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ÌÇÐÄVlog

Last updated

8 April 2026

zip, 59.13 KB
zip, 59.13 KB

This fully scripted 60-minute IB DP Theory of Knowledge (TOK) lesson explores the relationship between mathematics, beauty, and intuition. It asks why mathematicians often describe results as elegant, beautiful, or surprising, and whether these aesthetic and intuitive responses have any role in mathematical knowledge.

The lesson begins with a quick beauty scale activity in which students rate several mathematical results according to the feeling they produce. These include the angle sum of a triangle, infinitely many prime numbers, Euler’s identity, and the irrationality of √2. This is used to introduce the idea that mathematical results can produce emotional and aesthetic responses, not just logical agreement.

The first main task focuses on ugly versus elegant proofs. Students compare two proofs of the same result and discuss why one may feel more satisfying or revealing than the other. This helps them consider whether elegance is just a personal preference or whether it can actually matter in mathematical understanding.

The lesson then introduces the story of Srinivasa Ramanujan, whose mathematical results often came through intuition before formal proof. Students examine whether true results without proof should count as knowledge, and what Ramanujan’s case suggests about the role of intuition, imagination, and justification in mathematics.

A central activity is The Intuition Tribunal, where students take on different roles and debate whether mathematical intuition is a valid way of knowing. This is followed by a short mathematical autobiography task in which students reflect on a personal experience of mathematics that produced a feeling such as satisfaction, surprise, frustration, or confusion.

The resource includes a full teacher walkthrough, beauty-rating sheet, intuition tribunal activity, reflection task, TOK knowledge questions, and an exit ticket. It is useful for TOK lessons on mathematics, intuition, proof, beauty, imagination, and the role of personal response in knowledge. It can also support TOK Exhibition planning and essay discussion.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

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IB DP Theory of Knowledge (TOK): 19 Lesson Bundle - Part 2 - 2026

This bundle contains another 19 lessons covering the Areas of Knowledge and optional themes of the IB DP Theory of Knowledge course. There are multiple valid ways to sequence and teach these topics. This is not an exhaustive curriculum. These are just some ready-made lessons and activities for any teacher who needs something to use with their students, whether you follow this order or pick and choose what fits your context. Possible sequence and rationale This bundle picks up where the first 20 lessons left off, completing the Natural Sciences AOK before moving through Mathematics, History, Human Sciences, Ethics, Technology, Politics, the Arts, and Religious and Indigenous Knowledge Systems. The AOKs are ordered to build on each other: Natural Sciences and Mathematics sit together because both deal with formal knowledge and certainty, making comparison straightforward. History and Human Sciences follow because they raise similar questions about method, objectivity, and bias but in messier, more contested territory. Ethics comes next because the Human Sciences lessons, particularly the conformity material, lead naturally into questions of moral knowledge. The Technology and Politics optional themes close the AOK sequence because students are by then equipped to apply everything they have learned to the most current and contested knowledge contexts. The Arts and Religious and Indigenous Knowledge Systems sit last as a deliberate broadening; they challenge students to question the assumptions about knowledge they have built up across the rest of the course. What is included Paradigm Shifts Science Ethics and Values The Nature of Mathematical Knowledge Is Mathematics Invented or Discovered Mathematics Beauty and Intuition How Historians Know What They Know Perspective Bias and Revisionism in History History Language and Narrative Methods in the Human Sciences Ethics and Human Sciences Ethics and Conformity Moral Frameworks Applied Ethics and Knowledge Algorithms and the Architecture of Information AI and Knowledge Production Misinformation and the Digital Age Political Knowledge and Ideology Knowledge Through the Arts Religious and Indigenous Knowledge Systems Each lesson includes scripted teacher notes, student-facing materials, discussion questions, and at least one activity. Suitable for Grade 11 and 12 students in the IB DP TOK course. Aligns with the current IB TOK guide for 2026

£68.00

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