📚 Year 7 AQA Psychology: Formula & Theorem Quick Reference | AQA 7年级心理学：公式定理速查手册
Welcome to your essential quick-reference guide for Year 7 AQA Psychology. Here you will find the key ‘formulas’ and ‘theorems’ that underpin introductory psychology – from how memory works to the laws of learning and social influence. Think of each entry as a mental toolkit that helps you decode human behaviour, just like a maths formula helps you solve a problem. This handbook covers the core models, laws, and principles you need to know, presented in a clear, easy‑to‑review format.
欢迎使用你的 7 年级 AQA 心理学必备速查手册。在这里你会找到支撑心理学入门的关键“公式”和“定理”——从记忆如何运作到学习定律和社会影响。把每一条都当作一个心理工具箱，帮助你解读人的行为，就像数学公式帮助你解题一样。这本手册涵盖了你需要掌握的核心模型、定律和原理，以清晰易读的格式呈现。
1. The Memory Equation | 记忆的过程公式
The most fundamental law in cognitive psychology can be written as a simple equation: Memory = Encoding + Storage + Retrieval. This means that successful recall depends on three separate stages. First, information must be encoded (taken in and transformed into a mental representation). Then it must be stored (kept in the brain over time). Finally, it must be retrieved (brought back into consciousness when needed). If any one of these stages fails, the memory will not be accessible.
认知心理学最基础的定律可以写成一条简单的公式：记忆 = 编码 + 储存 + 提取。这意味着成功的回忆取决于三个独立的阶段。首先，信息必须被编码（接收并转化成心理表征）。然后必须被储存（随时间保留在大脑中）。最后必须被提取（需要时带回意识）。如果任何一个阶段出了问题，记忆就无从访问。
- Encoding: transforming sensory input into a code the brain can use.
- 编码：将感觉输入转化为大脑可以使用的代码。
- Storage: retaining that coded information over periods of time.
- 储存：将该编码信息保留一段时间。
- Retrieval: locating and recovering the stored information.
- 提取：定位并恢复所储存的信息。
2. Multi-Store Model Theorem | 多储存记忆模型定理
The Atkinson & Shiffrin (1968) multi-store model is often summarised with a flow‑like formula: Sensory Register → Short‑Term Memory (STM) → Long‑Term Memory (LTM). Information enters through the senses and is held briefly in a sensory register. If we pay attention, it passes into STM, which has a limited capacity (about 7 ± 2 chunks) and a short duration (around 18–30 seconds). Through rehearsal (repeating information), it can then be transferred to LTM, which is essentially unlimited in capacity and can last a lifetime.
Atkinson 与 Shiffrin（1968）的多储存模型常被概括为一个流程式定理：感觉登记 → 短时记忆（STM） → 长时记忆（LTM）。信息通过感官进入，短暂停留在感觉登记中。如果我们加以注意，它便进入短时记忆，短时记忆的容量有限（约 7 ± 2 个组块），持续时间短（约 18–30 秒）。通过复述（重复信息），它可以转入长时记忆，长时记忆的容量几乎是无限的，可以持续终生。
Sensory Register → [Attention] → STM → [Rehearsal] → LTM
The reverse flow also occurs when we retrieve memories: LTM → [Retrieval] → STM. Understanding this ‘memory pathway’ helps explain why rehearsal and attention are crucial for studying.
当我们提取记忆时，也会发生反向流动：长时记忆 → [提取] → 短时记忆。理解这条“记忆通路”有助于解释为什么复述和注意对学习至关重要。
3. Ebbinghaus’ Law of Forgetting | 艾宾浩斯遗忘定律
Hermann Ebbinghaus (1885) discovered that forgetting follows a predictable pattern, which can be expressed as the Forgetting Curve. In simplified form: Retention ≈ 100 × e-t/S (where t is time elapsed and S is the strength of the memory). In practice, this theorem tells us that forgetting is initially very rapid, but the rate of forgetting slows down over time. Most information is lost within the first hour unless it is reviewed.
赫尔曼·艾宾浩斯（1885）发现遗忘遵循一种可预测的模式，可以用遗忘曲线来表示。简化的形式为：保持量 ≈ 100 × e-t/S（其中 t 为经过的时间，S 为记忆强度）。实际上，这条定理告诉我们，遗忘一开始非常迅速，但遗忘的速度会随时间减慢。除非加以复习，大部分信息在第一个小时就会丢失。
Retention Rate = 100% – (Logarithmic Decay of Time)
The practical formula to beat the curve is Spaced Repetition: reviewing material at gradually increasing intervals strengthens the memory trace, making the curve much flatter.
战胜遗忘曲线的实用公式是间隔重复：以逐渐增长的间隔复习材料，能加强记忆痕迹，使曲线变得平缓得多。
4. Working Memory Model Components | 工作记忆模型组件
Baddeley and Hitch (1974) improved the idea of a single short‑term store by proposing a multi‑component Working Memory Model. The ‘formula’ for working memory can be thought of as: Central Executive + Phonological Loop + Visuospatial Sketchpad + Episodic Buffer = Working Memory. Each component has a specialised role, and they all work together to hold and manipulate information temporarily.
Baddeley 与 Hitch（1974）通过提出一个多组件的工作记忆模型，改进了单一短时储存的构想。工作记忆的“公式”可以视为：中央执行系统 + 语音回路 + 视空间画板 + 情节缓冲器 = 工作记忆。每个组件都有专门的功能，它们协同工作，暂时保持并操作信息。
- Central Executive: the boss; directs attention and coordinates the slave systems.
- 中央执行系统：主管；指引注意并协调两个从属系统。
- Phonological Loop: handles spoken and written material; has a limited capacity acoustic store.
- 语音回路：处理口语和书面材料；包含一个容量有限的声音存贮。
- Visuospatial Sketchpad: deals with visual images and spatial relations.
- 视空间画板：处理视觉意象和空间关系。
- Episodic Buffer: integrates information across domains and links to long‑term memory.
- 情节缓冲器：整合跨领域的信息，并连接长时记忆。
5. Classical Conditioning Formula | 经典条件作用公式
Pavlov’s classical conditioning can be written as a set of logical steps: UCS (Unconditioned Stimulus) → UCR (Unconditioned Response). Then NS (Neutral Stimulus) + UCS → UCR is repeated multiple times. Eventually, the neutral stimulus alone becomes a CS (Conditioned Stimulus) and now produces a CR (Conditioned Response), i.e. CS → CR. This learning theorem explains how reflexive responses can be attached to new stimuli.
巴甫洛夫的经典条件作用可以写为一组逻辑步骤：非条件刺激（UCS）→ 非条件反应（UCR）。然后多次重复中性刺激（NS）+ 非条件刺激 → 非条件反应。最终，中性刺激单独成为条件刺激（CS），并产生条件反应（CR），即 CS → CR。这一定理说明了反射性反应如何能附着到新刺激上。
UCS (Food) → UCR (Salivation) ； Bell (NS) + Food (UCS) → Salivation (UCR) ； Bell (CS) → Salivation (CR)
The key theorem: Acquisition = NS + UCS pairing; Extinction = CS presented alone repeatedly; Spontaneous Recovery = CR reappears after a pause.
关键定理：获得 = NS 与 UCS 的配对呈现；消退 = 单独反复呈现 CS；自发恢复 = 停顿后 CR 再次出现。
6. Operant Conditioning Law | 操作性条件作用定律
Skinner’s operant conditioning states that behaviour is controlled by its consequences. The basic probability theorem is: If a behaviour is followed by a reinforcer, the probability of that behaviour increases; if followed by a punisher, the probability decreases. This can be expressed as Behaviour Probability = f (Consequence Type, Schedule). Reinforcement can be positive (adding something pleasant) or negative (removing something unpleasant). Both increase behaviour.
斯金纳的操作性条件作用指出，行为由其后果控制。基本的概率定理是：如果一个行为之后跟随强化物，该行为出现的概率就增加；如果跟随惩罚物，概率则降低。可以表示为 行为概率 = f（后果类型，强化程序）。强化可以是正强化（增加愉快刺激）或负强化（移除不愉快刺激），两者都增加行为发生。
| Positive Reinforcement | Adding a desirable stimulus → behaviour ↑ |
| 正强化 | 增加一个令人愉快的刺激 → 行为增加 |
| Negative Reinforcement | Removing an aversive stimulus → behaviour ↑ |
| 负强化 | 移除一个令人厌恶的刺激 → 行为增加 |
| Positive Punishment | Adding an aversive stimulus → behaviour ↓ |
| 正惩罚 | 增加一个令人厌恶的刺激 → 行为减少 |
| Negative Punishment | Removing a desirable stimulus → behaviour ↓ |
| 负惩罚 | 移除一个令人愉快的刺激 → 行为减少 |
7. Yerkes‑Dodson Law of Arousal | 耶克斯‑多德森唤醒定律
The Yerkes‑Dodson law states that performance increases with physiological or mental arousal, but only up to a point. Beyond the optimal level, performance decreases. This can be graphed as an inverted‑U shape, summarised by the theorem: Performance = f(Arousal), where f follows an upside‑down U‑curve. For simple or well‑learned tasks, optimal arousal is higher; for complex or new tasks, optimal arousal is lower.
耶克斯‑多德森定律指出，生理或心理唤醒水平提高时，表现随之提高，但只到某一点。超过最佳水平后，表现反而下降。这可以画成一个倒 U 形曲线，概括为定理：表现 = f（唤醒），其中 f 是一条倒 U 形函数。对于简单或熟练掌握的任务，最佳唤醒水平较高；对于复杂或新任务，最佳唤醒水平较低。
Performance ∝ Arousal up to an optimum, then ∝ 1/Arousal
This theorem explains phenomena such as exam anxiety: a moderate level of stress can enhance focus, but excessive anxiety impairs recall. Top athletes and students use it to find their ‘flow’ zone.
该定理解释了考试焦虑等现象：适度的压力可以增强注意力，但过度焦虑会损害回忆。顶尖运动员和学生利用这一定理找到他们的“心流”区。
8. Social Influence Formulas | 社会影响公式
Social psychology offers several ‘formulas’ for conformity and obedience. Asch’s research showed that Conformity Rate = f(Group Size, Unanimity, Task Difficulty). Specifically, conformity increases with group size (up to about 3–4 people), is highest when the group is unanimous, and rises when the task is more difficult. Milgram’s obedience study suggests an Obedience = f(Authority Closeness, Proximity of Victim, Legitimacy of Context) formula.
社会心理学提供了若干针对从众和服从的“公式”。阿希的研究表明从众率 = f（团体规模，一致性，任务难度）。具体而言，从众率随团体规模增加而升高（直到约 3–4 人），当团体意见完全一致时最高，且任务难度增加时也更高。米尔格拉姆的服从研究则提示一个服从 = f（权威靠近度，受害者亲近度，情境合法性）的公式。
- Group Size: Conformity plateaus after about 3 confederates.
- 团体规模：大约 3 个同谋者后从众趋于平稳。
- Unanimity: Even one dissenter drastically reduces conformity.
- 一致性：哪怕只有一个异议者，也会大幅度降低从众。
- Legitimacy of Authority: Obedience is highest when commands come from a legitimate institution (e.g., university, uniform).
- 权威合法性：当指令来自合法机构（如大学、穿制服者）时，服从最高。
9. Attachment Theory Theorem | 依恋理论定理
John Bowlby proposed that the quality of an infant’s attachment is predicted by a caregiver responsiveness formula: Attachment Security = f(Caregiver Sensitivity, Consistency of Care). Mary Ainsworth later categorised attachment styles through the Strange Situation procedure. The theorem suggests that a caregiver who is sensitive and consistently responsive will likely foster a secure attachment; inconsistent care leads to insecure‑resistant, and rejecting or unresponsive care to insecure‑avoidant.
约翰·鲍尔比提出，婴幼儿的依恋质量可以由照顾者回应公式预测：依恋安全性 = f（照顾者敏感性，照护一致性）。玛丽·爱因斯沃斯后来通过陌生情境法对依恋类型进行了分类。该定理表明，敏感且始终如一回应婴儿的照顾者，很可能培养出安全型依恋；不一致的照护导致不安全‑矛盾型；而拒绝或无回应的照护导致不安全‑回避型。
Secure Base → Exploration → Return to Base
The internal working model (IWM) is a mental ‘formula’ of what relationships are like, which then guides future relationships. Securely attached children develop a positive IWM: ‘I am lovable, others are trustworthy.’
内部工作模型（IWM）是一套关于关系形态的心理“公式”，随后会引导未来的人际关系。安全型依恋的儿童发展出积极的 IWM：“我值得被爱，他人值得信赖。”
10. Piaget’s Cognitive Development Stage Theorem | 皮亚杰认知发展阶段定理
Piaget theorised that intellectual growth follows a sequential formula: Schemas → Assimilation & Accommodation → Equilibration. A schema is a mental framework. When new information fits an existing schema, assimilation occurs; when it does not, the schema must be adjusted – accommodation. This balancing act creates equilibrium, pushing the child into new stages. The stage theorem is: Sensorimotor (0‑2 years) → Preoperational (2‑7) → Concrete Operational (7‑11) → Formal Operational (11+), each with its own logical ‘operators’.
皮亚杰理论认为，智力成长遵循一个序列公式：图式 → 同化与顺应 → 平衡。图式是一个心理框架。当新信息符合已有图式时，发生同化；当不符合时，图式必须调整——这便是顺应。这种平衡作用创造了认知平衡，推动儿童进入新的阶段。阶段定理为：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 岁以上），每个阶段都有其自己的逻辑“运算符”。
- Sensorimotor: Object permanence – understanding objects exist even when out of sight.
- 感知运动阶段：客体永久性——理解物体即使看不见也继续存在。
- Preoperational: Egocentrism and use of symbols, but lack of conservation.
- 前运算阶段：自我中心和符号运用，但缺乏守恒概念。
- Concrete Operational: Logical thinking about concrete events; conservation mastered.
- 具体运算阶段：对具体事物进行逻辑思考；掌握守恒。
- Formal Operational: Abstract, hypothetical reasoning; can formulate ‘if‑then’ formulas.
- 形式运算阶段：抽象和假设性推理；能形成“若……则……”公式。
11. The Stress Performance Balance | 压力‑表现平衡律
Closely related to the Yerkes‑Dodson law, the Cognitive Performance Index = Ability × Motivation / (Anxiety + Distraction) is a simplified heuristic. While not a precise mathematical equation, it reflects the idea that performance is boosted by ability and motivation, but undermined by excessive anxiety and distractions. This ‘formula’ helps Year 7 students manage revision: reduce distractions, build your ability through practice, and keep anxiety at a manageable level.
与耶克斯‑多德森定律密切相关的是认知表现指数 = 能力 × 动机 / （焦虑 + 干扰）的简化经验法则。虽然并非精确的数学等式，但它反映了表现受到能力和动机的推动，却会被过度焦虑和干扰所削弱的概念。这个“公式”有助于 7 年级学生管理复习：减少干扰、通过练习增长能力，并将焦虑维持在可控水平。
Optimal Performance = High Focus + Moderate Pressure
This theorem accounts for the phenomenon of ‘choking’ under extreme pressure, where even well‑practised skills fail because the performer becomes over‑anxious and hyper‑self‑conscious.
这条定理解释了在极端压力下“窒息”的现象，即即便是熟练的技能也会失败，因为执行者变得过度焦虑和高度自我意识。
12. Research Methods Quick Formulas | 研究方法速查公式
In Year 7 AQA Psychology, you also need some basic research method formulas. The most common ones relate to experimental design: Independent Variable (IV) = what is changed; Dependent Variable (DV) = what is measured. A key measure of central tendency is the mean: Mean = (Sum of all scores) ÷ (Number of scores). The range is a measure of spread: Range = Highest score – Lowest score. The ethical formula is: Valid Study = Confidentiality + Informed Consent + Right to Withdraw + Protection from Harm.
在 7 年级 AQA 心理学中，你还需要一些基本的研究方法公式。最常见的与实验设计有关：自变量（IV）= 改变的东西；因变量（DV）= 测量的东西。集中趋势的一个关键度量是平均值：平均值 =（所有分数之和）÷（分数的个数）。全距是一个离散度量：全距 = 最高分 − 最低分。伦理公式则是：有效的研究 = 保密性 + 知情同意 + 退出权 + 免受伤害。
Mean = Σx / n ； Range = Xₘₐₓ – Xₘᵢₙ
Remember: the mean is sensitive to extreme scores, so sometimes the median is more appropriate. A quick recall formula for memory studies: Number of items recalled = f(Rehearsal time, Retrieval cues), showing that both time spent rehearsing and the presence of cues affect recall.
记住：平均数受极端数值的影响，所以有时中位数更合适。记忆研究的一个快速回忆公式：回忆的项目数量 = f（复述时间，提取线索），表明花在复述上的时间和线索的存在都会影响回忆。
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