📚 KS3 Cambridge Psychology: Quick Reference Handbook of Formulas and Theorems | KS3 剑桥心理学：公式定理速查手册
Welcome to your one-stop revision guide for the key ‘formulas and theorems’ in KS3 Cambridge Psychology. Although psychology is not a maths-based science in the same way as physics, it has its own powerful theoretical models, cause-and-effect relationships, and evidence-based laws that can be expressed as simple equations or diagrams. This handbook translates 10 essential psychological principles into easy-to-memorise ‘formulas’ to help you crack open exam questions and understand how the mind works.
欢迎来到 KS3 剑桥心理学关键“公式定理”一站式复习手册。虽然心理学不像物理那样以数学为基础，但它拥有强大的理论模型、因果关系和基于证据的定律，这些都可以表达成简单的方程或图示。本手册将 10 个核心心理学原理转化为易于记忆的“公式”，帮助你攻克考试难题，理解心智的运作方式。
1. Classical Conditioning: The Formula for Learned Associations | 经典条件反射：学习联结的公式
Pavlov’s classical conditioning can be expressed as a four-step transformation. A neutral stimulus that initially produces no response becomes associated with an unconditioned stimulus, eventually triggering a conditioned response on its own. The basic formula is: NS + UCS → UCR, and after conditioning, CS → CR.
巴甫洛夫的经典条件反射可以表达为一个四步转化过程。原本不引发反应的中性刺激与无条件刺激建立联系后，最终能单独引发条件反应。基本公式是：NS + UCS → UCR，经过条件化后，CS → CR。
- NS (Neutral Stimulus) + UCS (Unconditioned Stimulus) → UCR (Unconditioned Response)
- After repeated pairings: CS (Conditioned Stimulus) → CR (Conditioned Response)
NS + UCS → UCR → CS → CR
The bell (NS) was rung just before presenting food (UCS), which made the dog salivate (UCR). After learning, the bell alone (CS) triggered salivation (CR). This is the fundamental equation of associative learning.
在喂食（UCS）之前摇铃（NS），狗分泌唾液（UCR）。学习之后，单独铃声（CS）就会引发唾液分泌（CR）。这就是联结学习的基本方程式。
2. Operant Conditioning: Behaviour-Consequence Equation | 操作性条件反射：行为-后果方程
Skinner’s operant conditioning shows that behaviour is shaped by its consequences. The ‘theorem’ states: a behaviour followed by reinforcement is more likely to be repeated; a behaviour followed by punishment is less likely to occur. The formula can be expressed as B + R ↑ (reinforcement increases behaviour) and B + P ↓ (punishment decreases behaviour).
斯金纳的操作性条件反射表明，行为由其后果塑造。其“定理”指出：紧随强化之后的行为更可能重复出现；紧随惩罚之后的行为更不可能出现。可用公式表达为 B + R ↑（强化提高行为频率）和 B + P ↓（惩罚降低行为频率）。
| Type of Consequence | Effect on Behaviour | Formula |
|---|---|---|
| Positive Reinforcement | Increases | B + R⁺ → B ↑ |
| Negative Reinforcement | Increases | B + R⁻ (removes unpleasant) → B ↑ |
| Punishment | Decreases | B + P → B ↓ |
B + Reinforcement → B ↑ ; B + Punishment → B ↓
When a rat presses a lever (B) and receives food (R⁺), lever-pressing increases. If pressing a lever delivers an electric shock (P), the behaviour decreases. Remember that negative reinforcement still increases behaviour because it removes something unpleasant.
当老鼠按压杠杆（B）并获得食物（R⁺）时，按压杠杆的行为增加。如果按压杠杆会得到电击（P），行为就会减少。请记住，负强化同样会提高行为频率，因为它移除了令人不快的事物。
3. Observational Learning: The Modelling Formula | 观察学习：模仿公式
Bandura’s Social Learning Theory suggests we learn not just by direct reinforcement but by watching others. The modelling formula contains four necessary processes: Attention → Retention → Reproduction → Motivation. If any link in this chain is missing, learning through observation will not occur.
班杜拉的社会学习理论指出，我们不仅通过直接强化学习，还通过观察他人来学习。模仿公式包含四个必要过程：注意 → 保持 → 再现 → 动机。如果链条中任意一个环节缺失，观察学习就不会发生。
Attention + Retention + Reproduction + Motivation → Modelled Behaviour
The ‘Bobo doll’ experiment demonstrated that children who observed an aggressive model were more likely to imitate the aggressive acts. The formula helps explain why simply showing a behaviour is not enough; the learner must pay attention, remember it, have the physical ability to copy it, and be motivated to do so.
“波波玩偶”实验表明，观察到攻击性榜样的儿童更可能模仿攻击行为。这个公式有助于解释为什么仅仅展示行为是不够的；学习者必须注意它、记住它、具备模仿它的身体能力，并且有动机这样做。
4. Multi-Store Model: Memory Conversion Process | 记忆多储存模型：记忆转换过程
Atkinson and Shiffrin’s model treats memory as a system of three stores linked by processes of attention and rehearsal. The core ‘equation’ shows how information flows from sensory memory to long-term memory. The crucial step is rehearsal; without it, information decays.
阿特金森和谢夫林的模型将记忆视为通过注意和复述过程连接的三个存储系统。核心“方程”展示了信息如何从感觉记忆流向长时记忆。关键步骤是复述；没有复述，信息就会消退。
Sensory Input → Sensory Memory (decays ½ sec) → Attention → Short-Term Memory (7±2 chunks) → Rehearsal → Long-Term Memory (potentially unlimited)
- Without attention, information in sensory memory is lost.
- Without rehearsal, information in STM is displaced or decays after about 18-30 seconds.
没有注意，感觉记忆中的信息就会丢失；没有复述，短时记忆中的信息大约在18–30秒后被取代或消退。
In exam questions, you can draw this as a flowchart and label the capacity and duration at each stage: sensory memory (very large capacity, 0.5 seconds), STM (7±2 items, 18-30 seconds), LTM (unlimited capacity and duration). The formula is a perfect revision snapshot.
在考试中，你可以将此画成流程图，并标注每个阶段的容量和持续时间：感觉记忆（容量非常大，持续0.5秒）、短时记忆（7±2 个项目，18–30秒）、长时记忆（容量和持续时间无限）。这个公式是完美的复习快照。
5. Working Memory: Components Equation | 工作记忆：组成方程
Baddeley and Hitch updated the Short-Term Memory idea with the Working Memory Model, which is more like a mental workspace than a passive store. The model can be represented as a function of several interacting components: Central Executive + Phonological Loop + Visuospatial Sketchpad + Episodic Buffer = Working Memory.
巴德利和希奇用工作记忆模型更新了短时记忆的理念，它更像一个心理工作区，而非被动存储库。该模型可表示为若干相互作用成分的函数：中央执行系统 + 语音回路 + 视空间画板 + 事件缓冲器 = 工作记忆。
Working Memory = Central Executive (controls attention) + Phonological Loop (verbal info) + Visuospatial Sketchpad (visual/spatial info) + Episodic Buffer (integrates info)
The central executive is the ‘boss’ that directs focus. The phonological loop deals with spoken and written material (the inner voice). The visuospatial sketchpad handles images and spatial layouts (the inner eye). This ‘component formula’ helps explain why we can perform two tasks simultaneously if they use different subsystems (e.g., listening to music while drawing) but struggle when they compete for the same resource.
中央执行系统是指导注意力的“老板”，语音回路处理口头和书面材料（内部语音），视空间画板处理图像和空间布局（内部眼睛）。这个“组件公式”解释了为什么当两个任务使用不同子系统时，我们可以同时进行（例如一边听音乐一边画画），但当它们竞争同一资源时就会感到困难。
6. Piaget’s Stages: Developmental Equation | 皮亚杰认知发展阶段公式
Piaget proposed that cognitive development progresses through four invariant stages, each characterised by new logical abilities. The sequence forms a ‘staircase formula’: Sensorimotor → Preoperational → Concrete Operational → Formal Operational. Each stage must be mastered in order, and the age ranges serve as a guide.
皮亚杰提出认知发展按照四个不变的阶段进行，每个阶段以新的逻辑能力为特征。该序列形成一个“阶梯公式”：感知运动阶段 → 前运算阶段 → 具体运算阶段 → 形式运算阶段。每一个阶段必须按顺序掌握，年龄范围仅作为指导。
0-2 years: Sensorimotor (object permanence) → 2-7 years: Preoperational (symbolic play, egocentrism) → 7-11 years: Concrete Operational (conservation, reversibility) → 11+ years: Formal Operational (abstract reasoning, hypothesis testing)
A child in the Preoperational stage cannot solve conservation tasks (e.g., understanding that the amount of water remains the same when poured into a different shaped glass). Once they reach Concrete Operational, they grasp the logical ‘rule’ of conservation. The formula highlights the key achievement at each step, making it easy to diagnose a child’s stage.
处于前运算阶段的儿童无法解决守恒任务（例如，理解将水倒入不同形状的玻璃杯时水量不变）。一旦他们进入具体运算阶段，就会掌握守恒的逻辑“规则”。该公式突出了每一步的关键成就，使诊断儿童所处的阶段变得容易。
7. Vygotsky’s ZPD: The Scaffolding Formula | 维果茨基最近发展区公式
Vygotsky argued that learning is most effective when a child works within the Zone of Proximal Development (ZPD) with the support of a More Knowledgeable Other (MKO). The ‘theorem’ is that the actual developmental level plus scaffolding bridges the gap to potential developmental level. The formula can be expressed as Potential Development = Actual Development + Scaffolding from MKO.
维果茨基认为，当儿童在更有知识的他人（MKO）支持下，在最近发展区（ZPD）内学习时，效果最好。其“定理”是：实际发展水平加上支架作用，可以缩小与潜在发展水平之间的差距。公式可表达为：潜在发展 = 实际发展 + MKO 提供的支架。
ZPD = Potential Level (with guidance) − Current Independent Level
What a child can do today with assistance, they can do alone tomorrow. A teacher using scaffolding might break down a task, model strategies, and then gradually withdraw support as the learner becomes more competent. This is like building a bridge and removing the scaffolding once the bridge can stand on its own.
今天孩子在帮助下能做的事，明天就能独立完成。采用支架教学的教师可能会分解任务、示范策略，然后随着学习者能力提升逐步撤去支持。这就像搭一座桥，一旦桥能独立支撑，就移除脚手架。
8. Yerkes-Dodson Law: Arousal-Performance Curve | 耶克斯-多德森定律：唤醒-表现曲线
This classic law describes the relationship between arousal (mental alertness or stress) and performance. It states that performance increases with arousal up to an optimal point; after that, too much arousal impairs performance. The shape is an inverted U, which can be summarised as the formula Performance ∝ f(Arousal) with a peak at moderate arousal.
这条经典定律描述了唤醒水平（心理警觉或压力）与表现之间的关系。它表明，表现随唤醒水平上升而提高，到达最佳点后，过度唤醒反而削弱表现。形状是一个倒U形，可以概括为公式 表现 ∝ f(唤醒)，且在中等唤醒时达到峰值。
Performance ↑ as Arousal ↑ (up to optimum) → Performance ↓ as Arousal ↑ (beyond optimum)
For simple or well-practised tasks, the optimal level of arousal is higher; for complex or new tasks, a lower level of arousal is best. This helps explain why a little exam nerves can improve focus, but panic makes you go blank. The law is a powerful revision tool for evaluating studies on stress and eyewitness testimony.
对于简单或熟练的任务，最佳唤醒水平较高；对于复杂或新任务，较低的唤醒水平最好。这有助于解释为什么一点考试紧张可以提高注意力，但恐慌会让人大脑一片空白。该定律是评价压力与目击者证词研究的有力工具。
9. Social Identity Theory: In-Group & Out-Group Formula | 社会认同理论：内群体与外群体公式
Tajfel’s Social Identity Theory explains how the mere act of categorising people into groups can lead to prejudice and discrimination. The psychological mechanism can be written as Categorisation → Social Identification → Social Comparison → In-group bias. This sequence is the formula for intergroup behaviour.
泰弗尔的社会认同理论解释了仅仅将人划分为群体这一行为如何导致偏见和歧视。心理机制可写为：分类 → 社会认同 → 社会比较 → 内群体偏爱。这个序列就是群际行为的公式。
We vs. Them → Identify with ‘we’ → Compare ‘we’ favourably to ‘them’ → Boost self-esteem
Even minimal groups (e.g., randomly assigned ‘over-estimators’ vs ‘under-estimators’) produce in-group favouritism. By learning the formula, students can analyse real-world examples such as football rivalry or school cliques. The key is that the drive for a positive social identity makes us favour our own group to feel good about ourselves.
即使是随机划分的最小群体（如“高估者”与“低估者”），也会产生内群体偏爱。通过学习这个公式，学生可以分析现实世界的例子，如足球对抗或学校小团体。关键在于，对积极社会认同的追求使我们偏爱自己的群体以获得良好自我感觉。
10. Conformity & Obedience Factors: Social Influence Equation | 从众与服从因素：社会影响方程
Research by Asch and Milgram revealed that social pressure is a product of several situational and dispositional variables. Understanding these factors can be framed as a model: Conformity/Obedience = f(Group Size, Unanimity, Task Difficulty, Authority Proximity, Legitimacy, Social Support). The formula shows that changing any one variable can alter the outcome.
阿希和米尔格拉姆的研究揭示，社会压力是若干情境与性格变量的产物。理解这些因素可以构建一个模型：从众/服从 = f(群体规模, 一致性, 任务难度, 权威接近度, 合法性, 社会支持)。该公式表明，改变任意一个变量都能改变结果。
Conformity ↑ as Group Size ↑ (up to 3-4); Conformity ↓ if one ally disagrees (Social Support)
In Asch’s line judgment study, conformity peaked when the majority was 3-4 confederates, and dropped dramatically if just one confederate gave the correct answer. In Milgram’s shock experiment, obedience decreased when the experimenter’s authority was undermined (e.g., orders by phone) or when the victim’s proximity increased.
在阿希的线段判断研究中，当多数为3–4个同谋者时，从众率达到顶峰；只要有一个同谋者给出正确答案，从众就会显著下降。在米尔格拉姆电击实验中，当实验者的权威被削弱（如通过电话下命令）或受害者的接近度增加时，服从性就会下降。
This ‘equation’ gives you a framework to evaluate why people follow the crowd or obey destructive orders and is particularly useful for 6-mark exam questions.
这个“方程”为你提供了一个框架，用于评价为什么人们会随大流或服从破坏性命令，对6分考题尤其有用。
11. Attachment Theory: Caregiver-Infant Bond Formula | 依恋理论：照料者-婴儿纽带公式
Bowlby’s theory of attachment proposes that an infant’s bond with a primary caregiver is an evolved mechanism that ensures survival. The bond develops through interactional synchrony and reciprocity, and its quality forms an ‘internal working model’. You can summarise as: Sensitive Responsiveness → Secure Attachment → Positive Internal Working Model of relationships.
鲍尔比的依恋理论提出，婴儿与主要照料者之间的纽带是一种确保生存的进化机制。纽带通过互动同步和相互性发展，其质量形成“内部工作模型”。可概括为：敏感回应 → 安全依恋 → 积极的人际关系内部工作模型。
Sensitive Caregiver Response + Reciprocal Interactions → Secure Attachment → Healthy Social & Emotional Development
Ainsworth’s Strange Situation identified three attachment types: Secure (Type B), Insecure-Avoidant (Type A), and Insecure-Resistant (Type C). The type an infant shows correlates with caregiver sensitivity. This formula helps link parenting behaviour to a child’s later sociability and emotional regulation.
安斯沃思的陌生情境实验识别出三种依恋类型：安全型（B型）、不安全-回避型（A型）和不安全-反抗型（C型）。婴儿表现出的类型与照料者的敏感性相关。这个公式有助于将养育行为与儿童日后的社交能力和情绪调节联系起来。
12. Cognitive Dissonance: Attitude-Behaviour Formula | 认知失调：态度-行为公式
Festinger’s Cognitive Dissonance Theory states that when we hold two conflicting cognitions (beliefs, attitudes, or awareness of behaviour), we experience mental discomfort. To reduce this dissonance, we adjust our attitudes. The mathematical-style relationship is: Attitude ≠ Behaviour → Discomfort → Attitude Change to match behaviour.
费斯廷格的认知失调理论指出，当我们持有两种相互矛盾的认知（信念、态度或行为意识）时，会感到心理不适。为了减少这种失调，我们会调整态度。数学式关系为：态度 ≠ 行为 → 不适 → 态度改变以匹配行为。
Dissonance = (Inconsistent Attitude & Behaviour) → Motivation to reduce dissonance → Attitude shift (e.g., ‘I really did enjoy that boring task’)
In the classic study, participants paid $1 to lie about a boring task experienced greater attitude change (they said they enjoyed it) than those paid $20, because the lower payment provided insufficient justification for lying, creating more dissonance. The formula highlights the counter-intuitive idea that less reward can cause greater internalisation.
在经典研究中，收取1美元而对无聊任务撒谎的参与者，比收取20美元的参与者经历了更大的态度转变（他们说自己喜欢任务），因为较低的报酬为撒谎提供了不充分的理由，从而产生更多失调。该公式凸显了一个反直觉的观点：较少的奖励反而能导致更深层的内化。
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