📚 Year 7 CIE Psychology Formula & Theorem Quick Reference Handbook | 7年级CIE心理学公式定理速查手册
Welcome to your essential quick-reference guide for Year 7 CIE Psychology. In this handbook, we have gathered the most important formulas, theorems, and principles you will encounter in your studies. From thresholds of sensation to laws of learning, each entry is explained in clear, simple language with both English and Chinese translations. Mastering these core ideas will build a strong foundation for your psychological understanding.
欢迎使用这本7年级CIE心理学必备速查手册。我们汇集了学习过程中会遇到的最重要的公式、定理和原理。从感觉阈限到学习定律，每一条都用清晰简单的语言进行解释，并配有中英双语翻译。掌握这些核心概念将为你的心理学理解打下坚实的基础。
1. Weber’s Law | 韦伯定律
Weber’s Law states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. It helps explain why we notice small changes in a dim light but need large changes in a bright light.
韦伯定律指出，两个刺激之间的最小可觉差（JND）与原始刺激的强度成正比。它解释了为什么在昏暗光线下我们能注意到微小变化，而在强光下需要较大变化。
ΔI / I = k
Where ΔI is the change in stimulus intensity, I is the original intensity, and k is the Weber constant specific to each sensory modality.
其中 ΔI 是刺激强度的变化量，I 是原始强度，k 是每个感觉通道特有的韦伯常数。
Example: For weight, k ≈ 0.02, meaning you can detect a 2% increase in weight. For sound loudness, k ≈ 0.1.
例如：对于重量，k 大约为0.02，意味着你能察觉重量增加2%。对于声音响度，k 大约为0.1。
2. Fechner’s Law | 费希纳定律
Fechner’s Law extends Weber’s findings by describing the relationship between physical stimulus intensity and the perceived sensation magnitude. It states that sensation increases proportionally to the logarithm of the stimulus intensity.
费希纳定律扩展了韦伯的发现，描述了物理刺激强度与感知到的感觉大小之间的关系。它指出感觉量与刺激强度的对数成正比。
S = k · log(I)
Where S is the sensation magnitude, I is the stimulus intensity, and k is a constant depending on the sensory system.
其中 S 是感觉量，I 是刺激强度，k 是取决于感觉系统的常数。
This explains why doubling the brightness of a light does not make it seem twice as bright; the perceived change follows a logarithmic scale.
这解释了为什么将光的亮度加倍并不会让它看起来亮了两倍；感知变化遵循对数刻度。
3. IQ Formula | 智商公式
The Intelligence Quotient (IQ) was originally calculated as a ratio of mental age to chronological age, making it easy to compare children’s intellectual development.
智商最初被计算为智力年龄与实际年龄的比率，便于比较儿童的智力发展。
IQ = (Mental Age / Chronological Age) × 100
If a child’s mental age matches their chronological age, IQ = 100, which is the average. A higher mental age gives an IQ above 100.
如果一个孩子的智力年龄与实际年龄相当，智商为100，处于平均水平。智力年龄高于实际年龄则智商高于100。
Modern tests use deviation IQ, but this ratio formula is still a key historical theorem in psychology.
现代测试使用离差智商，但这个比率公式仍然是心理学中重要的历史定理。
4. Multi-Store Memory Theorem | 多存储记忆定理
The Multi-Store Model of Memory (Atkinson & Shiffrin, 1968) proposes three distinct stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Each store has its own capacity and duration, which can be expressed as a fundamental theorem of human memory.
多存储记忆模型（Atkinson & Shiffrin, 1968）提出了三个独立的存储系统：感觉记忆、短时记忆和长时记忆。每个存储系统都有自己的容量和持续时间，可视为人类记忆的基本定理。
| Memory Store 记忆存储 | Capacity 容量 | Duration 持续时间 |
|---|---|---|
| Sensory Memory 感觉记忆 | Very large (unlimited) 非常大 | 0.25–2 seconds 0.25–2秒 |
| Short-Term Memory (STM) 短时记忆 | 7 ± 2 items 7±2个项目 | 18–30 seconds 18–30秒 |
| Long-Term Memory (LTM) 长时记忆 | Potentially unlimited 潜在无限 | Lifetime 终生 |
The ‘7 ± 2’ rule for STM was discovered by George Miller, often called ‘Miller’s Law’. It explains why phone numbers are grouped into chunks.
短时记忆的“7 ± 2”规则由乔治·米勒发现，常被称为“米勒定律”。这解释了为什么电话号码被分成组块。
5. Serial Position Effect Theorem | 系列位置效应定理
When remembering a list of items, recall accuracy follows a U-shaped curve: items at the beginning (primacy effect) and end (recency effect) are remembered better than those in the middle. This phenomenon is a fundamental theorem of memory recall.
当记忆一系列项目时，回忆准确率呈U形曲线：开头（首因效应）和结尾（近因效应）的项目比中间的项目记得更好。这一现象是记忆提取的基本定理。
Recall Probability = f(Position) → U-shaped function
Where primacy effect is due to LTM rehearsal, and recency effect is due to STM holding the last items.
首因效应归因于长时记忆的复述，近因效应则由于短时记忆中保留着最后几个项目。
This theorem is used in revision techniques: start and end study sessions with the most important information.
这一定理可应用于复习技巧：将最重要的信息放在学习时段的开头和结尾。
6. Piaget’s Stage Theorem | 皮亚杰阶段定理
Jean Piaget proposed that cognitive development occurs in four fixed stages, each with distinct logical structures. This stage theorem implies that children cannot skip a stage or reach it before their biological readiness.
让·皮亚杰提出认知发展分为四个固定阶段，每个阶段都有独特的逻辑结构。这一阶段定理意味着儿童不能跳过某个阶段，也不能在生理成熟之前就达到该阶段。
| Stage 阶段 | Age Range 年龄范围 | Key Achievement 主要成就 |
|---|---|---|
| Sensorimotor 感知运动阶段 | 0–2 years 0–2岁 | Object permanence 客体永久性 |
| Preoperational 前运算阶段 | 2–7 years 2–7岁 | Symbolic thinking, egocentrism 符号思维，自我中心 |
| Concrete Operational 具体运算阶段 | 7–11 years 7–11岁 | Conservation, logical operations 守恒，逻辑运算 |
| Formal Operational 形式运算阶段 | 11+ years 11岁以上 | Abstract reasoning 抽象推理 |
Understanding this theorem helps educators design age-appropriate learning activities.
理解这一定理有助于教育者设计适合年龄的学习活动。
7. Operant Conditioning Reinforcement Theorem | 操作性条件作用强化定理
B.F. Skinner’s principle of operant conditioning states that behaviour is shaped by consequences. Reinforcement increases the probability of a behaviour, while punishment decreases it. This can be framed as a fundamental theorem of learning.
斯金纳的操作性条件作用原理指出，行为由后果塑造。强化增加行为发生的概率，而惩罚降低概率。这可以视为学习的基本定理。
Behaviour Probability ↑ if followed by Reinforcement; ↓ if followed by Punishment
Positive reinforcement: adding a pleasant stimulus (e.g., praise). Negative reinforcement: removing an unpleasant stimulus (e.g., stopping nagging).
正强化：添加愉快刺激（如表扬）。负强化：移除厌恶刺激（如停止唠叨）。
Schedules of reinforcement (fixed ratio, variable ratio, fixed interval, variable interval) create different response rates, which are essential for understanding addiction and gaming.
强化程式（固定比率、可变比率、固定间隔、可变间隔）产生不同的反应速率，这对于理解成瘾和游戏设计至关重要。
8. James-Lange Emotion Equation | 詹姆斯-兰格情绪方程
The James-Lange theory of emotion proposes that physiological arousal precedes the experience of emotion. This can be expressed as a causal equation: we feel afraid because our heart races, not the other way around.
詹姆斯-兰格的情绪理论提出，生理唤醒先于情绪的体验。这可以表达为一个因果方程：我们感到害怕是因为心跳加速，反之不成立。
Emotion = Perception of Bodily Changes
Stimulus → Bodily Reaction → Interpretation → Emotional Feeling.
刺激 → 身体反应 → 解释 → 情绪感受。
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