📚 GCSE CAIE Sociology: Formulas and Theorems Quick Reference Handbook | GCSE CAIE 社会学：公式定理速查手册
Welcome to your go‑to quick reference guide for GCSE CAIE Sociology. This handbook compresses the essential theoretical propositions (theorems) underpinning the sociological perspectives you must master, alongside the simple yet vital formulas for handling quantitative data and social indicators. Bookmark this page for last‑minute revision and make sure you can recall these building blocks with confidence.
欢迎使用 GCSE CAIE 社会学速查手册。本手册浓缩了你必须掌握的社会学视角背后的核心理论命题（定理），以及处理定量数据和社会指标时必不可少的简单但重要的公式。将此页面加入书签方便最后复习，确保你能自信地回忆起这些基础构件。
1. Marxist Core Theorems | 马克思主义核心定理
Marx’s historical materialism theorem: the economic base (forces and relations of production) determines the superstructure of institutions, ideology and the state.
马克思的历史唯物主义定理：经济基础（生产力与生产关系）决定上层建筑的制度、意识形态与国家。
Class struggle theorem: the history of all existing society is the history of class struggles; under capitalism the bourgeoisie and proletariat are locked in irreconcilable conflict.
阶级斗争定理：所有现存社会的历史都是阶级斗争的历史；在资本主义制度下，资产阶级与无产阶级处于不可调和的冲突之中。
Ideological state apparatuses (education, media, religion) function to reproduce class inequality by transmitting ruling‑class ideology and legitimising exploitation.
意识形态国家机器（教育、媒体、宗教）通过传播统治阶级的意识形态并使剥削合法化，来再生产阶级不平等。
Polarisation theorem: capitalism inevitably concentrates wealth, immiserates the proletariat and intensifies exploitation, creating the conditions for revolutionary overthrow.
两极分化定理：资本主义不可避免地集中财富、使无产阶级贫困化并加剧剥削，从而为革命性推翻创造条件。
Correspondence principle (Bowles & Gintis): schools mirror the capitalist workplace through hierarchical authority, fragmentation of tasks and extrinsic rewards, preparing students for alienated labour.
对应原则（鲍尔斯与金蒂斯）：学校通过等级权威、任务碎片化和外部奖励映照资本主义工作场所，为学生接受异化劳动做准备。
Resistance theorem (Willis): working‑class ‘lads’ may partially see through the meritocratic myth but develop an oppositional counter‑culture that ultimately funnels them into working‑class jobs.
抵制定理（威利斯）：工人阶级“小子们”可能部分看穿英才神话，但发展出一种对立的反文化，最终将他们导入工人阶级工作。
2. Functionalist Core Theorems | 功能主义核心定理
Durkheim’s social fact theorem: society is a reality sui generis, greater than the sum of its parts; social facts are external, constraining and general.
涂尔干的社会事实定理：社会是一个自成一体的实在，大于各部分之和；社会事实是外在的、具有约束力和普遍性的。
Organic analogy theorem (Parsons): societies are systems of interdependent institutions, each fulfilling a functional prerequisite to maintain equilibrium.
有机体类比定理（帕森斯）：社会是由相互依赖的制度组成的系统，每一制度履行一项功能先决条件以维持均衡。
AGIL schema theorem: all social systems must secure Adaptation, Goal attainment, Integration and Latency (pattern maintenance) to survive.
AGIL 图式定理：所有社会系统必须确保适应、目标达成、整合和维稳（模式维持）才能存续。
Education function theorem: education transmits shared norms and values, fosters social solidarity, sifts and sorts individuals into appropriate roles, and provides a bridge between the particularistic family and universalistic society.
教育功能定理：教育传递共享的规范与价值观，培养社会团结，筛选个体并将其分配至适当角色，并在特殊主义的家庭与普遍主义的社会之间架起桥梁。
Davis–Moore stratification theorem: social inequality is functionally necessary – the most important positions require the greatest talents and must offer higher rewards to motivate individuals to undergo lengthy training.
戴维斯–摩尔分层定理：社会不平等具有功能必要性——最重要的职位需要最优秀的才能，必须提供更高的报酬以激励个体接受长期训练。
Merton’s manifest and latent functions theorem: institutions have intended, recognised consequences (manifest) as well as unintended, hidden ones (latent), e.g. schools aiming to educate while also creating friendship networks.
默顿的显性功能与隐性功能定理：制度既有意欲的、被认可的后果（显性），也有非预期的、隐藏的后果（隐性），例如学校旨在教育，同时也创造友谊网络。
3. Feminist Theorems | 女性主义理论定理
Liberal feminist theorem: gender inequality stems from legal barriers, sexist attitudes and unequal socialisation; reform through legislation and equal opportunities can bring about change.
自由主义女性主义定理：性别不平等源于法律障碍、性别歧视态度和不平等的社会化过程；通过立法和机会均等改革可以实现变革。
Marxist feminist theorem: women’s oppression originates in the capitalist mode of production; women’s unpaid domestic labour reproduces the workforce cheaply, and patriarchy serves capitalism.
马克思主义女性主义定理：女性压迫起源于资本主义生产方式；女性的无偿家务劳动廉价再生产劳动力，父权制服务于资本主义。
Radical feminist theorem: patriarchy is the fundamental, trans‑historical oppression; male control over female sexuality, reproduction and domesticity is the root of all inequality, and separatism is sometimes advocated.
激进女性主义定理：父权制是根本的、跨历史的压迫；男性对女性性事、生育和家庭生活的控制是一切不平等的根源，有时倡导分离主义。
Intersectionality theorem: gender cannot be analysed in isolation; it intersects with class, ethnicity and other axes of stratification to produce varied experiences of oppression.
交叉性定理：性别不能孤立分析；它与阶级、族裔和其他分层轴心交织，产生多样化的压迫体验。
Triple shift theorem (Duncombe & Marsden): many women perform paid work, housework and emotional labour simultaneously, intensifying their workload and reinforcing gender inequality.
三重劳动定理（邓科姆与马斯登）：许多女性同时从事有偿工作、家务劳动和情感劳动，强化了她们的工作负荷并加剧性别不平等。
4. Weberian Stratification Theorem | 韦伯分层理论定理
Weber’s multi‑dimensional stratification theorem: social inequality cannot be reduced to class alone; it emerges from the interplay of class (market situation), status (social honour) and party (power).
韦伯的多维分层定理：社会不平等不能仅归结为阶级；它产生于阶级（市场处境）、地位（社会荣誉）和党派（权力）的相互作用。
Class theorem: class is defined by life chances in the market – those who own property and marketable skills have superior chances.
阶级定理：阶级由市场中的生活机会界定——拥有财产和可销售技能的人享有更优越的机会。
Status theorem: status groups are formed around shared lifestyles, consumption patterns and levels of social prestige; status honour can cut across class lines.
地位定理：地位群体围绕共享的生活方式、消费模式和社会声望水平形成；地位荣誉可以跨越阶级界限。
Party (power) theorem: parties are organisations seeking to influence the distribution of power, often through rational‑legal authority, and can override class interests.
党派（权力）定理：党派是寻求影响权力分配的组织，常通过理性–法律型权威运作，并可能凌驾于阶级利益之上。
Social closure theorem (neo‑Weberian): privileged groups monopolise resources and restrict access to opportunities by erecting barriers such as credentials and professional qualifications.
社会封闭定理（新韦伯主义）：特权群体通过设立证书和专业资格等壁垒，垄断资源并限制机会准入。
5. Merton’s Strain Theorem | 默顿失范定理
Merton’s strain theorem: deviance arises when there is a disjunction between culturally prescribed goals and the legitimate means available to achieve them.
默顿的失范定理：当文化规定的目标与可获得的合法手段之间出现断裂时，越轨行为便会产生。
Conformity: individuals accept both the goals and the legitimate means; this is the most common adaptation in stable societies.
顺从：个人既接受目标也接受合法手段；这是稳定社会中最常见的适应模式。
Innovation: individuals accept the goals but resort to illegitimate or illegal means (e.g. theft, fraud) when legitimate routes are blocked.
创新：个人接受目标，但在合法途径受阻时诉诸非法手段（如盗窃、欺诈）。
Ritualism: individuals abandon or scale down the goals but compulsively adhere to the means, following rules for their own sake without expecting success.
仪式主义：个人放弃或降低目标，但刻板地遵守手段，为遵守规则而遵守规则，不期望成功。
Retreatism: individuals reject both goals and means, withdrawing from society (e.g. substance abusers, drop‑outs).
退却主义：个人拒绝目标和手段，从社会中退出（如物质滥用者、辍学者）。
Rebellion: individuals reject existing goals and means and seek to replace them with new, alternative social arrangements.
反叛：个人拒绝现有目标和手段，并寻求以新的替代社会安排取而代之。
6. Labelling Theory Theorem | 标签理论定理
Becker’s labelling theorem: deviance is not a quality of the act but a consequence of the application of rules and sanctions. An act becomes deviant only when labelled as such.
贝克尔的标签定理：越轨不是行为本身的特性，而是规则和制裁被应用的结果。行为只有在被贴上标签时才成为越轨。
Primary deviance: initial, often situational acts that have little effect on self‑concept, going largely unnoticed.
初级越轨：最初的、往往是情境性的行为，对自我概念影响很小，大多未被察觉。
Secondary deviance (Lemert): when a person is labelled and internalises the deviant identity, leading to a self‑fulfilling prophecy and a deviant career.
次级越轨（莱默特）：当一个人被贴上标签并内化越轨身份，导致自我实现的预言和越轨生涯。
Master status theorem: once labelled, the deviant label becomes the master status, overriding all other identities and shaping how others react to the individual.
首要地位定理：一旦被贴上标签，越轨标签就成为首要地位，凌驾于所有其他身份之上，并塑造他人对此人的反应。
Differential enforcement theorem: agencies of social control (police, courts) apply labels unevenly, so working‑class and ethnic minority youth are more likely to be criminalised for the same behaviour.
差异化执行定理：社会控制机构（警察、法院）并非均匀应用标签，因此工人阶级和少数族裔青年更可能因同样行为被定罪。
7. Measures of Central Tendency & Spread | 集中趋势与离散程度公式
The arithmetic mean is the sum of all values divided by the number of values. It uses all data points but can be distorted by outliers.
算术平均数是所有数值之和除以数值个数的商。它使用所有数据点，但可能被异常值扭曲。
Mean = Σx ÷ n
The median is the middle score when data are sorted; for an odd number of observations it is the (n+1)/2ᵗʰ term, for an even number it is the average of the n/2ᵗʰ and next term. It ignores outlier effects.
中位数是数据排序后的中间值；当观测数为奇数时是第 (n+1)/2 项，偶数时为第 n/2 项与下一项的均值。它不受异常值影响。
The mode is the most frequently occurring value; a dataset can have one mode (unimodal), two modes (bimodal) or more.
众数是出现频率最高的数值；数据集可以有一个众数（单峰）、两个众数（双峰）或更多。
The range is the simplest measure of spread: it is the difference between the maximum and minimum values.
全距是最简单的离散度量：
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