Certainty in Mathematics, Lesson 4
Lesson 4: Writing a TOK Essay
Focus: How can knowledge users develop strong, structured arguments?
Suggested Length: 1 hour
Learning Objectives:
- Write a fully developed TOK essay claim using the TOK essay structure.
- Apply real-world examples and counterclaims to support arguments.
- Engage critically with TOK concepts (e.g., certainty, power, and perspective).
| Critical Thinking Concepts | TOK Concepts | Reflection Questions |
|---|---|---|
| Bias & Power: Examine the assumption that mathematics is inherently neutral, questioning how funding priorities, government agendas, or corporate interests shape how models are constructed, applied, or interpreted. Exploring Contexts and Expert Opinions: Reflect on how institutional authority influences perceptions of credibility. Extrapolation and Reapplication of Principles: Connect issues of algorithmic bias to broader debates about democracy, social justice, and public trust in institutions. | Certainty: What responsibilities do mathematicians, corporations, and governments have when presenting models as objective or certain? Power: Who ultimately decides which models are legitimate, trustworthy, or acceptable to use in education, justice, or politics? Perspective: Can mathematical applications ever be universally “fair,” or are they always influenced by context and values? | What was the most challenging part of writing this? How do different perspectives influence debates on mathematical models? How does this practice help prepare for the TOK essay assessment? |
Resources and Preparation
- Slides, attached below.
- TOK Essay Checklist, attached below.
- Students will need to create their own Kialo discussion to plan their essay paragraph. Instructions for this can be found in the slides.
- You may find it useful to have additional TOK essay prompts to supplement the examples in the slides.
Introduction
Guiding Question: “How do we develop a strong argument in a TOK essay?"
Recap: What makes a TOK essay unique?
- Focus on knowledge (not merely opinions).
- Use real-world examples drawn from multiple Areas of Knowledge (AOKs).
- Include counterclaims.
- Refer to TOK concepts.
- Reflect on the implications and limitations of your argument.
Teacher Tip: Show a quick visual of the TOK essay structure (introduction, body claims, conclusion), highlighting where this developed paragraph fits in.
Main Activity
Examining a Strong TOK Essay Claim
Break down an example paragraph of your choice with students. Ask them to annotate:
- Claim: The stance or argument addressing the TOK prompt.
- Example: A real-world situation supporting or illustrating the claim.
- Counterclaim: A contrasting perspective that challenges the claim.
- TOK Links: Explicit connection to TOK concepts and reflection on how knowledge is produced or validated.
Discussion Questions:
- How does the example strengthen the claim?
- Which Ways of Knowing (WOKs) or Areas of Knowledge (AOKs) are relevant here?
- Does the counterclaim effectively challenge the claim, encouraging deeper exploration?
Writing Task: Drafting a TOK Paragraph
Select a prompt: Provide students with a list of essay prompts to choose from. These could be prompts that you have prepared (e.g., “To what extent does certainty of mathematical models influence truth in society?”) or a prescribed title from the official IB list.
Students plan the paragraph, including notes on:
- Claim: A statement connecting directly to the prompt.
- Example: A real-life scenario that demonstrates the claim.
- Counterclaim: An alternative viewpoint or critique that challenges the initial argument.
- TOK Link: Reference how the TOK concepts influence what is considered reliable scientific knowledge.
Write the paragraph: Emphasise clarity, coherence, and the TOK focus (not just describing the event but analysing how it affects knowledge).
Teacher Tip: Remind students to refer to the AOK and avoid simply praising or criticizing — instead, focus on how knowledge is formed, judged, and communicated.
Peer Review & Refinement
Students exchange their writing in pairs or small groups, and use the essay checklist to give feedback. Use the following discussion points to help students’ develop their feedback:
- Claim: Is it clearly stated, and does it tie back to the prompt?
- Example: Is it concrete, relevant, and well-explained?
- Counterclaim: Is it meaningfully different or just a weaker version of the claim?
- TOK Link: Does it show awareness of how knowledge is justified, constructed, or challenged?
- Language and Clarity: Are there any vague statements or unclear references?
If time permits, students revise immediately based on peer feedback.
Reflection Activity
Discuss the following reflection questions in open discussion or exit ticket format:
- What was the most challenging part of writing this?
- How do different perspectives influence debates on mathematical models?
- How does this practice help prepare for the TOK essay assessment?
Extension or Homework Activity
Extension / Homework
- Option A: Expand the paragraph by adding another real-world example or a deeper analysis of the counterclaim.
- Option B: Research a different context (another region or era) to see if the claim holds universally or changes with cultural/political conditions.
- Option C: Draft an introductory or concluding paragraph linking the argument to a broader TOK theme.
