Year 7 CAIE Psychology: Quick Reference Handbook of Formulas and Theorems | Year 7 CAIE 心理学：公式定理速查手册

📚 Year 7 CAIE Psychology: Quick Reference Handbook of Formulas and Theorems | Year 7 CAIE 心理学：公式定理速查手册

Welcome to your quick reference guide for essential psychological concepts, framed as ‘formulas’ and ‘theorems’ to help you memorise and apply them with ease. In Year 7 CAIE Psychology, we explore the fundamental laws of behaviour, memory, and development. This handbook distils complex ideas into simple, memorable statements.

欢迎使用你的心理学必备概念速查手册，这些概念以“公式”和“定理”的形式呈现，便于你记忆和应用。在 Year 7 CAIE 心理学课程中，我们将探索行为、记忆和发展的基本规律。本手册将复杂的理论提炼成简洁、易记的要点。

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1. Classical Conditioning: The Stimulus-Response Formula | 经典条件作用：刺激-反应公式

Classical conditioning, discovered by Ivan Pavlov, explains how we learn to associate a neutral stimulus with a meaningful one. The process can be written as a three‑step formula. First, an unconditioned stimulus (US) naturally produces an unconditioned response (UR): US → UR. Second, a neutral stimulus (NS) is repeatedly paired with the US before the response occurs: NS + US → UR. After many pairings, the NS becomes a conditioned stimulus (CS) that elicits a conditioned response (CR): CS → CR.

由伊万·巴甫洛夫发现的经典条件作用解释了我们如何学会将中性刺激与有意义的刺激联系起来。这一过程可以写成三步公式。首先，无条件刺激（US）自然地引起无条件反应（UR）：US → UR。其次，中性刺激（NS）在反应发生前反复与US配对：NS + US → UR。多次配对后，NS变成条件刺激（CS），引发条件反应（CR）：CS → CR。

US → UR
NS + US → UR
CS → CR

For example, food (US) causes salivation (UR). A bell (NS) is rung just before food is presented. After several trials, the bell alone (CS) makes the dog salivate (CR). This ‘learning formula’ underpins many everyday fears and preferences.

例如，食物（US）引起分泌唾液（UR）。在呈现食物之前摇铃（NS）。几次试验后，单独的铃声（CS）就会让狗分泌唾液（CR）。这一“学习公式”是许多日常恐惧和偏好的基础。

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2. Operant Conditioning: The Reinforcement Contingency | 操作性条件作用：强化联结

B. F. Skinner’s operant conditioning focuses on how consequences shape voluntary behaviour. The basic formula is: Behaviour (R) → Consequence → Future probability of behaviour changes. Consequences are classified by whether they add or remove a stimulus, and whether they increase or decrease the behaviour.

B. F. 斯金纳的操作性条件作用关注后果如何塑造自愿行为。基本公式是：行为（R）→ 后果 → 行为未来发生的概率变化。后果根据是增加还是移除刺激以及是增加还是减少行为来分类。

The four types of contingency form a 2×2 grid. Positive reinforcement adds a pleasant stimulus to increase behaviour; negative reinforcement removes an unpleasant stimulus to increase behaviour. Positive punishment adds an unpleasant stimulus to decrease behaviour; negative punishment removes a pleasant stimulus to decrease behaviour.

四种联结类型构成一个2×2表格。正强化添加愉快刺激以增加行为；负强化移除不愉快刺激以增加行为。正惩罚添加不愉快刺激以减少行为；负惩罚移除愉快刺激以减少行为。

Type / 类型	Stimulus change / 刺激变化	Effect on behaviour / 对行为影响
Positive Reinforcement / 正强化	Add pleasant (+)	Increase ↑
Negative Reinforcement / 负强化	Remove unpleasant (–)	Increase ↑
Positive Punishment / 正惩罚	Add unpleasant (+)	Decrease ↓
Negative Punishment / 负惩罚	Remove pleasant (–)	Decrease ↓

A student studies hard and earns praise (positive reinforcement). A driver puts on a seatbelt to stop the annoying beep (negative reinforcement). A child touches a hot stove and feels pain (positive punishment). A teenager loses phone privileges for breaking curfew (negative punishment). Understanding these contingencies helps us predict and influence behaviour.

学生努力学习获得表扬（正强化）。司机系上安全带来停止烦人的蜂鸣声（负强化）。小孩摸热炉子感到疼痛（正惩罚）。青少年因违反宵禁失去手机使用权（负惩罚）。理解这些联结有助于我们预测和影响行为。

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3. Multi-Store Model of Memory: The Information Flow | 记忆的多贮存模型：信息流

Atkinson and Shiffrin proposed that memory consists of three separate stores through which information flows like a pipeline. The flow can be summarised as: Sensory input → Sensory memory (very brief, large capacity) → Attention → Short‑term memory (STM, 7±2 items, ~20 seconds) → Elaborative rehearsal → Long‑term memory (LTM, potentially unlimited).

阿特金森和希夫林提出记忆由三个独立的贮存组成，信息像管道一样流过。流程可概括为：感觉输入 → 感觉记忆（极短时，容量大）→ 注意 → 短时记忆（STM，7±2个项目，约20秒）→ 精细复述 → 长时记忆（LTM，可能无限）。

Sensory input → Sensory memory (attention) → STM (rehearsal) → LTM

Without attention, sensory information decays rapidly. Without rehearsal, items in STM are lost through displacement or decay. Maintenance rehearsal keeps information in STM, but only elaborative rehearsal – linking new information to existing LTM – transfers it to long‑term storage. This model explains why we remember some things for years but forget a phone number seconds after hearing it.

没有注意，感觉信息会迅速衰退。没有复述，短时记忆中的项目会因替代或衰退而丢失。维持性复述让信息保持在短时记忆中，但只有精细复述——将新信息与已有的长时记忆联系起来——才能将其转入长时储存。这一模型解释了为什么有些东西我们能记住多年，而一个电话号码听过后几秒就忘了。

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4. Ebbinghaus Forgetting Curve: Memory Retention Decay | 艾宾浩斯遗忘曲线：记忆保持衰减

Hermann Ebbinghaus discovered that forgetting follows a predictable, exponential‑like pattern. The retention R of nonsense syllables after t minutes can be approximated by:

赫尔曼·艾宾浩斯发现遗忘遵循一种可预测的、类似指数的规律。无意义音节在 t 分钟后的保持量 R 可以近似为：

R ≈ 100 × e^(–t/20)

This formula shows that memory loss is fastest soon after learning and then levels off. The table below displays typical retention values from Ebbinghaus’ original work.

这一公式表明记忆丧失在学习后最初最快，随后趋于平缓。下表显示了艾宾浩斯原始研究中的典型保持值。

Time since learning / 学习后时间	Retention (approx.) / 保持量（约）
20 minutes	58%
1 hour	44%
1 day	33%
6 days	25%

The curve demonstrates the power of spaced repetition: reviewing material at increasing intervals dramatically flattens the forgetting curve and strengthens long‑term memory. The ‘savings’ method Ebbinghaus used measured how much less time it took to relearn the same list.

曲线展示了间隔重复的力量：以逐渐增大的间隔复习材料能显著拉平遗忘曲线并强化长时记忆。艾宾浩斯使用的“节省法”测量的是重新学习同一列表所需时间减少了多少。

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5. Piaget’s Stages of Cognitive Development Theorem | 皮亚杰认知发展阶段定理

Jean Piaget proposed that children’s thinking develops through four invariant, universal stages. Each stage is characterised by qualitatively different mental operations. The theorem can be summarised by age ranges and key cognitive milestones.

让·皮亚杰提出儿童的思维发展经过四个不变的、普遍性的阶段。每个阶段都有质上不同的心理运算特征。该定理可用年龄段和关键认知里程碑来总结。

Stage / 阶段	Approximate Age / 大致年龄	Key Feature / 关键特征
Sensorimotor / 感知运动	0–2 years	Object permanence; world understood through senses and actions.
Preoperational / 前运算	2–7 years	Symbolic thought; egocentrism; lack of conservation.
Concrete operational / 具体运算	7–11 years	Logical reasoning about concrete events; conservation mastered.
Formal operational / 形式运算	11+ years	Abstract, hypothetical thinking; scientific reasoning.

Piaget argued that children actively construct knowledge through assimilation and accommodation. Moving to a new stage requires cognitive conflict—disequilibrium—that prompts a shift in mental structures. This theorem reminds us that a Year 7 student is typically entering formal operations, capable of thinking about possibilities and testing hypotheses.

皮亚杰认为儿童通过同化和顺应主动建构知识。进入新阶段需要认知冲突——失衡——这促使心理结构发生转变。这一定理提醒我们，Year 7的学生通常正进入形式运算阶段，能够思考可能性并检验假设。

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6. Maslow’s Hierarchy of Needs Theorem | 马斯洛需求层次定理

Abraham Maslow proposed that human motivation is organised into a pyramid of five needs. The theorem states that lower‑level needs must be substantially satisfied before higher‑level needs become active motivators. The hierarchy, from base to apex, is:

亚伯拉罕·马斯洛提出人类动机组织成一个五层需求的金字塔。定理表明，较低层次的需求必须得到基本满足后，较高层次的需求才会成为积极的激励因素。层次从底层到顶层为：

• Physiological needs (food, water, sleep) / 生理需求 (食物、水、睡眠)
• Safety needs (security, shelter, stability) / 安全需求 (安全、住所、稳定)
• Love and belongingness (friendship, family) / 爱与归属 (友谊、家庭)
• Esteem needs (respect, achievement, status) / 尊重需求 (尊重、成就、地位)
• Self‑actualisation (fulfilling one’s potential) / 自我实现 (发挥潜能)

Maslow later added a sixth layer — self‑transcendence — but the five‑stage model remains a powerful formula for understanding behaviour. For example, a student who feels unsafe or hungry will struggle to focus on learning, which belongs to higher esteem and self‑actualisation needs. Teachers use this theorem to ensure basic needs are met so that intellectual curiosity can flourish.

马斯洛后来增加了第六层——自我超越——但五阶段模型依然是理解行为的一个有力公式。例如，一个感到不安全或饥饿的学生很难专注于学习，而学习属于更高的尊重和自我实现需求。教师运用这一定理来确保基本需求得到满足，从而使求知欲得以蓬勃发展。

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7. Social Learning Theory: Bandura’s Observational Learning Formula | 社会学习理论：班杜拉观察学习公式

Albert Bandura demonstrated that we do not need direct reinforcement to learn; we can learn simply by watching others. Observational learning can be broken down into four mediational processes, often remembered as ARRM:

阿尔伯特·班杜拉证明我们不需要直接强化就能学习；我们可以仅通过观察他人来学习。观察学习可以分解为四个中介过程，常记作ARRM：

Attention → Retention → Reproduction → Motivation

First, the learner must pay attention to the model. Then, they must retain the observed behaviour in memory. Next, they must be able to reproduce the action physically. Finally, motivation determines whether the learned behaviour is performed — reinforcement and punishment experienced by the model influence this motivation vicariously.

首先，学习者必须注意榜样。然后，他们必须将观察到的行为保持在记忆中。接着，他们必须能够在身体上再现该动作。最后，动机决定习得的行为是否会表现出来——榜样所经历的强化和惩罚会间接影响这一动机。

Bandura’s famous Bobo doll experiment showed that children who watched an adult behave aggressively towards a doll were more likely to imitate that aggression, especially if the adult was rewarded. The formula highlights that learning is a cognitive process that can occur without a change in behaviour until an appropriate incentive appears.

班杜拉著名的波波玩偶实验表明，观看成人对玩偶做出攻击行为的儿童更可能模仿这种攻击行为，尤其是在成人受到奖励时。这一公式强调学习是一个认知过程，可以在没有行为改变的情况下发生，直到出现适当的诱因。

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8. Cognitive Dissonance Theory: Attitude-Behaviour Balancing Theorem | 认知失调理论：态度-行为平衡定理

Leon Festinger’s cognitive dissonance theory states that we are motivated to maintain consistency between our beliefs and our actions. When there

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