{"id":2492,"date":"2026-01-21T09:54:47","date_gmt":"2026-01-21T09:54:47","guid":{"rendered":"https:\/\/resources.kialo-edu.com\/?post_type=docs&#038;p=2492"},"modified":"2026-01-21T09:54:51","modified_gmt":"2026-01-21T09:54:51","password":"","slug":"certainty-in-mathematics-lesson-4","status":"publish","type":"docs","link":"https:\/\/resources.kialo-edu.com\/en\/docs\/certainty-in-mathematics-lesson-4\/","title":{"rendered":"Certainty in Mathematics, Lesson 4"},"content":{"rendered":"<h2 class=\"wp-block-heading\" id=\"block-6e802e7d-7c4e-4f99-b41e-a4ef37f4252c\">Lesson 4: Writing a TOK Essay<\/h2><p id=\"block-8fe6ce35-0778-450a-88b8-2643dda463a0\"><strong>Focus: <\/strong><em>How can knowledge users develop strong, structured arguments?<\/em><\/p><p id=\"block-3f778713-12d5-4d8d-9bde-ac25005c77ee\">Suggested Length: 1 hour<\/p><p id=\"block-28b95357-4496-445d-ab77-2a82dd1c4323\">Learning Objectives:<\/p><ul id=\"block-62729a0c-dcd1-49a0-8f49-ba87f1485895\" class=\"wp-block-list\">\n<li>Write a fully developed TOK essay claim using the TOK essay structure.<\/li>\n\n\n\n<li>Apply real-world examples and counterclaims to support arguments.<\/li>\n\n\n\n<li>Engage critically with TOK concepts (e.g., certainty, power, and perspective).<\/li>\n<\/ul><figure class=\"wp-block-table align-top\"><table class=\"has-background has-fixed-layout\" style=\"background-color:#e9f1f9\"><thead><tr><th>Critical Thinking Concepts<\/th><th>TOK Concepts<\/th><th>Reflection Questions<\/th><\/tr><\/thead><tbody><tr><td><strong>Bias &amp; Power<\/strong>: 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.<br><br><strong>Exploring Contexts and Expert Opinions<\/strong>: Reflect on how institutional authority influences perceptions of credibility.<br><br><strong>Extrapolation and Reapplication of Principles<\/strong>: Connect issues of algorithmic bias to broader debates about democracy, social justice, and public trust in institutions.<\/td><td><strong>Certainty: <\/strong>What responsibilities do mathematicians, corporations, and governments have when presenting models as objective or certain? <br><br><strong>Power:<\/strong> Who ultimately decides which models are legitimate, trustworthy, or acceptable to use in education, justice, or politics?<br><br><strong>Perspective: <\/strong>Can mathematical applications ever be universally &ldquo;fair,&rdquo; or are they always influenced by context and values?<\/td><td>What was the most challenging part of writing this?<br><br>How do different perspectives influence debates on mathematical models?<br><br>How does this practice help prepare for the TOK essay assessment?<\/td><\/tr><\/tbody><\/table><\/figure><style>#sp-ea-2505 .spcollapsing { height: 0; overflow: hidden; transition-property: height;transition-duration: 300ms;}#sp-ea-2505.sp-easy-accordion>.sp-ea-single {margin-bottom: 10px; border: 1px solid #e2e2e2; }#sp-ea-2505.sp-easy-accordion>.sp-ea-single>.ea-header a {color: #444;}#sp-ea-2505.sp-easy-accordion>.sp-ea-single>.sp-collapse>.ea-body {background: #fff; color: #444;}#sp-ea-2505.sp-easy-accordion>.sp-ea-single {background: #eee;}#sp-ea-2505.sp-easy-accordion>.sp-ea-single>.ea-header a .ea-expand-icon { float: left; color: #444;font-size: 16px;}<\/style><div id=\"sp_easy_accordion-1766324068\"><div id=\"sp-ea-2505\" class=\"sp-ea-one sp-easy-accordion\" data-ea-active=\"ea-click\" data-ea-mode=\"vertical\" data-preloader=\"\" data-scroll-active-item=\"\" data-offset-to-scroll=\"0\"><div class=\"ea-card sp-ea-single\"><h3 class=\"ea-header\"><a class=\"collapsed\" id=\"ea-header-25050\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse25050\" aria-controls=\"collapse25050\" href=\"#\" aria-expanded=\"false\" tabindex=\"0\"><i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Resources and Preparation<\/a><\/h3><div class=\"sp-collapse spcollapse spcollapse\" id=\"collapse25050\" role=\"region\" aria-labelledby=\"ea-header-25050\"> <div class=\"ea-body\"><ol><li>Slides, attached below.<\/li><li>TOK Essay Checklist, attached below.<\/li><li>Students will need to create their own Kialo discussion to plan their essay paragraph. Instructions for this can be found in the slides.<\/li><li>You may find it useful to have additional TOK essay prompts to supplement the examples in the slides.<\/li><\/ol><\/div><\/div><\/div><div class=\"ea-card sp-ea-single\"><h3 class=\"ea-header\"><a class=\"collapsed\" id=\"ea-header-25051\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse25051\" aria-controls=\"collapse25051\" href=\"#\" aria-expanded=\"false\" tabindex=\"0\"><i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Introduction<\/a><\/h3><div class=\"sp-collapse spcollapse spcollapse\" id=\"collapse25051\" role=\"region\" aria-labelledby=\"ea-header-25051\"> <div class=\"ea-body\"><p><b>Guiding Question:<\/b> <i>&ldquo;How do we develop a strong argument in a TOK essay?\"<\/i><\/p><p><b>Recap: <\/b>What makes a TOK essay unique?<\/p><ul><li>Focus on knowledge (not merely opinions).<\/li><li>Use real-world examples drawn from multiple Areas of Knowledge (AOKs).<\/li><li>Include counterclaims.<\/li><li>Refer to TOK concepts.<\/li><li>Reflect on the implications and limitations of your argument.<\/li><\/ul><p><strong>Teacher Tip:<\/strong> Show a quick visual of the TOK essay structure (introduction, body claims, conclusion), highlighting where this developed paragraph fits in.<\/p><\/div><\/div><\/div><div class=\"ea-card sp-ea-single\"><h3 class=\"ea-header\"><a class=\"collapsed\" id=\"ea-header-25052\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse25052\" aria-controls=\"collapse25052\" href=\"#\" aria-expanded=\"false\" tabindex=\"0\"><i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Main Activity<\/a><\/h3><div class=\"sp-collapse spcollapse spcollapse\" id=\"collapse25052\" role=\"region\" aria-labelledby=\"ea-header-25052\"> <div class=\"ea-body\"><p><b>Examining a Strong TOK Essay Claim<\/b><\/p><p>Break down an example paragraph of your choice with students. Ask them to annotate:<\/p><ul><li>Claim: The stance or argument addressing the TOK prompt.<\/li><li>Example:&nbsp; A real-world situation supporting or illustrating the claim.<\/li><li>Counterclaim: A contrasting perspective that challenges the claim.<\/li><li>TOK Links: Explicit connection to TOK concepts and reflection on how knowledge is produced or validated.<\/li><\/ul><p>Discussion Questions:<\/p><ul><li>How does the example strengthen the claim?<\/li><li>Which Ways of Knowing (WOKs) or Areas of Knowledge (AOKs) are relevant here?<\/li><li>Does the counterclaim effectively challenge the claim, encouraging deeper exploration?<\/li><\/ul><p><b>Writing Task: Drafting a TOK Paragraph<\/b><\/p><p>Select a prompt: Provide students with a list of essay prompts to choose from. These could be prompts that you have prepared (e.g., &ldquo;To what extent does certainty of mathematical models influence truth in society?&rdquo;) or a prescribed title from the official IB list.<\/p><p>Students plan the paragraph, including notes on:<\/p><ul><li>Claim: A statement connecting directly to the prompt.<\/li><li>Example: A real-life scenario that demonstrates the claim.<\/li><li>Counterclaim: An alternative viewpoint or critique that challenges the initial argument.<\/li><li>TOK Link: Reference how the TOK concepts influence what is considered reliable scientific knowledge.<\/li><\/ul><p><strong>Write the paragraph<\/strong>: Emphasise clarity, coherence, and the TOK focus (not just describing the event but analysing how it affects knowledge).<\/p><p><strong>Teacher Tip:<\/strong> Remind students to refer to the AOK and avoid simply praising or criticizing &mdash; instead, focus on how knowledge is formed, judged, and communicated.<\/p><p><b>Peer Review &amp; Refinement<\/b><\/p><p>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&rsquo; develop their feedback:<\/p><ul><li>Claim: Is it clearly stated, and does it tie back to the prompt?<\/li><li>Example: Is it concrete, relevant, and well-explained?<\/li><li>Counterclaim: Is it meaningfully different or just a weaker version of the claim?<\/li><li>TOK Link: Does it show awareness of how knowledge is justified, constructed, or challenged?<\/li><li>Language and Clarity: Are there any vague statements or unclear references?<\/li><\/ul><p>If time permits, students revise immediately based on peer feedback.<\/p><\/div><\/div><\/div><div class=\"ea-card sp-ea-single\"><h3 class=\"ea-header\"><a class=\"collapsed\" id=\"ea-header-25053\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse25053\" aria-controls=\"collapse25053\" href=\"#\" aria-expanded=\"false\" tabindex=\"0\"><i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Reflection Activity<\/a><\/h3><div class=\"sp-collapse spcollapse spcollapse\" id=\"collapse25053\" role=\"region\" aria-labelledby=\"ea-header-25053\"> <div class=\"ea-body\"><p>Discuss the following reflection questions in open discussion or exit ticket format:<\/p><ul><li>What was the most challenging part of writing this?<\/li><li>How do different perspectives influence debates on mathematical models?<\/li><li>How does this practice help prepare for the TOK essay assessment?<\/li><\/ul><\/div><\/div><\/div><div class=\"ea-card sp-ea-single\"><h3 class=\"ea-header\"><a class=\"collapsed\" id=\"ea-header-25054\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse25054\" aria-controls=\"collapse25054\" href=\"#\" aria-expanded=\"false\" tabindex=\"0\"><i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Extension or Homework Activity<\/a><\/h3><div class=\"sp-collapse spcollapse spcollapse\" id=\"collapse25054\" role=\"region\" aria-labelledby=\"ea-header-25054\"> <div class=\"ea-body\"><p>Extension \/ Homework<\/p><ul><li>Option A: Expand the paragraph by adding another real-world example or a deeper analysis of the counterclaim.<\/li><li>Option B: Research a different context (another region or era) to see if the claim holds universally or changes with cultural\/political conditions.<\/li><li>Option C: Draft an introductory or concluding paragraph linking the argument to a broader TOK theme.<\/li><\/ul><\/div><\/div><\/div><\/div><\/div><figure class=\"wp-block-embedpress-embedpress aligncenter\" data-source-id=\"source-cbb0b11d-ae68-457c-a19a-dbead5867dfe\" data-embed-type=\"GoogleDocs\"><div class=\"gutenberg-block-wraper  \"><div class=\"position-right-wraper ep-embed-content-wraper   \" style=\"position:relative;display:inline-block\"><div class=\"ose-google-docs ose-uid-71ace6de15a9317f061779c7321f8c9d ose-embedpress-responsive\" style=\"width:600px; 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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 [&hellip;]<\/p>\n","protected":false},"author":52,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"_acf_changed":false,"wds_primary_doc_category":0,"wds_primary_doc_tag":0,"footnotes":""},"doc_category":[42],"doc_tag":[],"class_list":["post-2492","docs","type-docs","status-publish","hentry","doc_category-maths-dp"],"acf":[],"year_month":"2026-05","word_count":365,"total_views":"2","reactions":{"happy":"0","normal":"0","sad":"0"},"author_info":{"name":"stephanie","author_nicename":"stephanie","author_url":"https:\/\/resources.kialo-edu.com\/en\/author\/stephanie\/"},"doc_category_info":[{"term_name":"Mathematics","term_url":"https:\/\/resources.kialo-edu.com\/en\/docs-category\/maths-dp\/"}],"doc_tag_info":[],"knowledge_base_info":[],"knowledge_base_slug":[],"_links":{"self":[{"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/docs\/2492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/users\/52"}],"replies":[{"embeddable":true,"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/comments?post=2492"}],"version-history":[{"count":0,"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/docs\/2492\/revisions"}],"wp:attachment":[{"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/media?parent=2492"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/doc_category?post=2492"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/resources.kialo-edu.com\/en\/wp-json\/wp\/v2\/doc_tag?post=2492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}