📚 IGCSE CCEA Sociology: Formula & Theorem Quick Reference Handbook | IGCSE CCEA 社会学：公式定理速查手册
This handbook summarises the key “formulae” and “theorems” you need for IGCSE CCEA Sociology. In Sociology, formulae often mean statistical tools for analysing data, while theorems are the theoretical frameworks used to explain social patterns. Use this guide for quick revision, but always link each concept to real examples and exam-style evidence.
本手册总结了 IGCSE CCEA 社会学所需的关键“公式”与“定理”。在社会学中，公式通常指分析数据的统计工具，定理则指解释社会模式的理论框架。请使用本指南快速复习，但务必把每个概念与实际案例和考试型证据联系起来。
1. How to Use This Handbook | 如何使用本手册
This handbook is not a replacement for your textbook. It condenses recurring CCEA Sociology content into ‘formulae’ (statistical and methodological tools) and ‘theorems’ (theoretical perspectives). For each entry, learn the definition, a supporting study or example, and a strength or weakness. In the exam, you must apply the formula, not just state it.
本手册不能替代教材。它将 CCEA 社会学中反复出现的内容压缩为“公式”（统计与方法工具）和“定理”（理论视角）。每一条都要掌握定义、支持性研究或例子，以及一个优点或局限。考试中必须应用公式，而不能只写出公式。
2. Theoretical Perspectives as Theorems | 社会学理论视角即定理
Sociological ‘theorems’ are broad frameworks that explain how society works. The main perspectives are functionalism, Marxism, feminism, interactionism and the New Right. Each offers a different answer to questions about order, conflict, inequality and change.
社会学“定理”是解释社会如何运作的宽泛框架。主要视角包括功能主义、马克思主义、女性主义、互动论和新右派。它们对社会秩序、冲突、不平等与变迁等问题给出了不同答案。
Functionalism: Society is like a biological organism; institutions (family, education, religion) perform functions that maintain stability. Key thinkers: Durkheim, Parsons. Strength: explains social order. Weakness: ignores conflict and inequality.
功能主义：社会如同生物有机体；制度（家庭、教育、宗教）发挥维持稳定的功能。代表人物：涂尔干、帕森斯。优点：解释社会秩序。缺点：忽视冲突和不平等。
Marxism: Society is divided by class conflict between bourgeoisie and proletariat; institutions reproduce capitalist ideology. Key thinkers: Marx, Althusser. Strength: highlights power and inequality. Weakness: economic determinism.
马克思主义：社会因资产阶级与无产阶级之间的阶级冲突而分裂；制度再生产资本主义意识形态。代表人物：马克思、阿尔都塞。优点：强调权力和不平等。缺点：经济决定论。
Feminism: Society is patriarchal; gender inequality is structured into institutions. Types include liberal, Marxist, radical. Strength: reveals gendered power. Weakness: sometimes underplays class and ethnicity.
女性主义：社会是父权制的；性别不平等被嵌入制度之中。类型包括自由派、马克思主义派、激进派。优点：揭示性别权力。缺点：有时低估阶级和族裔。
Interactionism: Society is constructed through everyday interactions and labels; focus on micro-level meanings. Key thinkers: Mead, Becker, Goffman. Strength: rich detail. Weakness: neglects wider structures.
互动论：社会通过日常互动和标签建构；关注微观层面的意义。代表人物：米德、贝克尔、戈夫曼。优点：细节丰富。缺点：忽视更宏观的结构。
New Right: Society works best when individuals take responsibility; state intervention can create dependency. Strength: policy influence. Weakness: blames the poor for structural problems.
新右派：个人承担责任时社会运行最佳；国家干预可能造成依赖。优点：政策影响力大。缺点：把结构性问题归咎于穷人。
3. Social Stratification Formulae | 社会分层公式
Stratification refers to the unequal distribution of resources, opportunities and status. In CCEA questions, you may need to calculate or interpret measures such as the poverty rate, income quintile ratio and unemployment rate.
分层指资源、机会和地位的不平等分配。在 CCEA 题目中，你可能需要计算或解读贫困率、收入五等分比和失业率等指标。
Unemployment rate = (Number unemployed ÷ Labour force) × 100%
This measures the proportion of the labour force that is actively seeking work but cannot find a job.
该公式衡量劳动力中积极寻找工作但无法找到工作的人所占的比例。
Poverty rate = (Number below poverty line ÷ Total population) × 100%
This shows the percentage of the population living below a defined poverty threshold.
该公式显示生活在既定贫困线以下的人口所占百分比。
Income quintile ratio = Average income of top 20% ÷ Average income of bottom 20%
A higher ratio indicates greater income inequality between the richest and poorest fifths.
该比值越高，表明最富有和最贫困的五分之一人口之间的收入不平等越严重。
The Gini coefficient is not calculated as a simple formula at IGCSE, but you should know that 0 means perfect equality and 1 means perfect inequality. Use it to compare stratification between countries or over time.
基尼系数在 IGCSE 阶段不需要用简单公式计算，但你应知道 0 表示完全平等，1 表示完全不平等。用它来比较不同国家或不同时期的分层程度。
4. Family and Household Statistics | 家庭与住户统计
The family is a core CCEA topic. You need to know key trends such as divorce rate, marriage rate, cohabitation rate and single-parent household percentage. These are often expressed as rates per 1,000 population.
家庭是 CCEA 的核心主题。你需了解离婚率、结婚率、同居率和单亲住户比例等关键趋势，这些通常以每千人口的比率表示。
Divorce rate = (Number of divorces ÷ Total population) × 1,000
The divorce rate is a crude rate because it uses the whole population, not only married couples.
离婚率是一种粗略比率，因为它以总人口为分母，而不仅以已婚夫妇为分母。
Marriage rate = (Number of marriages ÷ Total population) × 1,000
Falling marriage rates can reflect increased cohabitation, secularisation or changing gender roles.
结婚率下降可能反映同居增加、世俗化或性别角色的变化。
Nuclear family theorem: Parsons argued the isolated nuclear family fits industrial society because it is geographically mobile and performs primary socialisation and stabilisation of adult personalities.
核心家庭定理：帕森斯认为孤立的核心家庭适合工业社会，因为它具有地理流动性，并承担初级社会化和成人人格稳定功能。
Remember that a statistical trend is not the same as a social explanation; always connect rates to sociological reasons.
请记住，统计趋势不等于社会解释；务必把比率与社会学原因联系起来。
5. Education and Achievement Gap Formulae | 教育与成就差距公式
Education research uses pass rates, exclusion rates and free school meal (FSM) gaps to measure inequality. The attainment gap is often the percentage point difference between two groups, such as FSM and non-FSM pupils.
教育研究使用通过率、排斥率和免费校餐（FSM）差距来衡量不平等。成就差距通常指两组之间（如 FSM 与非 FSM 学生）的百分点差。
Attainment gap = Pass rate of advantaged group − Pass rate of disadvantaged group
A positive gap means the advantaged group outperforms the disadvantaged group.
若差距为正，说明优势群体的表现优于弱势群体。
Pass rate = (Number achieving target grade ÷ Number entered) × 100%
Always check whether the pass rate refers to all pupils or only those entered for an examination.
务必检查通过率指的是所有学生还是仅指参加考试的学生。
Key theorem: Bowles and Gintis’ correspondence principle states that schools mirror workplace hierarchy, preparing working-class pupils for obedience and middle-class pupils for leadership.
关键定理：鲍尔斯与金蒂斯的“对应原则”认为学校反映职场等级，让工人阶级学生学会服从，让中产阶级学生学会领导。
Use this theorem to evaluate explanations such as material deprivation, cultural capital and teacher labelling.
请用该定理评价物质剥夺、文化资本和教师标签等解释。
6. Crime and Deviance Measurement | 犯罪与偏差测量
Crime statistics are socially constructed. The official crime rate is a key formula, but it misses undetected offences, known as the dark figure of crime. Victim surveys and self-report studies supplement official data.
犯罪统计是社会建构的。官方犯罪率是重要公式，但它遗漏未被发现的犯罪，即犯罪黑数。受害调查和自我报告研究补充官方数据。
Crime rate = (Number of recorded crimes ÷ Total population) × 1,000
The crime rate is influenced by reporting, policing and recording practices, so it is not an objective count of all offending.
犯罪率受报案、警务和记录方式的影响，因此并非所有犯罪行为的客观统计。
Clear-up rate = (Number of crimes solved ÷ Number of crimes recorded) × 100%
This measures police effectiveness, but a high clear-up rate does not mean crime is low.
该指标衡量警方效率，但破案率高并不意味着犯罪率低。
Theorems: Merton’s strain theory argues crime occurs when individuals accept cultural goals but lack legitimate means; Becker’s labelling theory states deviance is defined by powerful groups who attach labels.
定理：默顿的紧张理论认为，当个人接受文化目标却缺乏合法手段时就会犯罪；贝克尔的标签理论指出偏差是由掌权群体贴标签来界定的。
7. Research Methods Formula Sheet | 研究方法公式表
Sociological research uses qualitative and quantitative methods. Quantitative research relies on sampling, response rates and measures of central tendency. Validity and reliability are not formulae, but they are the ‘theorems’ of research quality.
社会学研究使用定性和定量方法。定量研究依赖抽样、回收率和集中趋势测量。效度与信度不是公式，但它们是研究质量的“定理”。
Response rate = (Number of completed responses ÷ Number of people approached) × 100%
A low response rate can reduce the representativeness of the findings.
回收率低会降低研究结果的代表性。
Sampling fraction = Sample size ÷ Population size
This tells you how much of
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