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1 The Course
1.1 Core theme: Knowledge and the Knower (compulsory)
1.2 Optional theme: Knowledge and Technology
1.3 Optional theme: Knowledge and Language
1.4 Optional theme: Knowledge and Politics
1.5 Optional theme: Knowledge and Religion
1.6 Optional theme: Knowledge and Indigenous Societies
1.7 Area of knowledge: The Natural Sciences
1.8 Area of knowledge: The Human Sciences
1.9 Area of knowledge: History
1.10 Area of knowledge: Mathematics
1.11 Area of knowledge: The Arts
2 The Exhibition
2.1 The exhibition at a glance
2.2 The instrument: one question, one best-fit judgement out of 10
2.3 Choosing a prompt: narrowing 35 to 1
2.4 Objects that work: specific real-world context
2.5 Linking an object to the prompt
2.6 The commentary: 950 words across three objects
2.7 The Year 1 exhibition calendar
2.8 Coaching within the rules: what guidance is allowed
2.9 The exhibition event and the administrative requirements
2.10 Moderation: what the IB does with your marks
2.11 Exemplars with band reasoning
2.12 The 35 IA prompts
3 The Essay
3.1 The essay at a glance
3.2 The instrument: one question, five bands
3.3 What separates 9-10 from 7-8
3.4 Structure without formula
3.5 Examples are evidence, not decoration
3.6 Introductions, definitions, conclusions
3.7 Counter-pressure that does not cancel: four shapes
3.8 Unpacking any title: the method
3.9 The 1,600 words and the formal requirements
3.10 Exemplars with band reasoning
3.11 Practice titles: using the archive
4. May 2027 TOK Titles
4.1 M27 Title 1
4.2 M27 Title 2
4.3 M27 Title 3
4.4 M27 Title 4
4.5 M27 Title 5
4.6 M27 Title 6
1.10.1 What mathematics is about
28 minute read
1.10.2 Axioms, definitions and systems
29 minute read
1.10.3 Proof and deductive certainty
31 minute read
1.10.4 What proof cannot do
30 minute read
1.10.5 Non-Euclidean geometry and axiom choice
1.10.6 Infinity and counterintuitive results
32 minute read
1.10.7 Invented or discovered?
1.10.8 Platonism, formalism and other positions
34 minute read
1.10.9 Beauty and elegance as criteria
1.10.10 Why mathematics works so well in physics
1.10.11 Mathematics as the language of other areas of knowledge
1.10.12 Modelling and idealisation
1.10.13 Statistics: what numbers can and cannot show
1.10.14 Misleading with true numbers
1.10.15 Responsibility for models and algorithms
1.10.16 Assessment bridge: mathematics in essay titles
1.10 Area of Knowledge: Mathematics