Thinking and Problem-Solving
Introduced| English | Meaning |
|---|---|
| Concepts/ˈkɒnsepts/ | Concepts |
| prototype/ˈprəʊtəʊtaɪp/ | A mental representation of the most typical example of a category. |
| Schemas/ˈskiːməz/ | Mental frameworks that organise knowledge and guide interpretation of new information. |
| assimilation/əˌsɪmɪˈleɪʃn/ | Incorporating new information into an existing mental schema. |
| accommodation/əˌkɒməˈdeɪʃn/ | Changing an existing mental schema to incorporate new information or experience. |
| algorithm/ˈælɡərɪθəm/ | A finite sequence of precise steps for solving a problem or carrying out a task. |
| heuristic/hjuːˈrɪstɪk/ | A practical shortcut or rule of thumb used to solve a problem or make a decision without guaranteeing an optimal or correct result. |
| mental set/ˈmentl set/ | mental set |
| Framing/ˈfreɪmɪŋ/ | The way a choice is presented changes the decision. |
| gambler's fallacy/ˈɡæmbləz ˈfæləsi/ | The mistaken belief that past independent chance outcomes make a compensating outcome more likely next. |
| sunk-cost fallacy/sʌŋk kɒst ˈfæləsi/ | Continuing a course of action because of resources already spent, rather than judging its future costs and benefits. |
| Creativity/kriːˌeɪˈtɪvɪti/ | The ability to produce ideas or solutions that are both original and useful or appropriate. |
| Executive functions/eɡˈzekjuːtɪv ˈfʌŋkʃnz/ | The set of skills for planning, updating, and inhibiting. |
| divergent thinking/daɪˈvɜːdʒənt ˈθɪŋkɪŋ/ | Generating several possible ideas or solutions rather than seeking a single answer immediately. |
| Convergent thinking/kənˈvɜːdʒənt ˈθɪŋkɪŋ/ | Convergent thinking |
A shortcut that usually works, and sometimes fails
- People do not solve most problems by checking every possibility.
- They use shortcuts that are fast and usually right.
- The systematic errors those shortcuts produce are what this topic is really about.
Concepts, prototypes and schemas
- Concepts 概念 form the basis of thought; a prototype 原型 is the ideal example of a concept.
- Schemas 图式 are frameworks for thinking, changed through assimilation 同化 (fitting new information into an existing schema) and accommodation 顺应 (changing the schema to fit).
- The prototype explains why a robin feels more "bird" than a penguin does.
Four mental shortcuts: availability, representativeness, anchoring and confirmation bias
Accommodation means fitting new information into a schema you already have.
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That is assimilation. Accommodation changes the schema itself to fit the new information.
Algorithms and heuristics
- An algorithm 算法 tries all possible solutions until the correct one is found — slow but guaranteed.
- A heuristic 启发式 uses a mental shortcut — fast, but it can lead to errors in judgement.
- The trade is always the same: certainty against speed.
An algorithm differs from a heuristic in that it...
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The trade is certainty against speed: algorithms guarantee, heuristics hurry.
A heuristic is not simply "a mistake". It is a shortcut that is usually right — which is exactly why people keep using it. An exam answer should say what the shortcut normally buys you and the error it can produce.
Algorithm, heuristic, or error?
Sort each description by the kind of thinking it names.
Continuing a failing course of action because of resources already spent is the ____-cost fallacy.
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Only the remaining costs and benefits should decide; spent resources are gone either way.
Select all the thinking errors the CED names in this topic.
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Transduction is a sensation term, not a thinking error.
Where thinking goes wrong
- A mental set 心向 is relying on what worked before, even when it no longer fits.
- Framing 框架效应 means the way a choice is presented changes the decision.
- The gambler's fallacy 赌徒谬误 and the sunk-cost fallacy 沉没成本谬误 both keep people committed to a losing course.
Match each term to what it does.
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Divergent opens up options, convergent narrows them, and executive functions run the plan.
Executive function and creativity
- Executive functions 执行功能 are the processes that generate, organise, plan and carry out goal-directed behaviour.
- Creativity 创造力 generates novel ideas through divergent thinking 发散思维 — many possible answers.
- Convergent thinking 聚合思维 narrows to one correct answer instead.
A student has already spent forty hours on a failing project and keeps going "because of all that work". The hours are gone either way — that is the sunk-cost fallacy, and only the remaining costs and benefits should decide.
Concepts and prototypes organise thought; schemas change by assimilation and accommodation. Algorithms guarantee an answer, heuristics are fast but error-prone, and mental set, framing, the gambler's and sunk-cost fallacies are the named errors. Executive functions plan; divergent thinking creates.
Write from a coin that has already landed heads 6 times
- A fair coin has landed heads 6 times in a row.
- State the probability that the next flip is tails.
A fair coin lands heads 6 times in a row. What is the probability that the next flip is tails, and which fallacy says otherwise?
Independent events do not compensate for a recent run.
What is the probability of tails on the next flip?
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A fair coin stays at 1/2. The past run is the gambler's fallacy.