new information and fitting it into an existing schema without changing the schema

    • E.g. a child who has a schema for "dog" sees a poodle for the first time and calls it a dog. They have assimilated the new animal into their existing schema without modifying it

  • Accommodation: taking in new information that does not fit the existing schema and changing the schema to incorporate it

    • E.g. the same child learns that some four-legged animals are cats, not dogs. They must accommodate by modifying their schema to distinguish between the two

• Schemas can also lead to errors

  • If a new situation does not fit neatly into an existing schema, the brain may distort or misremember information to make it fit

Problem-solving

• Problem-solving involves removing one or more impediments to finding a solution

• Problems can be:

  • well-structured, with a clear, single correct answer, or

  • ill-structured, with multiple possible solutions and no clear path

• Two main strategies are used to solve problems:

  • Algorithms and heuristics

Algorithms

• An algorithm is a systematic, step-by-step procedure that guarantees the correct solution if followed correctly

• Algorithms are reliable but time-consuming as they work by testing every possible solution until the correct one is found

  • E.g. trying every possible combination of letters to crack a password guarantees success eventually, but could take an enormous amount of time

Heuristics

• A heuristic is a mental shortcut or rule of thumb that allows quick judgments without exhaustively testing every option

• Heuristics are faster than algorithms but can lead to errors because they rely on approximation rather than certainty

  • E.g. when trying to remember a password, guessing actual words rather than random letter combinations narrows the possibilities dramatically - this is a heuristic

• Two common heuristics that can lead to errors in judgment:

  • The availability heuristic is where we judge the likelihood of an event based on how easily an example comes to mind

  • Vivid or recent events feel more likely than they actually are

    • E.g. many people overestimate the danger of air travel because plane crashes are reported so vividly in the news, even though car travel is statistically more dangerous

  • The representativeness heuristic is where we judge the likelihood of something based on how closely it resembles a typical example (prototype) of a category

    • E.g. assuming a quiet, bookish person is more likely to be a librarian than a salesperson because they match the prototype of a librarian, even though there are far more salespeople than librarians

Impediments to problem-solving

• Several cognitive biases can hinder effective problem-solving:

  • Mental set (also called rigidity) is the tendency to approach a new problem using strategies that worked in the past, even when a different approach would be more effective

    • E.g. a student who always uses a particular formula to solve math problems may fail to notice a simpler solution because they default to their habitual approach

  • Functional fixedness is the tendency to see objects only in terms of their typical function, making it difficult to think of new or creative uses for familiar objects

    • E.g. not thinking to use a coin to tighten a screw when a screwdriver is not available, as the coin is mentally fixed to its usual purpose

  • Confirmation bias is the tendency to search for, favor, and remember information that confirms existing beliefs while ignoring contradictory evidence

    • E.g. a teacher who believes a student is weak may focus on their mistakes and overlook their successes, reinforcing the existing belief

  • Hindsight bias is the tendency after learning an outcome to believe you knew it all along

    • E.g. after a sports team loses, people who predicted they would win often feel they somehow knew the outcome was inevitable

  • Belief perseverance is the tendency to maintain a belief even when presented with evidence that contradicts it

    • E.g. continuing to hold a strong opinion even after the evidence that originally supported it has been shown to be flawed