📚 Year 8 CCEA Psychology: Formula & Theorem Quick Reference Handbook | 八年级 CCEA 心理学：公式定理速查手册
Psychology may seem like a subject built on stories and descriptions, but many of its most powerful ideas can be expressed as clear 'formulas' or 'theorems' – logical rules that predict how we think, feel and behave. This quick reference handbook for Year 8 CCEA Psychology rewrites essential models, principles and laws in a formula-style layout, making them easier to memorise and apply in class discussions, homework and assessments.
心理学或许看起来像一门由故事和描述组成的学科，但许多最有影响力的思想其实都可以用清晰的“公式”或“定理”来表达——这些逻辑规则能够预测我们的思维、情感和行为。这本面向八年级 CCEA 心理学的速查手册将重要模型、原理和定律用公式风格重新编排，让你在课堂讨论、作业与测评中更容易记住并运用它们。
1. The Multi-Store Model of Memory 'Formula' | 记忆的多存储模型“公式”
The Atkinson-Shiffrin model describes memory as a three-stage system and can be written as a simple process formula: sory Memory → (attention) → Short-Term Memory (STM) → (rehearsal) → Long-Term Memory (LTM) ry decays in less than a second. Without rehearsal, STM holds around 7±2 items for only 15– ssful rehearsal transfers information into LTM, where capacity and duration are unlimited.
阿特金森-希夫林模型将记忆描述为一个三阶段系统，可以用简单的过程公式表示：感觉输入 → 感觉记忆 →（注意）→ 短时记忆（STM）→（复述）→ 长时记忆（LTM）。没有注意，感觉记忆中的信息会在一秒内消退。没有复述，短时记忆只能保持约 7±2 个项目，持续 15–30 秒。成功的复述能将信息转入长时记忆，后者的容量和持续时间都是无限的。
- Key 'variables': attention acts as a filter; rehearsal acts as a transfer mechanism.
- 关键“变量”：注意扮演过滤器；复述扮演传递机制。
2. Ebbinghaus Forgetting Curve Theorem | 艾宾浩斯遗忘曲线定理
Ebbinghaus discovered that memory retention drops sharply soon after learning and then levels off. The forgetting curve theorem can be approximated by: R ≈ e–t/T, where R is retention, t is time, and T is a time constant that depends on the strength of the initial memory. In simpler terms, most forgetting happens in the first hour, and overlearning and spaced repetition flatten the curve.
艾宾浩斯发现，记忆保持量在学习后很快急剧下降，随后趋于平缓。遗忘曲线定理可以近似表示为：R ≈ e–t/T，其中 R 为保持量，t 为时间，T 为取决于初始记忆强度的时间常数。简单来说，大部分遗忘发生在第一个小时，而过度学习和间隔重复能使曲线变得平坦。
Memory retention R ≈ e–t/T
| Time after learning | Approximate retention |
| 20 minutes | 58% |
| 1 hour | 44% |
| 1 day | 34% |
| 1 week | 21% |
3. Classical Conditioning Formula (Pavlov) | 经典条件反射公式（巴甫洛夫）
The classical conditioning 'formula' shows how a neutral stimulus becomes a conditioned stimulus after repeated pairing with an unconditioned stimulus: US → UR; NS + US → UR; (after pairing) CS → CR. For Pavlov's dogs, food (US) naturally triggered salivation (UR). The bell (NS) was paired with food until the bell alone (CS) produced salivation (CR). The key theorem is that a conditioned response will be learned most quickly when the NS is presented just before the US.
经典条件反射的“公式”展示了中性刺激在与无条件刺激反复配对后如何转变为条件刺激：US → UR；NS + US → UR；（配对后）CS → CR。在巴甫洛夫的实验中，食物（US）自然引发唾液分泌（UR）。铃声（NS）与食物配对，直到单独出现铃声（CS）也能引起唾液分泌（CR）。关键定理在于：当中性刺激刚好在无条件刺激之前呈现时，条件反应学习得最快。
- ned Response; NS = Neutral Stimulus; CS = Conditioned Stimulus; CR = Conditioned Response.
- US = 无条件刺激；UR = 无条件反应；NS = 中性刺激；CS = 条件刺激；CR = 条件反应。
4. Operant Conditioning Reinforcement Theorem | 操作性条件反射强化定理
Operant conditioning can be summarised by the rule: Behaviour → Consequence → Change in likelihood of that behaviour. Reinforcement increases behaviour; punishment decreases it. Whether a stimulus is added (+) or removed (–) determines the type. The 'reinforcement theorem' states that behaviours followed by pleasant consequences are more likely to be repeated, while those followed by unpleasant consequences are less likely.
操作性条件反射可以概括为以下规则：行为 → 后果 → 该行为发生概率的变化。强化增加行为；惩罚减少行为。刺激是被添加（+）还是被移除（–）决定了具体类型。其“强化定理”指出：伴随愉快后果的行为更可能被重复，而伴随不愉快后果的行为则更不可能重复。
| Consequence added (+) | Consequence removed (–) |
| Positive Reinforcement (increases behaviour) | Negative Reinforcement (increases behaviour) |
| Positive Punishment (decreases behaviour) | Negative Punishment (decreases behaviour) |
5. Social Learning Theory Observational Steps | 社会学习理论观察学习步骤
Bandura's social learning theory describes how we learn by watching others. The observational learning formula can be written as: Attention → Retention → Reproduction → Motivation (ARRM). We must pay attention to the model, remember what they did, be physically able to copy the behaviour, and have a reason (motivation) to do so. Motivation often comes from seeing the model rewarded – vicarious reinforcement.
班杜拉的社会学习理论描述了我们如何通过观察他人来学习。观察学习的公式可以写作：注意 → 保持 → 再现 → 动机（ARRM）。我们必须注意榜样，记住他的行为，身体上能够复制该行为，并且有理由（动机）这么做。动机通常来自看到榜样得到奖励——替代强化。
- Attention – focus on the model's actions.
- Retention – store a mental representation of the behaviour.
- Reproduction – translate the memory into actual behaviour.
- Motivation – reinforcement or punishment determines whether the behaviour is performed.
- 注意 – 关注榜样的行为。
- 保持 – 存储行为的心理表征。
- 再现 – 将记忆转化为实际行为。
- 动机 – 强化或惩罚决定行为是否被表现。
6. Conformity Equation (Asch's Factors) | 从众影响因素方程（阿希）
Asch's line experiments revealed that conformity can be seen as a function of several key factors. The 'conformity equation' can be imagined as: Conformity likelihood = f (group size, unanimity, task difficulty, cultural norms). Conformity increases when the majority is unanimous, larger (up to about 4–5 confederates), and the task is ambiguous. A single dissenter drastically reduces conformity.
阿希的线条实验揭示，从众可以看作几个关键因素的函数。“从众方程”可以想象为：从众可能性 = f（群体规模、一致性、任务难度、文化规范）。当多数派意见一致、群体规模较大（约 4–5 名假被试）且任务模糊时，从众程度会增加。只要有一个持不同意见者，从众率就会大幅降低。
Conformity = Group size (up to ~5) × Unanimity × Task difficulty / Dissent
7. Attachment Types Theorem (Ainsworth) | 依恋类型定理（安斯沃思）
Ainsworth's Strange Situation study identified three main attachment types, which can be expressed as a matching 'theorem': the type of attachment a child shows is a function of caregiver sensitivity. Secure attachment ← responsive caregiver; Insecure-avoidant ← rejecting caregiver; Insecure-resistant/ambivalent ← inconsistent caregiver. Securely attached children use the caregiver as a safe base to explore, are distressed when the caregiver leaves, and are comforted on reunion.
安斯沃思的陌生情境研究识别出三种主要的依恋类型，可以用一个匹配“定理”来表达：儿童表现出的依恋类型取决于照顾者的敏感度。安全型依恋 ← 回应及时的照顾者；不安全-回避型 ← 拒绝型照顾者；不安全-反抗/矛盾型 ← 不一致的照顾者。安全型依恋的儿童会将照顾者当作安全基地去探索，照顾者离开时感到不安，重逢时得到安慰。
| Attachment type | Caregiver style | Child's reunion behaviour |
| Secure (B) | Sensitive, responsive | Seeks comfort, calms quickly |
| Insecure-avoidant (A) | Rejecting, distant | Ignores caregiver, avoids contact |
| Insecure-resistant (C) | Inconsistent, unpredictable | Ambivalent; clings yet resists comfort |
8. Piaget's Cognitive Stage Theorem | 皮亚杰认知发展阶段定理
Piaget proposed that children's thinking develops through four fixed stages, each with a characteristic 'cognitive structure'. The stage theorem states: Thinking changes qualitatively at each stage and follows an invariant sequence: Sensorimotor (0–2 years), Preoperational (2–7 years), Concrete Operational (7–11 years), Formal Operational (11+ years). Children cannot skip a stage, though the ages are approximate.
皮亚杰提出，儿童的思维按四个固定阶段发展，每个阶段都有其典型的“认知结构”。其阶段定理指出：思维在每个阶段发生质变，并遵循不变顺序：感知运动阶段（0–2岁）、前运算阶段（2–7岁）、具体运算阶段（7–11岁）、形式运算阶段（11岁及以上）。儿童无法跳过一个阶段，年龄仅为近似值。
- Sensorimotor: object permanence develops; world known through senses and actions.
- Preoperational: egocentrism, symbolic play, lack of conservation.
- Concrete operational: logical thinking about concrete objects, mastery of conservation and reversibility.
- Formal operational: abstract reasoning, hypothesis testing, systematic problem-solving.
- 感知运动阶段：客体永久性发展；通过感官和动作认识世界。
- 前运算阶段：自我中心、象征性游戏、缺乏守恒概念。
- 具体运算阶段：对具体事物进行逻辑思考，掌握守恒与可逆性。
- 形式运算阶段：抽象推理、假设检验、系统性解决问题。
9. The Working Memory Model Equation | 工作记忆模型方程
Baddeley and Hitch's working memory model can be expressed as a component equation: : Working Memory = Central Executive + Phonological Loop + Visuospatial Sketchpad + Episodic Buffer. The central executive is the control system, directing attention and coordinating the two storage subsystems – the phonological loop for verbal/sound information and the visuospatial sketchpad for visual/spatial information. The episodic buffer integrates information across domains and links working memory to long-term memory.
巴德利和希奇的工作记忆模型可以用一个组件方程来表达：工作记忆 = 中央执行器 + 语音回路 + 视空间画板 + 情景缓冲器。中央执行器是控制系统，引导注意并协调两个储存子系统——处理言语/声音信息的语音回路和处理视觉/空间信息的视空间画板。情景缓冲器整合不同领域的信息，并将工作记忆与长时记忆连接起来。
WM = CE + PL + VSS + EB
10. Yerkes-Dodson Law of Arousal | 耶基斯-多德森唤醒定律
The Yerkes-Dodson law describes the relationship between arousal and performance as an inverted U-shaped curve. The theorem states that optimal performance occurs at a moderate level of arousal; too little arousal leads to boredom and low performance, while too much arousal leads to anxiety and impaired performance. Moreover, the optimal arousal level is lower for complex tasks and higher for simple tasks. This can be written as Performance ≈ max – k × (arousal – optimum)².
耶基斯-多德森定律将唤醒与表现之间的关系描述为一条倒 U 形曲线。该定律指出最佳表现出现在中等程度的唤醒水平上；唤醒过低会导致无聊和低表现，唤醒过高则会导致焦虑并损害表现。此外，复杂任务的最佳唤醒水平较低，简单任务则较高。这可以用公式表示为 表现 ≈ 最大值 – k ×（唤醒 – 最佳值）²。
Performance ≈ max – k × (arousal – optimum)²
11. Cognitive Dissonance Formula | 认知失调公式
Festinger's cognitive dissonance theory can be condensed into a formula-like principle: Dissonance magnitude = (importance × inconsistency) / number of consonant cognitions. When two beliefs, or a belief and a behaviour, clash, the person feels psychological discomfort. To reduce dissonance, they may change their attitude, change their behaviour, or add new consonant cognitions. The greater the importance and the smaller the number of supporting beliefs, the stronger the pressure to reduce dissonance.
费斯廷格的认知失调理论可以浓缩为一个类似公式的原理：失调程度 =（重要性 × 不一致程度）/ 协调认知的数量。当两种信念，或信念与行为发生冲突时，人会产生心理不适。为了减少失调，他们可能会改变态度、改变行为或增加新的协调认知。事情越重要、支持性信念越少，减少失调的压力就越大。
Dissonance ∝ (Importance × Inconsistency) / Consonant Cognitions
12. Fundamental Attribution Error Theorem | 基本归因错误定理
The fundamental attribution error (FAE) can be stated as a probabilistic theorem: When explaining another person's behaviour, P(internal attribution) >> P(situational attribution). Observers tend to overestimate dispositional factors (personality, ability) and underestimate situational factors (luck, context). For our own behaviour, however, we often reverse the pattern – the actor-observer bias. This 'error' helps explain why we blame people for accidents while ignoring the circumstances.
基本归因错误（FAE）可以用一个概率性定理来表述：在解释他人行为时，P（内部归因）远大于 P（情境归因）。观察者倾向于高估个人特质因素（性格、能力）而低估情境因素（运气、环境）。但对自己的行为，我们往往反转这一模式——这就是行动者-观察者偏差。这一“错误”有助于解释为什么我们常因意外而指责他人，却忽视了当时的环境。
FAE: P(internal attribution for others' actions) > P(situational attribution)
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