Theory of Knowledge
- ToK subject brief
- TOK Essay Assessment Rubric
- TOK Exhibition Assessment Rubric
- Prescribed Essay Titles
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
Knowledge Questions
In the IB Theory of Knowledge (TOK) course, Knowledge Questions (KQs) are open-ended questions about knowledge itself, rather than about a specific topic or event. They encourage students to think critically about how knowledge is created, justified, interpreted, evaluated, and communicated across different contexts. A Knowledge Question is not asking “What happened?” or “What is the answer?” Instead, it asks “How do we know?”, “To what extent can we know?”, or “What influences what we know?”
- Is mathematics the most ‘fundamental’ of all the areas of knowledge?
- Does mathematics provide us with certain knowledge?
- Are mathematical axioms the same as truth?
- Is the term ‘mathematical proof’ different from other types of proof?
- Is mathematics defined by its content or method?
- How does mathematical reasoning differ from other forms of reasoning?
- Is mathematical knowledge always abstract?
- Why is mathematics so highly esteemed?
- Is mathematics based on ‘unproven truths’?
- Are there special ethical responsibilities regarding how mathematical knowledge is produced and used?
- Does basing decisions on algorithms create solid ethical knowledge?
- Can ethical knowledge be objectively calculated via mathematics?
- How different are mathematics and ethics in terms of the evidence used to justify knowledge claims?
- Who should create the ethical framework used to produce and use mathematical knowledge?
- Does mathematics provide us with the most objective form of language?
- How can data visualizations be manipulated in order to spin the knowledge they communicate?
- Do mathematical symbols convey the same type of meaning as ordinary words?
- How can the intention behind statistics interfere with its objectivity?
- How can statistics be used to manipulate people?
- Is it possible to present data objectively?
- Is mathematics ever aligned to a particular culture or tradition?
- How easy is it to establish consensus in mathematics?
- Is it a paradox that mathematics is both a human construct, and objectively true about the world?
- To what extent do assumptions underpin our understanding of mathematics?
- Can we draw on personal experiences to help produce and understand mathematical knowledge?
- How has the development of technology impacted mathematics?
- Does mathematics progress cumulatively, or does new knowledge violently destroy old knowledge?
- Is mathematics invented or discovered – or created in some other way?
- Why is it so difficult to produce mathematical proof?
- Does mathematics develop in the same way as other areas of knowledge?
- Is mathematical knowledge driven forward by individual thinkers?
Characteristics of a Strong Knowledge Question
A good Knowledge Question should:
- Be open-ended, with no single correct answer.
- Focus on knowledge, rather than facts or opinions.
- Be general, allowing it to be applied across different situations and disciplines.
- Encourage analysis, evaluation, and multiple perspectives.
- Usually connect one or more Areas of Knowledge (AOKs) and Themes in TOK.
What Examiners Look For
High-scoring TOK responses demonstrate that students:
- Focus on knowledge, not just the topic.
- Explore different perspectives.
- Compare how knowledge works across Areas of Knowledge.
- Support arguments with real-life examples.
- Evaluate the strengths and limitations of different ways of knowing and knowledge claims.
Common Knowledge Question Starters
Strong Knowledge Questions often begin with phrases such as:
- How do we know…?
- To what extent…?
- What role does… play in…?
- How reliable is…?
- What counts as evidence…?
- What makes knowledge trustworthy?
- Can knowledge ever be certain?
- How does language influence knowledge?
- When should we question accepted knowledge?
- What is the relationship between knowledge and belief?
Knowledge Questions vs. Content Questions
| Mathematical Content Question | ToK Knowledge Question |
| Calculus: What is the maximum height reached by a projectile launched at 25 m/s and an angle of 40°? | Calculus: To what extent do mathematical models accurately represent real-world phenomena? |
| Probability & Statistics: What is the probability of drawing two aces from a standard deck of cards without replacement? | Probability & Statistics: To what extent can probability provide reliable knowledge for predicting real-world events? |
| Geometry: How can the sine rule and cosine rule be used to determine the unknown sides and angles of a triangle? | Geometry: How do the assumptions and axioms of geometry influence what can be considered mathematical truth? |
| Functions: How do exponential functions model population growth? | Functions: What are the strengths and limitations of using mathematics to model complex real-world situations? |
Knowledge Questions in the TOK Exhibition and Essay
- TOK Exhibition: Students choose three objects and explain how they relate to one of the prescribed IA prompts. Their discussion should naturally raise and explore Knowledge Questions about the prompt.
TOK Essay: The prescribed essay titles are themselves broad Knowledge Questions. Students analyse them by developing arguments, counterclaims, and real-life examples across different Areas of Knowledge.
