📚 Year 8 WJEC Psychology: Formula & Theorem Quick Reference Handbook | WJEC八年级心理学公式定理速查手册
Psychology may not be filled with algebraic equations, but it is built on elegant formulas and powerful theorems that explain why we think, feel, and behave the way we do. This quick reference handbook gathers the most essential 'formulas' of Year 8 WJEC Psychology — from memory equations to learning principles and research design — into one clear, bilingual guide. Use it to revise key concepts, strengthen your understanding, and boost your confidence before assessments.
心理学或许没有密密麻麻的代数方程，但它建立在简洁的公式和有力的定理之上，解释了我们的思维、情感和行为。这本速查手册汇集了 WJEC 八年级心理学最核心的“公式”——从记忆方程到学习原理，再到研究设计——用清晰的双语呈现。用它来复习关键概念、加深理解，并在评估前提升你的自信。
1. The Memory Equation: Encoding + Storage + Retrieval | 记忆方程：编码 + 存储 + 提取
For a memory to form and be recalled, three processes must work together like parts of a simple equation. Encoding transforms sensory input into a mental code. Storage holds that code over time. Retrieval brings it back into conscious awareness when needed. If any part fails, the whole equation breaks down — you forget.
要形成并回忆起一段记忆，三个过程必须像一个简单方程那样协同工作。编码将感觉输入转化为心理代码。储存将代码长时间保留。提取在需要时把它带回意识之中。任何一部分失败，整个方程就失效——你便会遗忘。
- Encoding: Paying attention and linking new information to what you already know. | 编码：集中注意，并将新信息与已知内容相联系。
- Storage: Keeping the memory trace stable, often through rehearsal. | 储存：通过复述等方式保持记忆痕迹稳定。
- Retrieval: Accessing stored memories using cues or recognition. | 提取：利用线索或再认获取存储的记忆。
Memory = Encoding + Storage + Retrieval
记忆 = 编码 + 存储 + 提取
This model helps explain everyday forgetting: if you didn't encode a classmate's name properly, no amount of trying will retrieve it later.
这个模型有助于解释日常遗忘：如果你没有适当编码同学的名字，日后怎么努力也提取不出来。
2. Miller’s Magic Number Theorem: 7 ± 2 | 米勒神奇数字定理：7 ± 2
Psychologist George Miller proposed that the capacity of short-term memory is roughly 7 items, plus or minus 2. This means most people can hold between 5 and 9 chunks of information at once. A chunk is a meaningful unit — a digit, a letter, or even a whole word if it's familiar.
心理学家乔治·米勒提出，短时记忆的容量大约是 7 个项目，上下浮动 2。这意味着大多数人一次能同时记住 5 到 9 个信息块。信息块是有意义的单位——可以是一个数字、一个字母，甚至一个熟悉的单词。
Short-Term Memory Capacity = 7 ± 2 chunks
短时记忆容量 = 7 ± 2 个组块
This theorem explains why phone numbers and postcodes are often grouped into small chunks: we are naturally limited processors. When you try to remember a list of ten random words, you may lose the ones beyond the magic number without rehearsal or chunking.
这条定理解释了为什么电话号码和邮政编码常被分成小段：我们天生就是容量有限的加工者。当你试图记住十个随机单词列表时，不经过复述或组块化，就可能丢失超出神奇数字的部分。
| Chunking Strategy | 组块策略 | Example | 示例 |
|---|---|
| Group digits | 数字分组 | 020 7946 0341 → two chunks |
| Create acronyms | 创建首字母缩写 | ROYGBIV for rainbow colours |
| Make sentences | 造句 | 'My Very Educated Mother' for planet order |
Using chunking expands your functional memory capacity within the 7 ± 2 limit.
运用组块化可以在 7 ± 2 的限制内扩展你的功能性记忆容量。
3. Classical Conditioning Formula: UCS + NS → CS → CR | 经典条件作用公式：无条件刺激 + 中性刺激 → 条件刺激 → 条件反应
Pavlov’s classical conditioning follows a clear sequence, almost like a chemical reaction formula. An unconditioned stimulus (UCS) naturally produces an unconditioned response (UCR). When a neutral stimulus (NS) is repeatedly paired with the UCS, it becomes a conditioned stimulus (CS) that elicits a conditioned response (CR) on its own.
巴甫洛夫的经典条件作用遵循清晰的顺序，几乎像化学反应式。无条件刺激（UCS）自然引发无条件反应（UCR）。当中性刺激（NS）反复与 UCS 配对后，它就变成了条件刺激（CS），能单独引发条件反应（CR）。
Stage 1: UCS (food) → UCR (salivation)
阶段1：UCS（食物）→ UCR（分泌唾液）
Stage 2: NS (bell) + UCS (food) → UCR (salivation)
阶段2：NS（铃声）+ UCS（食物）→ UCR（分泌唾液）
Stage 3: CS (bell) → CR (salivation)
阶段3：CS（铃声）→ CR（分泌唾液）
Key principles such as extinction (CR weakens when UCS is absent) and spontaneous recovery (CR returns after a pause) are also part of this learning theorem.
关键原则如消退（UCS 不出现时 CR 减弱）和自发恢复（暂停后 CR 重现）也是这一学习定理的组成部分。
4. Operant Conditioning Theorem: Reinforcement Strengthens Behaviour | 操作性条件作用定理：强化增强行为
Skinner’s operant conditioning can be summarised by a simple theorem: behaviour is shaped by its consequences. Positive reinforcement adds something pleasant to increase a behaviour, while negative reinforcement removes something unpleasant to strengthen a behaviour. In contrast, punishment decreases a behaviour, either by adding an aversive stimulus or removing a pleasant one.
斯金纳的操作性条件作用可以用一条简单定理概括：行为由其后果塑造。正强化增加愉悦刺激以提高行为频率；负强化移除厌恶刺激以增强行为。相反，惩罚则通过增加厌恶刺激或移除愉悦刺激来减少行为。
Reinforcement → Behaviour ↑
强化 → 行为增加
Punishment → Behaviour ↓
惩罚 → 行为减少
- Positive reinforcement: Giving a sticker for homework completion. | 正强化：完成作业后奖励贴纸。
- Negative reinforcement: Turning off a loud alarm by pressing a snooze button. | 负强化：按下贪睡键关掉闹铃。
- Positive punishment: Adding extra chores for misbehaviour. | 正惩罚：因行为不当增加额外家务。
- Negative punishment: Removing screen time when rules are broken. | 负惩罚：违反规则时取消屏幕时间。
Remember, 'negative' here means removing, not bad; 'positive' means adding, not good. This theorem is central to understanding how habits form and how rewards shape classroom behaviour.
记住，这里的“负”指移除，不是坏；“正”指增加，不是好。这一定理对理解习惯如何形成以及奖励如何塑造课堂行为至关重要。
5. The Multi-Store Model of Memory Formula | 记忆的多重存储模型公式
Atkinson and Shiffrin proposed that memory flows through three distinct stores, much like a data-processing formula. Information enters sensory memory, where it lasts only a split second. With attention, it moves into short-term memory, and through rehearsal, it can be encoded into long-term memory.
阿特金森和谢夫林提出，记忆流经三个不同的仓库，就像一个数据处理公式。信息先进入感觉记忆，仅持续一瞬间。通过注意，信息转移到短时记忆，再经过复述，就能被编码进入长时记忆。
Input → Sensory Memory → (Attention) → Short-Term Memory → (Rehearsal) → Long-Term Memory
感觉输入 → 感觉记忆 →（注意）→ 短时记忆 →（复述）→ 长时记忆
| Store | 仓库 | Capacity | 容量 | Duration | 持续时间 |
|---|---|---|
| Sensory Memory | 感觉记忆 | Very large | 非常大 | Less than 1 second | 不到1秒 |
| Short-Term Memory | 短时记忆 | 7 ± 2 chunks | 7 ± 2 组块 | About 18–30 seconds | 约18–30秒 |
| Long-Term Memory | 长时记忆 | Potentially unlimited | 潜在无限 | Up to a lifetime | 可达一生 |
The model explains why we must rehearse information (like a shopping list) to remember it beyond a few seconds, and why distractions cause information to decay before reaching long-term storage.
这个模型解释了为什么我们必须复述信息（如购物清单）才能记住超过几秒，也说明了为什么干扰会使得信息在进入长时仓库前就消退。
6. The Forgetting Curve Equation | 遗忘曲线方程
Hermann Ebbinghaus discovered that memory loss follows a systematic path, which he plotted as the forgetting curve. Most forgetting happens rapidly within the first hour, then the rate slows down over days. The curve can be expressed as a mathematical relationship: retention drops sharply without rehearsal, and regular review flattens the curve.
赫尔曼·艾宾浩斯发现，遗忘遵循系统化的路径，他将其绘制为遗忘曲线。大部分遗忘发生在第一个小时内，十分迅速，随后几天遗忘速率减慢。该曲线可以表达为一种数学关系：未经复述时记忆保持急剧下降，而定期复习会使曲线趋于平缓。
Retention ∝ 1 / Time (without rehearsal)
保持量 ∝ 1 / 时间（未经复述时）
Spaced repetition is the antidote: reviewing material after 1 day, 3 days, and 1 week greatly improves long-term retention. This theorem is why cramming before an exam rarely works — it doesn't fight the natural shape of the forgetting curve.
间隔重复是解药：在1天后、3天后和1周后复习材料，可以极大地提升长期记忆保持。这一定理说明了考前临时抱佛脚很少奏效的原因——它无法对抗遗忘曲线的自然形状。
7. 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 fixed stages, moving from concrete actions to abstract logical thought. These stages are universal and sequential, much like a developmental formula: each child must pass through them in order, though the exact age can vary slightly.
让·皮亚杰提出，儿童思维发展经过四个固定阶段，从具体动作逐渐发展为抽象逻辑思维。这些阶段具有普遍性和顺序性，就像一个发展公式：每个孩子都必须按顺序经历，尽管具体年龄略有不同。
Sensorimotor (0–2 years) → Preoperational (2–7 years) → Concrete Operational (7–11 years) → Formal Operational (11+ years)
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）
- Sensorimotor: Learning through senses and movement; object permanence develops. | 感知运动阶段：通过感觉和运动学习；客体永久性得到发展。
- Preoperational: Symbolic thinking but egocentric; animism and irreversibility present. | 前运算阶段：出现符号思维但以自我为中心；存在泛灵论和不可逆性。
- Concrete Operational: Logical thinking about concrete events; conservation and reversibility mastered. | 具体运算阶段：对具体事件进行逻辑思考；掌握守恒和可逆性。
- Formal Operational: Abstract and hypothetical reasoning; systematic problem solving. | 形式运算阶段：进行抽象和假设推理；系统化的问题解决。
This stage theorem helps explain why Year 8 students can grasp abstract metaphors while younger siblings interpret them literally.
这一阶段定理有助于解释为什么八年级学生能理解抽象比喻，而年幼的弟妹却按字面意思理解。
8. Research Method Formula: IV → DV (Extraneous Variables Controlled) | 研究方法公式：自变量 → 因变量（控制额外变量）
In WJEC Psychology, experiments follow a core formula: the independent variable (IV) is manipulated to see its effect on the dependent variable (DV), while all other variables are kept constant or controlled. Only then can we claim a cause-and-effect relationship.
在 WJEC 心理学中，实验遵循一条核心公式：操纵自变量（IV）以观察其对因变量（DV）的影响，同时保持所有其他变量恒定或加以控制。只有这样，我们才能断言因果关系。
Change in IV → Change in DV (if extraneous variables are controlled)
自变量的变化 → 因变量的变化（若额外变量被控制）
Extraneous variables are known as 'nuisance' factors — such as time of day, noise, or participant emotions — that must be minimised. If they are not controlled, they become confounding variables that ruin the internal validity of the experiment.
额外变量被称为“干扰”因素——如时间、噪音或参与者情绪——必须尽量减小。若不加控制，它们就成为混淆变量，破坏实验的内部效度。
| Variable | 变量 | Role | 角色 |
|---|---|
| IV | 自变量 | Manipulated by experimenter | 由研究者操纵 |
| DV | 因变量 | Measured outcome | 测量结果 |
| Extraneous | 额外变量 | Kept constant to avoid interference | 保持恒定以避免干扰 |
Thinking of research design as a formula makes it easier to spot flaws in a study and to plan your own psychological investigation for class projects.
将研究设计视为公式，更容易发现研究中的缺陷，并为课堂项目规划自己的心理学调查。
9. Ethical Principles Theorem: Respect, Competence, Responsibility, Integrity | 伦理原则定理：尊重、能力、责任、诚信
Every psychological study must obey an ethical theorem summarised by the British Psychological Society (BPS) into four overarching principles: respect, competence, responsibility, and integrity. These act like mathematical axioms that, if violated, invalidate the research regardless of its findings.
每一项心理学研究都必须遵守一条伦理定理，英国心理学会将其归纳为四个首要原则：尊重、能力、责任和诚信。这些原则如同数学公理，一旦违反，即便研究结果再好，研究本身也会变得无效。
Ethical Study = Respect × Competence × Responsibility × Integrity
伦理研究 = 尊重 × 能力 × 责任 × 诚信
- Respect: Informed consent, right to withdraw, confidentiality. | 尊重：知情同意、退出权、保密。
- Competence: Researchers must be qualified and follow guidelines. | 能力：研究者必须胜任工作并遵循指导方针。
- Responsibility: Protect participants from harm; debrief after deception. | 责任：保护参与者免受伤害；欺骗研究后须进行事后解释。
- Integrity: Be honest; avoid plagiarism and data fabrication. | 诚信：诚实；避免抄袭和数据捏造。
When evaluating a study in an exam, always check whether these ethical 'multipliers' are present — a zero in any category brings the score to zero.
在考试中评估一项研究时，务必检查这些伦理“乘数”是否具备——任何一个类别为零，总分即为零。
10. Social Influence Equation: Conformity = Normative + Informational | 社会影响方程：从众 = 规范性与信息性
Conformity — changing your behaviour to fit in with a group — can be broken down into a simple equation proposed by Deutsch and Gerard. Normative social influence occurs when we conform to be liked or accepted. Informational social influence happens when we conform because we believe the group knows better.
从众——改变自身行为以适应群体——可以分解为多伊奇和杰拉德提出的简单方程。规范性社会影响是指我们为了被喜欢或接纳而从众。信息性社会影响是指我们因为相信群体更懂而从众。
Conformity = Normative Influence + Informational Influence
从众 = 规范性影响 + 信息性影响
Asch’s line experiment famously demonstrated both: many participants gave the wrong answer to avoid ridicule (normative), while some genuinely doubted their own vision (informational). Factors that affect conformity include group size, unanimity, and task difficulty.
阿希的线段实验经典地展现了这两种影响：许多参与者为免遭嘲笑给出错误答案（规范性），而有些人真的质疑自己的视力（信息性）。影响从众的因素包括群体规模、一致性和任务难度。
11. The Yerkes-Dodson Law: Performance = f(Arousal) | 耶基斯-多德森定律：表现 = f(唤醒)
The Yerkes-Dodson Law states that performance increases with arousal up to an optimal point, after which further arousal causes performance to decline. It can be expressed as an inverted U-shaped function. For simple or well-learned tasks, the optimal level is higher; for complex tasks, it is lower.
耶基斯-多德森定律指出，表现随唤醒水平提高而上升，直至最佳点，之后更高的唤醒反而使表现下降。它可以用倒 U 形函数来表达。对于简单或熟练的任务，最佳唤醒水平较高；对于复杂任务，则较低。
Performance = f(Arousal) with an inverted-U curve
表现 = f(唤醒)，曲线呈倒 U 形
This law is crucial for understanding exam stress: a little anxiety sharpens focus, but too much leads to blanking out. Sport psychologists use it to help athletes find their 'zone of optimal functioning'.
这一定律对理解考试压力至关重要：少许焦虑能使注意力更敏锐，但过度焦虑会导致大脑一片空白。运动心理学家利用它帮助运动员找到“最佳功能区”。
12. Correlation Coefficient Formula: r = Direction & Strength | 相关系数公式：r = 方向与强度
A correlation coefficient (r) is a statistical 'formula' that tells us the direction and strength of a relationship between two co‑variables. The value of r ranges from -1 to +1. The sign indicates direction (positive or negative), and the number indicates strength (closer to 1 means stronger). Importantly, correlation does not imply causation — there may be a hidden third factor.
相关系数（r）是一条统计“公式”，它告诉我们两个协变量之间关系的方向和强度。r 的值在 -1 到 +1 之间。正负号表示方向（正或负），数值表示强度（越接近 1 越强）。重要的是，相关不能推出因果——可能存在隐藏的第三因素。
-1 ≤ r ≤ +1
-1 ≤ r ≤ +1
- Positive correlation: As one variable increases, the other increases too (e.g., revision time and test scores). | 正相关：一个变量增加，另一个也增加（如复习时间与考试成绩）。
- Negative correlation: As one variable increases, the other decreases (e.g., stress and sleep). | 负相关：一个变量增加，另一个减少（如压力与睡眠）。
- Zero correlation: No relationship (e.g., shoe size and IQ). | 零相关：无关系（如鞋码与智商）。
Scattergrams are used to plot these relationships, and the gradient of the points hints at the r value. Always remember to say 'may be linked' rather than 'causes' when writing about correlational findings.
散点图用来描绘这些关系，点的趋势提示了 r 值的大小。在描述相关发现的结论时，永远记得说“可能有关联”而不是“导致”。
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