Page 1 UWCSEA East Campus TOK Teacher Support Click the topic to hyperlink to the relevant page Overview of course structure ......................................................................................................................... 2 Course Narrative ............................................................................................................................................ 2 Course Timeline ............................................................................................................................................. 3 Introduction .................................................................................................................................................... 6 Natural Sciences ............................................................................................................................................. 8 The Arts ........................................................................................................................................................ 12 Mathematics ................................................................................................................................................. 16 Reason .......................................................................................................................................................... 20 Emotion ........................................................................................................................................................ 24 Ethics ............................................................................................................................................................ 28 Practice Essays ............................................................................................................................................. 32 Human Sciences ........................................................................................................................................... 34 History .......................................................................................................................................................... 37 Presentations................................................................................................................................................. 42 Perception ..................................................................................................................................................... 43 Paradigms and Culture ................................................................................................................................. 44 Language ...................................................................................................................................................... 48 Assessed Essays ........................................................................................................................................... 51 NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 1 Page 2 Overview of course structure and a possible set of unit and lesson plans References are to Alchin, N. (2004) Theory of Knowledge Student and Teacher Books, Hodder Murray Please can we stick reasonably closely to the following structure, but not slavishly. If your sessions on, say, Natural Sciences, are going well and you want to spend an extra few lessons then do so - you will need to cut something else somewhere to compensate, but I'd rather you went with the interests of the class than cut short interesting lessons. Please do not deviate too far however, as we should all touch on each topic for at least a few lessons. Please also treat the plans with appropriate skepticism. They are meant to be neither prescriptive nor a model for the 'correct' lessons; please do look through the Teacher Book and anywhere else for different ideas and of course do your own thing! Please - make the lessons your own; and share things that work! As ever, I live in the hope of constructive criticism. Failing that, overt flattery is preferable to personal insults. Please note that some of these lesson plans require significant preparation – for example, printing a sheet, cutting into bits for class activity (eg Introductory Unit, Lesson 2). If you do this in time to laminate the paper, and take care in class to keep the bits in separate envelopes (I tend to print different sets on different coloured paper to avoid confusion) you can save a great deal of time for future years. Course Narrative Introduction; what are we trying to do? Why is knowledge problematic? What are areas of knowledge and ways of knowing? What is the point of TOK? Expectations, journals etc. If TOK is about justified true beliefs and a search for certainty, then Natural Science is the current triumphant model for knowledge, with its great successes and basis in observation and experiment. Explore this. But despite scientific successes something is missing... as students will tell us, science isn't everything (explaining it doesn't explain it away; mention experience..); religion; morality; aesthetics etc and so we can consider Art as not amenable to scientific method - perhaps a more 'human endeavour' - but at the cost of loss of objectivity and 'certainty'. So why do we have different opinions about Art? Are there 'truths' there to be found? What is artistic (c.f. scientific) truth? Back to our search for certainty... if art cannot help us be certain, how about 1+1=2 and Maths as the most certain discipline? Discuss Maths as an axiomatic deductive system, see how it can be both compelling and maybe even beautiful. Of course contrast mathematical 'truth' with the other types already seen, and then ask if we can broaden the mathematical method to embrace other areas? Lead into Rationalism as the general system of logical deduction. Stress this is the first Way of Knowing and deal with inductive logic, deductive logic, axioms, hidden assumptions, fallacies, lateral thinking etc. Of course 'reasoning' leads us to consider it's own limitations, and we can immediately see that as a model for human behaviour, rationalism is seriously flawed (and even if not, how did we choose our axioms?) hence …Emotions.. what are they? Are they really as opposed to reason? How are they related to intuition? Are emotions innate or culturally related and what does either view mean for knowledge? At this point we will have a special day for religion, which we can treat as a case study in reason and NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 2 Page 3 emotion – these may not be enough, but the interplay between them and their strength and weaknesses should become apparent. We should be able to get in some outside speakers to look at the issues from several perspectives. We follow up with Ethics as a further case study in the roles of reason and emotion, and a natural step from religion and faith. Strengths and weaknesses of various ethical systems; case studies as appropriate. Then, thinking about ethics will almost certainly throw up some areas which are amenable to scientific analysis but is a scientific approach possible with humans? And so we consider the Social Sciences. Aren't we all unique and unpredictable? What are the problems? Cover the general issues and if time use these to motivate a discussion of the classic problems of free will and nature/nurture. Issues here lead to another way of understanding human behaviour – via history - in fact, is it a social science? Why does it have a different place in the TOK diagram? What are the problems of history? Stress the issue of selection and interpretation and use this as motivation to introduce empirical knowledge – i.e. sense perception - as an areas worthy of detailed scrutiny. We can consider the (perhaps artificially) distinct issues of both practical and philosophical problems, and the provisional and interpretative nature of sensory knowledge can leads us straight to Paradigms and Culture as the paradigm par excellence. This will review so many areas and also be very closely related to the students' own experience, and we will have a day to look at the central role of this in relation to UWC values. Paradigms which will have many components, and in particular, Language as a possible influence of what we know and how we know it. There are some 'obvious' and important points here - language and values; misleading language, language and thought - and also some very difficult ones - language and meaning, language and experience. Bringing it all together at the end; we will have some closing lecture/activity; wrapping it up; what journey have we taken? Where have we come, and more importantly, where are we going now? Course Timeline NB remember you don’t need to stick exactly to this – if the class is more interested in one area than another then spend a little longer on it. We do need to touch on all areas, but please adjust according to your professional judgement. Grade 11 Aug Aug Aug Sept Sept Sept Sept Oct Oct 0 1 2 3 4 5 6 7 8 Introduction 1 or 2 lessons Natural Sciences 5 lessons Arts 1 day (Oct 2) and 1 lesson Half term Oct/Nov Nov Nov Nov Nov 9 10 11 12 13 Maths 3 lessons Reason 4 lessons NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 3 Page 4 Dec Dec 14 15 Christmas Jan Jan Jan Jan Feb 16 17 18 19 20 Feb Feb Mar Mar Mar Mar 21 22 23 24 25 26 Apr Apr Apr/May May 27 28 29 30 May 31 May May June June June 32 33 34 35 36 Grade 12 Aug Aug Aug Sept Sept Sept Sept Oct Oct 0 1 2 3 4 5 6 7 8 Oct/Nov Nov Nov Nov Nov Dec 9 10 11 12 13 14 Emotion 4 Ethics 1 Half term [ Faith, God 1 day (4 Feb) ] Ethics 2 Human Sciences 3 Practice Essays 1 Easter (variable – adjust each year) Exams – no TOK Practice Essays 2 History 3 Practice Presentations Preparation and Performance (also catch-up, and chance to focus on individual class interests as appropriate) NB Project week, Grp 4… very disrupted; plan carefully Summer Review; 12 Angry Men and Perception Day Perception History / Paradigms and Culture 3 Presentation Prep Paradigms and Culture 4 Presentations Half term Language / Presentations 4 NB depending on individual class circumstances, teachers will need to be flexible with Essay Preparation essay/language/presentation 1 day (4 Dec), 3 lessons. lessons. Aim is certainly to Each lessons to have a 30 minutes on language activity finish presentations before Dec 15 before allowing time to work on essays. starting essays, both for workload reasons, but also so NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! 4 that the presentationPage real-life situations can inform the essays. However, some Best to schedule 2 presentations per lesson and fill time left with language points Page 5 Christmas Mock Exams Jan 15 Jan Jan Jan Jan Feb 16 17 18 19 20 Mock Exams Finish Essays Usually spend half lesson on a specific language idea, or essay skill, and half on general help. Closing activity (MAS?) Half term; course closes NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 5 Page 6 Introduction Shall I teach you what knowledge is? When you know a thing, to recognise that you know it; and when you do not know a thing, to recognise that you do not know it. That is knowledge. Confucius Significant Concept: Student will understand that knowledge claims are problematic, that knowledge comes in different forms and can be justified in different ways, some of which may be better than others. Overview Lesson 1: Lesson 2: Lesson 3: Knowledge Claims, Justifications How can we categorise knowledge? What is Knowledge? Introduction Lesson 1: Learning Outcomes Students will understand what a knowledge claim is, and why a claim can be problematic. 1. Introductions, expectations, textbooks, DP points, hand out journals. (10 minutes) 2. Introduction to Knowledge Claims; ask the following questions (take in props as necessary) is this a good bottle of wine? what colour is my shirt? do herbal remedies work? is (current political issue) justified? what do angles in a triangle sum to? is this map of the world correct? do love songs tell you something about love? what does a banana taste like? if I want to be a good person should I do what it says in the Koran? Or the Bible? Stress that answers to these everyday questions are called Knowledge claims; in groups as students to problematise them and show they are complex; ask students to justify their answers (in preparation for task 3 here) and as a class generate a list of various forms of justification – and suggest that perhaps some justifications are better than others. (20 minutes) 3. Introductions to justification. So we have seen there are many perspectives. How do we know which ones to choose? Discuss (5 minutes) and show The Value of a Balanced Argument (Introductory Video Clips on Portal); discuss the clip and its implications. Could use textbook exercise p10. (20 minutes) Homework Task: In ‘The Value of Balance’ clip, the comedian suggests that some views are very poorly justified. Pick one form of justification you believe to be very strong, and one that you believe are very weak, explaining your reasoning carefully. Use your own examples to support your point of view. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 6 Page 7 Introduction Lesson 2: Learning Outcomes Students will categorise knowledge, and understand that such categorisations can be problematic. 1. Sentences task (sheet on portal). If we are looking at knowledge, then we need to see what types of knowledge there are. Just like biologists who could say ‘plants and animals’ but who in fact make much more precise distinctions, so we TOK students should seek to go beyond simply ‘fact’ vs ‘opinion’. Students should take the list and put the sentences into groups; the aim is to find at least 6 groups of different types of knowledge. Pair work Share with another pair and come to an agreement Feedback and class discussion Presentation of IB TOK diagram, and a critical discussion of its strengths, weaknesses, omissions (introduce AOK, WOK) Homework Task: (10 minutes) (10 minutes) (10 minutes) (20 minutes) Rank your six Diploma subjects according to the quality of knowledge you can learn from them. Justify your ranking carefully. Introduction Lesson 3 : What is Knowledge? Students will understand some of the problems of defining knowledge, and come to a working definition for the course. 1. We have looked at what we know (lesson 1), and how we know it (lesson 2) – but what is knowledge? Ask students for synonyms, and to try and find definitions (think, pair, share). Lead the class to justified true belief (Plato) and address the crucial distinction between belief and knowledge (textbook p 6, 7). 2. Is JTB correct? Try to pick holes (artistic knowledge? Experiential knowledge? Does it have to be true?) but stress that it helps if we can agree on what we are talking about (language issue) Point out that the issue is 'how do we know if the belief is true or justified.....' and the circularity problem. Then TOK is the study of what we believe, the reasons for believing, and whether or not these are likely to be good reasons – give this definition to students. 4. So then look at the TOK diagram (portal introduction) and ask if JTB works (art? ethics?). Discuss the fact that we will come across lots of questions, and critique the diagram (missing bits? Overlapping bits? Could use Good Will Hunting clip from portal (introductory page video clips) to stress experiential knowledge) but stress that we need a working model, even if we reject it later on (like science, maths, history…) NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 7 Page 8 Natural Sciences Science is built with facts just as a house is built with bricks, but a collection of facts cannot be called a science any more than a pile of bricks can be called a house. Henri Poincare Significant Concept: Despite significant theoretical and practical problems, the scientific method is an extremely powerful tool which can be used to acquire knowledge in a surprisingly wide range of areas. Overview: Lesson 1, 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 The Scientific Method; strengths and weaknesses The Role of Humans in Science Science and Scepticism Truth in Science The Scope of Science Natural Sciences Lesson 1,2: Learning Outcomes Students will understand the scientific method, and some of the practical and theoretical issues surrounding it. 1. Introduce via the game of chess (textbook pX). If some students don’t know the rules then could get a set and watch two students playing, and see if the watchers can deduce the rules. 2. Play the Card Game (pack of card required) as described on pX of teacher book. 3. Get the class to draw a flow chat – see pX teacher book or this one below. Falsified theory discarded Observation Hypothesis /theory Prediction Experiment Theory / hypothesis confirmed and tentatively accepted 4. Discuss the issues that can arise at each point- see teachers book pX. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 8 Page 9 Homework Task: Describe the scientific method, evaluating carefully its strengths and weaknesses as a tool to arrive at knowledge. Refer to specific examples from your experience doing science at school. Natural Sciences Lesson 3: Learning Outcomes Students will understand the role of humans in science, and the implications of this. 1 So far we have looked at an 'objective' model of science. Show Friends : The One where Heckle dies (portal – science video clips)What is it reasonable to believe? Students in small groups to discuss: • What is Pheobe's point about Science? Are her beliefs reasonable? • What is Ross's point? Are his beliefs reasonable? 2 3 4 So what is the role for humans in science? How is science a human endeavor? Read p20 – 23, discuss questions on p23. Discuss some scientific controversies. Steer kids away from the fact that science is totally a social endeavor; the experimental methods keeps us ‘close to the truth’ in some sense. Homework Task: After watching the Friends clip, describe and evaluate the positions taken by Ross and Phoebe about the role of certainty in science. Natural Sciences Lesson 4: Learning Outcomes Students will understand the various notions of truth within science. 1 Show students the diagram ‘Six Scientific Graphs’ - on portal Science page. 2 Ask students to decide which best represents scientific knowledge (k) against time (t) and to justify their choice with reference to what we have already seen in TOK. Ask also for other graphs. 3 Move on by mentioning something about 'science and truth'. Ask students about physics : F=ma. Or about electrons and protons as 'hard balls' within atoms. These things are 'wrong'. How come? Why do we still use it? Discuss then use 'Right', 'Wrong' and Scientific 'Truth'. P25 - 26 to get at a more sophisticated notion of 'truth' than previously encountered (maybe mention the concept of 'truth' as a problem of language). Ask students to summarise the key points of the essay. Suggest that science is forever increasing the scope of its application; perhaps science will begin to find the answers to areas which currently seem like metaphysics. Discuss the model of science increasing its domain continuously, until perhaps it encompasses everything? Mention limits of human cognition (rats will never understand differential equations....) NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 9 Page 10 Natural Sciences Lesson 5: Learning Outcomes Students will understand the claims that science, while not perfect, gives us a way to cut through the human tendency to self deception, and to maintain a skeptical approach. 1. Watch ‘Scepticism’ (on portal, science video clips). Discuss the main points of the talk, and link back to (a) the scientific method (b) the clip from Friends. 2. Offer to students some beliefs that we have that we do or do not hold up to skeptical enquiry (cultural beliefs? Religious beliefs? Ethical beliefs? Emotional beliefs about family, friends?), and ask them to explain (a) why we do not approach all beliefs skeptically (b) if we should approach all beliefs skeptically. Natural Sciences Lesson 6: Learning Outcomes Students will understand the arguments for and against the position that science will, eventually, give us all types of knowledge – it is , in some sense, ‘supreme’. 1. Review the progress attainable by the scientific method, and the graphs task done earlier. Then ask students ‘Will the scope of science increase inexorably, and one day encompass all other fields of knowledge? If not, which fields are independent and why?’ 2. Watch ‘Face Value’ (under Art in Portal) (00.00 - 14.26 and 19.33 – 24.23) and discuss the strengths and weaknesses of the sciences in relation to beauty. Begin to get at the idea that art may be about more than beauty – what could science do with regard to plays, or books? 3. Watch ‘Beauty and Science Commercial’; what does this transformation tell us about art/science (at the very least, that our reactions to certain images is predictable and uniform?); a broader discussion about beauty and commercial pressure and female body image may emerge. Homework Task: Read Articles p 46 – 49. What can Science tell us about the arts? Is there anything it can never tell us? Do not just state, but justify your answer carefully. For extension, able students can read http://moreintelligentlife.com/story/the-science-of-humour ALTERNATIVE Natural Sciences Lesson 6: Learning Outcomes Students will understand the arguments for and against the position that science will, eventually, give us all types of knowledge – it is , in some sense, ‘supreme’. 1. Review the progress attainable by the scientific method, and the graphs task done earlier. Then ask students ‘Will the scope of science increase inexorably, and one day encompass all other fields of knowledge? If not, which fields are independent and why?’ NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 10 Page 11 2. In fours; two to read ‘Biology of Beauty’; two to read ‘What the Whole World Likes Best’; then to discuss in pairs and present to each other. Try to identify the main issues; and then to consider if science can tell us anything about art/emotion. Ensure students address the difference between ‘cannot currently tell us’ vs ‘can never in principle tell us’. 4. Watch ‘Beauty and Science Commercial’; what does this transformation tell us about art/science (at the very least, that our reactions to certain images is predictable and uniform?); a broader discussion about beauty and commercial pressure and female body image may emerge. Homework Task: Considering the nature of the scientific method, and astonishing advances in the past, is there anything which is in principle beyond the scope of scientific inquiry? You might consider the TOK syllabus (arts, reason, language, ethics, maths, emotion, perception, history… as well as other sources of knowledge). Do not just state, but justify your answer carefully. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 11 Page 12 The Arts Poetry begins in delight and ends in wisdom Robert Frost Significant Concept: The Arts provide us with and allow us to express certain aspects of knowledge (meaning and values) in way that sometimes transcends language. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Nu couche – introductory task What is art about? Is it all subjective? (slides 1 – 16) Qualities of Art 17 - relate to language Art, Transformation, Truth (Proust, American beauty) Beauty Parade The Arts Lesson 1: Learning Outcomes Students will engage with the process of creating art, and consider the qualities that make art valuable. Task: Print & laminate Picasso’s nu couche (on portal Arts page) on A3 paper – make copies for 1 between 2 or 3. Cut the copies into shapes (see NSA to see how) and place each set in separate envelope. Give each pair/trio of pupils a set, a sheet of A3, coloured pencils. Tell them to create a picture that they believe has artistic merit (use blu-tack to stick shapes so it is recyclable – it takes a while to prepare so re-use with other classes and other years). When done, each group explains what they created and what they were trying to do. Teacher draws out significant points (representative, structure, form, balance, colour, impact etc). Teacher sneaks in a picture very similar to nu couche saying it’s from another class. Voting: each person has 10 votes and can distribute these between pictures, or give all to one. Remind them that they are voting for the picture with most artistic merit – not just the one they like best (this is an important distinction) In my experience, nu couche usually wins. You can then show them where the shapes have come from – the coloured version of Picasso’s nu couche. The discussion which follows should ask questions such as: What makes a picture a ‘work of art’? Was there such a good consensus of opinion agreeing what was good and what was not? Was it just opinion or was there some more concrete reason to rate some pictures better than others? Read Textbook p37 - 39. Is Art all about subjective opinion, or can there be some more objective truths in the arts? NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 12 Page 13 The Arts Lesson 2: Learning Outcomes Students will consider the vocabulary of art, and the idea of artistic competence (comparison with science) 1. Re-cap last lesson; contrast with science – art appears to be about creation, science about discovery. Reminder about scientific vocabulary – logic, evidence, falsification etc. 2. Show Jill Greenberg’s picture (‘Child Abuse or Art?’ – on portal). Go through first set in silence, with a couple of seconds on each picture. Then again, and ask students to write down what they think is the appropriate vocabulary with which to discuss this ‘art’. Think-pair-share and establish again the fact that art is about more than just beauty – it has possible moral, political, human significance (contrast with science). Go through again with the second set. 3. Go through ‘The Art Lecture’ slides 1 – 17 9portal, arts page) and stress competence and the comparison with science (of course, leaving this all open to question by the students!). Task: Re-visit the last task; write a further response in light of what has been covered this lesson. You are free to re-enforce your previous view, or to repudiate it. The Arts Lesson 3: Learning Outcomes Students will consider the qualities that great art should have, and consider problems of definition and family resemblance. 1 2 Re-cap the last lesson – what might constitute artistic competence? What qualities might the ‘expert’ look for? Go through the rest of the Art Lecture (portal art page – slide 17 onwards) , presenting each possibility as capturing a facet of the nature of art – but each one has problems (often presented by modern art); present this as a problematic sequence, stopping frequently for discussion. Read and discuss textbook p33 top The Arts Lesson 4: Learning Outcomes Students will explore the idea of art as transforming experience. 1 Re-visit the idea from lesson 3; discuss the quote “Once you have read Tolstoy and Turgenev, you will simply love differently..” Robert Dessaix Clip from American Beauty or Modern Art (TOK portal – Art video clips). Ask if it is possible to see a plastic bag or a urinal differently? Perhaps A doesn’t just inform us; it also allows us to reinterpret our own experience and thererby it enriches our interactions with the world. Show and discuss Guernica - The Power of Art (show 0 – 2.30, and then 48.25 -50.00) Read p40 – 44 and discuss. Homework Task: See attached sheet and rubric below. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 13 Page 14 TASK: Find a picture/book/film etc that you believe has great artistic merit. It may be one that has profoundly changed the way in which you interact with the world, or you may value it for some other reason. Bring some representation in to class and explain why you chose the piece, and ‘the truth’ it communicated. TASK: Find a picture/book/film etc that you believe has great artistic merit. It may be one that has profoundly changed the way in which you interact with the world, or you may value it for some other reason. Bring some representation in to class and explain why you chose the piece, and ‘the truth’ it communicated. Excellent understanding of issues. Example from own experience is used to explore the ideas of artistic value and artistic truth in an analytical manner. Student approach is highly reflective and self-aware in terms of the student’s own experience. Excellent understanding of issues. Example from own experience is used to explore the ideas of artistic value and artistic truth in an analytical manner. Student approach is highly reflective and self-aware in terms of the student’s own experience. 7 6 Very good understanding of issues. Example from own experience is used to address the ideas of artistic value and artistic truth. Student approach is thoughtful and self-aware. 5 Reasonable understanding of issues. Example from own experience is used to discuss the ideas about art in a largely descriptive fashion. Student approach is thoughtful at points. 4 Medicore understanding of issues. Example from own experience is used to discuss the ideas of artistic value and artistic truth in a largely descriptive fashion. Student approach is narrow and remote from own experience. 7 6 Very good understanding of issues. Example from own experience is used to address the ideas of artistic value and artistic truth. Student approach is thoughtful and self-aware. 5 Reasonable understanding of issues. Example from own experience is used to discuss the ideas about art in a largely descriptive fashion. Student approach is thoughtful at points. 4 Medicore understanding of issues. Example from own experience is used to discuss the ideas of artistic value and artistic truth in a largely descriptive fashion. Student approach is narrow and remote from own experience. 3 Poor understanding of issues. The example is clichéd and/or has little relation to students’ own experience. Awareness of ideas of artistic value and artistic truth is minimal. 3 Poor understanding of issues. The example is clichéd and/or has little relation to students’ own experience. Awareness of ideas of artistic value and artistic truth is minimal. 2 No awareness of issues. Student talks generally about art without reference to a specific piece of art or to his or her own experience. 2 No awareness of issues. Student talks generally about art without reference to a specific piece of art or to his or her own experience. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 14 Page 15 The Arts Lesson 5: Learning Outcomes Students will understand what their classmates consider to be great art, and enter into an exploratory discussion about their reasons for valuing the art in this way. Presentations from students. Students awarded marks for (a) personal voice (b) depth of analysis NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 15 Page 16 Mathematics Significant Concept: The mathematical method allows us to generate conclusions with a very high degree of certainty, but that mathematical knowledge is dependent on the axiomatic system chosen. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 What is Maths about? The nature of proof. More on axiom/theorem nature Maths, Real World, Modelling Maths and Beauty Fermat’s Last Theorem Fermat’s Last Theorem Maths Lesson 1: Learning Outcomes Students will understand that mathematics has both subject matter and method. 1. Ask "What is Mathematics?". If students give a list of content then say 'is physics just about atoms? Is English just about letters?" So as well as subject matter, there must be method, and as in science, it is the method that we are interested in. Point out that number, shape and algebra as studied at school form a minute part of mathematics... mention other mathematical objects (vectors, matrices, groups, rings, fields, representations, projections, , ). 2. Take protractors and rulers. Ask to draw a triangle and to measure the angles. Find total. Discuss how we find the 'answer' and reinforce the distinction between inductive and deductive reasoning; point out that experiment evidence is akin to science; and that we need ‘proof’. Discuss three ‘proof's: The class evidence of 180º, 181 º etc (this is inductive science, not deductive maths!) The axiomatic proof (its easy – ask NA if unsure) The ‘physical’ proof from ripping paper. Discuss strengths and weaknesses of each method. Which is more convincing? Does it depend on the person or is none way ‘really’ more convincing? Establish that maths may start inductively, but what distinguishes it (at least initially) is deductive proof from axioms. So what about axioms? Discuss the ’truth’ of ‘180 degrees in a triangle’ vs ‘angles in triangle add up the same as angles on straight line’. Both rest on certain axioms; some of these axioms may be pure convention; others may have ‘better’ status. Task: Using examples from your own eduction, describe the ‘Mathematical Method’? What are the strengths and weaknesses? NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 16 Page 17 Maths Lesson 2: Learning Outcomes Students will understand the axiom/theorem nature of maths. 1 Proof 2, 4, 8 16, 31 exercise… why we need it… evidence. 2 But what is a proof? SHIP to DOCK puzzle on one side of the board. Rules are: A You can change one letter at a time. B Each word created must be in the English Dictionary. e.g. LIKE to MATH goes LIKE LAKE LATE MATE MATH Several solutions should emerge – here are a few SHIP SLIP SLOP SLOT SOOT LOOT LOOK LOCK DOCK SHIP SHOP CHOP COOP COOK COCK DOCK SHIP SLIP SLIT SUIT SPIT SPOT SOOT MOOT LOOT TOOT LOOT LOOK LOCK DOCK SHIP SHIT SUIT SUET DUET DUCT DUCK DOCK SHIP SLIP SLOP PLOP POOP COOP COOK COCK POCK PECK DECK DOCK Put all student solutions on board, and ask which is ‘best’. Possibilities: The shortest, most efficient (solution 3 is almost offensive in it’s ‘wastefulness’) The ‘cleverest’ (I am trying to complete solution 5 with a nautical theme – help!) The one with the ‘nicest’ words (does the ‘shit’ in 3 counter-balance the rather lovely ‘duet’, ‘suet’ and ‘duct’?) The ones with the most unexpected and elegant changes (i.e. a swap from ‘look’ to ‘loot’ is fine, but from ‘shit’ to ‘suit’ has rather more finesse, wouldn’t you say?) So how does this relate to the mathematical method? Ask students what the similarities are: There must be a starting point (axioms or established theorems) There must be fixed and verifiable rules (rules of algebra or logic) There is often an endpoint (theorem) to be established (although sometimes with an apparently open question – e.g. ‘which words can be converted to others?’ there might be a long period of exploration and ‘playing’ before results can even be conjectured. There are many (infinite) ways to complete the chain. Some ways are much better than others, though people may differ about this according to mathematical taste. We can do ‘proofs about the proofs’. The easiest thing would be to ask ‘what is the shortest conceivable number of steps in the proof?’ Note this is what we might call an existence proof – NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 17 Page 18 even if we know the length of the shortest possible chain, we might have no idea how to find it. For example, we can observe that all solutions have, at some point, words with two vowels. Now a little thought should convince you that this must in fact be the case - so you may be surprised to see SHIP, SKIP, SKIS, SKYS, SAYS, SACS, SACK, SOCK, DOCK and this and this raises excellent questions about definition, language and the way maths progresses. There are great discussions here: http://www.cut-the-knot.org/books/natnum/sample.shtml http://www.cut-the-knot.org/books/natnum/discussion.shtml 3 Task: If there is time, following on from the point above, introduce the triangles with 270º (north pole to equator, round a quarter way, and then back to north pole) to get at the idea that we may find cases that don’t fit the axioms – so we may need to amend axioms – so perhaps proofs aren’t 100% certain after all… Read 53 - 58; Find 2 points of similarity and 2 points of difference between the search for truth in Mathematics, and the search for truth in the Sciences. So how similar are the two areas? Maths Lesson 3: Learning Outcomes Students will consider possible links between maths and the ‘real world’, in terms of a platonic approach and a modelling approach. This is possibly a lesson for a maths teacher – do ask for assistance! 1 Show ‘Nature by Numbers’ (portal Maths video page) and discuss e.g phi; that ‘maths appears everywhere’. But note that we never ‘see’ numbers – we just see things. We have never ‘seen’ numbers; they are abstractions from nature. So what in what sense is nature mathematical? Are we imposing numbers on nature? 2 See clip from Pi ‘Patterns in Nature’ and discuss; then the clip on ‘Maths and physics groups’ 12.18 – 16.40 which suggest that maths is ‘out there’. 3 So this is the Platonic debate – but even if we are imposing maths on nature; follow up with the modeling approach - Mathematical Modelling (portal Maths video page ) clip about war. Link to Human Sciences. Task: Read ‘Using Maths to decide who to marry’ (photocopy from Maths portal page). Find and evaluate two reasons why we can use maths in the real world, and two reasons why we cannot. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 18 Page 19 Maths Lesson 4: Learning Outcomes Students will understand that nature of mathematical elegance, and mathematical insight. 1. Stimulus: “Hillbilly Maths” (Maths portal video page) – so maths is about rules and proofs? Yes, but “Beautiful Number Phi” (on portal); discuss the idea (already seen) that mathematicians want to use axioms that are sensible, but also beautiful. Maybe use ‘Mandelbrot 2’ (portal Arts video clips). 2. Activity: Tennis tournament puzzle. A tennis club arranges a knockout tournament in which the winner takes it all. There are 843 participants. Round 1: 843 players, matched so 421 matches Round 2: 421 winners + odd player so 211 matches played So how many matches played before final winner found? 421+211 +…. Better solution: At the end of the tournament all players except the finalist will have lost one match; in each match there is one loser; so the number of matches = the number of players excluding the final winner Beautiful, elegant, eye opener, aha! General, productive, practical, useful. 3. Textbook p59 – 61; discuss and relate to students’ own experiences. Maths Lesson 5, 6: Learning Outcomes Students will understand the community-based nature of maths, and contrast this with the lone individual approach. Also get insight into one of the great achievements of recent years. 1. Use these lessons as a way of re-enforce note taking skills (essential for university, and indeed DP). Task is to end up with significant notes, not about the maths but about what we learn about mathematical knowledge, and the role of reason, insight, revelation, certainty, truth, surprise etc. Students can ask to stop video or rewind to hear a key point again. Notes will be marked for brevity, clarity and relevance to task. This means it will take 2 lessons to show the 50 minute video. 2. Start with the ‘Basic Structure’ presentation slides 1,2 (on portal; see also ‘Notes’ on portal for help if necessary). Don’t show slides 3, 4 yet. 3. Hand out the ‘Sheet for Students watching movie’ and ensure students know what to do. 4. Show FLT video, stopping to stress nature of proof, the use of terms like ‘revelation’ etc. Also, at appropriate point, show Basic Structure slides 1-4, to drive home the logic of the proof (19.22 minutes). 5. Discuss as a class NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 19 Page 20 Reason We should take care not to make the intellect our god; it has of course, powerful muscles, but no personality. It cannot lead; it can only serve. Albert Einstein Significant Concept: As a way knowing that underpins several areas, reason is an immensely powerful tool in the search for knowledge, but one that is limited by issues of fallacies, choice of axiom and language. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Build on Maths; inductive/deductive, truth, validity The problems of reasoning – axioms and fallacies Dan Gilbert – cognitive errors 9 Dots; hidden assumptions Axioms, Arguments: Meaning of Words Axioms, Arguments, Assumptions exercices Reason Lesson 1: Learning Outcomes Students will understand the nature of a reasoned argument, and the inductive/deductive approaches. Also, distinctions between validity and truth. 1 Let us take Mathematics as a model for certainty and try to extend it beyond Maths itself; point out that this is hardly surprising - we use reason all the time; when a stick appears bent in water we use reason to tell us that it is not , and so on . So perhaps reason is a way forward - but notice that we are moving way from Areas of Knowledge to an underlying Way of Knowing. Point out the similarities between rationalism and mathematics - in fact define rationalism as the general mathematical system. 2 Discuss the nature of an argument... use ‘What is an argument?’ (portal Reasoning video clips) to stress the technical definition. Go over IF.......THEN......... and use ‘Intro to truth and validity’ (TOK portal reasoning page) 3 Ask students to make up arguments which are (a) logically valid; true premises. (b) logically invalid; true premises; false conclusion. (c) logically valid; false premises; true conclusion. (d) logically valid with true premises and false conclusion (impossible 3 Discuss ‘induction’ and ‘deduction’ p76, 77. Go over examples from book p80 Homework task: Read quotes p74. Explain what you believe is the role of reasoning in the search for knowledge. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 20 Page 21 Reason Lesson 2: Learning Outcomes Students will understand that axioms cannot be proven, and also some logical fallacies. Recap the previous lesson and the use of syllogisms. Set it up as a great system – we can get to truths! But what are the problems of reasoning? Do a think-pair-share exercise, and in class discussion draw out three important problems of reasoning; 1 Problem 1: Truth of premises/axioms : Which premises to choose? How do we know if they are true? In Mathematics truth simply doesn't apply to the axioms but in 'real world' problems it will. And how can we check them.. either by sense data (we have already seen this is problematic and we will see so again later) or by use of logic... which clearly leads to infinite regress! And this is the fundamental problem with rationalism... Mention Girls are Evil (TOK portal reasoning page) example as valid logic but clear nonsense 2 Problem 2: People make errors that in attempting to apply logic to axioms. We call these fallacies... students to read the list 87-89 and discuss them (we return to this lesson 3) 3 Problem 3: Homework Task: Hidden assumptions (we return to this one lesson 4). From a current real-life situation (newspaper, school, home) find 3 examples of logical fallacies. Describe the fallacy and explain if it matters that it is technically an example of invalid reasoning. Reason Lesson 3: Learning Outcomes Students will understand the cognitive biases that affect humans when they come to make decisions. 1 Discuss homework (ask a few students to present). This should lead to how it is that we cannot rely on reasoning all the time.. so what’s the answer? One answer is to reject reasoning, or looks for another tool. Another answer is to use reasoning better… which leads us to the next activity… 2 Show Dan Gilbert video called (TED) Cognitive Errors (TOK portal videos on reasoning page) it is 24 minutes long (with 10 more minutes of interesting but non-essential questions). Gilbert discusses how we make decision, and some of the errors we make. This is brilliant, and ends with a strong ethical appeal to reason as the best way to enact our Stewardship of the planet. NB Gilbert basis his analysis on some maths – which is not entirely straightforward,. Don’t worry too much about it; the point is that the argues that errors in decision making can be broken down into: Errors in estimating the odds of an event happening Errors in estimating the value of the outcome on an event Homework Task: Describe a time when you made a bad decision because you made one of the errors that Dan Gilbert discussed. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 21 Page 22 Reason Lesson 4: Learning Outcomes Students will understand the way our brains have to make assumptions, the impact this can have on our ability of solve problems, and hence the link between lateral thinking and logic. 1 An application of reason : 9 dots (p50 teachers book) as example; use of reason is difficult. Our brain tells us a story... we need to be careful. Ask for examples from students when they needed to 'think outside the box'. Though reasoning may in theory be straightforward, in real life examples it is very difficult. 2 Now we are aware of the problems, are we any more able to apply good reasoning to problems? Do exercises (student book p82, 83, teacher book p47) and stress how much our brain tells us a story... how much it adds and interprets without us even realising it. We have so many hidden assumptions that applying this is very difficult. Link back to the 9 dots problem - link to paradigms and point out that hidden assumptions are a problem but also a huge advantage - we simply couldn't do without them. 3 If there is time, then ask students to write an exercise similar to those p82, 83 student book (it’s harder than it looks) OR use Lateral Thinking Puzzles (teacher book p53 or do an internet search) in pairs (give A to one and B to another; Y/N answers only) Homework Task: Describe a time where you told yourself a story which seemed plausible, but which actually turned out to be wrong. Identify what assumptions you made that meant you went wrong. Reason Lesson 5: Learning Outcomes Students will understand that reason is dependent on language to define terms, but that language, and the meaning of words, can present problems of their own. Note that this is beginning to reach into Language as a way of knowing. 1. Discuss these and the like : All squares have four sides; this shape is a square… so…. Logically, this shape must have four sides A unmarried adult male is a bachelor; Peter is an unmarried adult male… so…. Logically, Peter must be a bachelor Could these be untrue? Mention that as long as we agree on what the words mean, they must be true; we cannot imagine a world where the premises are true, and the conclusion is not (this is what we mean by a valid argument of course). This seems certain. 2. But then read and discuss the bachelor example (p86 student book), and that the meaning of words is in fact a problem, not a simple matter. Is a bachelor identical to an unmarried male? The NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 22 Page 23 dictionary says so, but perhaps the dictionary is wrong. In fact, our knowledge of things is richer than we can capture in words (this is a profound language point that we return to in DP2). Stress this link between language and logic; that unless we know what the words mean (which is problematic), our deductions lose at least some of their force. 3. Follow up either with some of the exercises (p87 student book) or play the definition game (p110 teacher book). Homework Task: Find and analyse an issue from your own experience/current affairs where the meaning of words presented a problem. Reason Lesson 6: Learning Outcomes Students will learn that applying logic in the real world is possible, though difficult for all the reasons that we have looked at. Here we will try to put it all together to actually use logic in examples taken from the real world. By all means get topical examples from current affairs to replace the exercises suggested in Axioms, Arguments and Assumptions (p84 – 86 student book, answers and comments p47, 48 teacher book) 1. Exercise q1 – 6 is about validity, though the language used presents its own problems. Take great care to stress the different parts of the argument, and once again the difference between truth and validity. Q6 is one that students find difficult to see; it even has a special name ‘affirming the consequent’ and has the logical form of (i) here: (i) AB, B A which is invalid but very close to the valid (ii) (ii) AB, A B (this is the form of example top of p84 student book) To see that (i) is invalid, think of these examples (you could ask students to make up their own examples): If I am normal then I have two arms (AB) If I am normal then I have two arms (AB) I have two arms (B) I am normal (A) I am normal (A). I have two arms (B). 2. Ask students to examine the syllogisms in Exercise q7 – 10; they are all logically valid, but they come up with contradictory conclusions. Ask students how this can be… and they should come up with something along the lines that we can use logic to support our beliefs – we just need to choose our premises carefully in the first place and then reason can ‘do its thing’ and get the conclusion we want. To some extent this undermines reason as a sound way of reaching truth – it really will help us get where we want to go, rather than tell us where we should go. 3. Exercise q11 – 16 all have hidden assumptions, which are not necessarily wrong, but are unstated. Homework Task: To what extent do you think reason is an objective, reliable way of knowing? Do not list the problems, but evaluate their importance for reasoning overall. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 23 Page 24 Emotion The heart has its reasons whereof Reason knows nothing Blaise Pascal Significant Concept: Emotion provides us with a way of knowing that is not separable from reason, and that also offers an affective approach to some areas of knowledge, with all the strengths and weaknesses that entails. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 What are emotions/feelings? Classification Emotions – private? Relationship between reason/emotion Intuition – a ‘feeling’; faces and scientific Emotion and Culture Can Science tell us about Happiness? Emotion Lesson 1: Learning Outcomes Students will understand possible distinctions between emotions, feelings, sensations and consider how to classify emotions. Link to reason: If reason has its problems, and is not wholly objective, it is partly because we, for example, sometimes choose our premises according to how we feel about the conclusion. So perhaps we should examine emotions more carefully. 1. We consider the question What is an emotion, what is a feeling? Examine the list p101 student book and ask the students, in pairs to make some distinctions It’s interesting to make an analogy with studying animals – the first thing we need to do is decide how to categorise them, and what are obvious categories may not be the right ones (dolphins and whales look like fish but aren’t!). Students usually make a distinction between ‘physical feelings’ like hunger and ‘mental emotions’ like love. This distinction seems reasonable, but seems hard to apply in cases like fear or embarrassment. There are clear links to issues of language here, which can be re-enforced. Questions A – F p101 usually generate some excellent discussion and reflection. Homework Task: Read p101 – 104 and draw a Venn diagram with circles showing emotions, feelings, sensations and add in a few examples in each reason. Emotion Lesson 2: Learning Outcomes Students will understand the communal/individual nature of emotions and whether or not we can ever ‘know’ what someone else is feeling. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 24 Page 25 1. One of the strengths of reasoning, despite the issues, was that it was public and open to scrutiny. We can examine each other’s reasoning and try to improve it where necessary. Ask students how this contrasts with emotions; the following points will probably emerge: (a) Emotions are private; we can never know each others emotions (this lesson) (b) We cannot ‘improve’ our emotions – emotions are not better or worse, or in error, like reasoning (lesson 3) (c) We cannot be wrong about our own emotions (lesson 6) We shall examine each of these claims. 2. Emotions are private; we can never know each others emotions (a) Look at Pictures of various people; can you read their emotions? (TOK Portal, Emotions page) and it is quickly apparent that we make consistent judgements cross-culturally. (b) An excellent follow up is to test the class’s ability to read emotions. Eyes and Emotions (TOK Portal, Emotions page) shown 36 images of eyes, and students have to assess the emotions being portrayed. Print the response sheet first, and project the pictures to the students. The lesson needs careful preparation – and you will need to assess students’ language ability first - but is fascinating. The students should get 9 correct answers by chance, but usually get many more than this – even though they are unable to say how. It’s also interesting to see if girls are better than boys at this… they usually are. These cases do not show that we know other’s emotions for sure, but they do indicate that we make consistent assessments a lot of the time. We could barely function as a society if we did not manage to accurately gauge each other’s emotions most of the time. All social interactions, literature, theatre, TV, group interactions pre-suppose that this is the case. Of course, we are fallible, but that the emotions are completely private cannot be the complete story. This is not really too surprising - that our mental lives are reasonably similar, despite some differences, mirrors the way that our bodies are all pretty similar, despite differences (just as well, or we would have no doctors or medicines, as there would be no science of how our bodies worked, as they would all be different). Homework Task: To what extent can we ever know what someone else is feeling? What might make it easier or harder to know what they are feeling? Emotion Lesson 3: Learning Outcomes Students will understand the relationships between reason and emotion and so better understand the nature of emotion. 1 Stimulus: I, Robot clip (TOK Portal, Videos on Emotions page). In this clip Reason and Emotion are set up as opposites; it is argued that reason would (incorrectly) tell one to save the life of an easily-saved adult over a difficult-to-save child, whereas emotion would (correctly) suggest the opposite. Discuss this argument, briefly – noting that we can construct arguments to say exactly the opposite (link to reasoning)! 2 Whatever the merits of the argument, it is traditional to set up reason and emotion as opposites. If they mean anything to the students, show the Spock and Hulk cartoons (TOK Portal, Emotions NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 25 Page 26 Page) which show emotions as irrational, unreasonable. But in fact this is not tenable. 3 Discuss the ideas on p104 – 105; and ask students to read p106, then discuss the questions A, B, C D. Break down the polar opposition between reason and emotion; they are intertwined in a more subtle way; and emotions can only appear as a result of some rational processing. 4 Read p107, and discuss. Further to previous point, not only do emotions appear as a result of some rational processing, emotions are at the root of all that means anything to us. Homework Task: What is the relationship between reason and emotion? Make your points using examples from your own experience. Emotion Lesson 4: Learning Outcomes Students will understand the ‘feeling’ of intuition and its strengths and weaknesses. 1. Intuition - perhaps not really an emotion, but perhaps also not really reason. What is intuition? Discuss the examples student book p108, 109. Also refer to the Eyes and Emotion test where we seemed to read people’s emotions pretty well, even though we couldn’t say how we did. Is this intuition? 2. List p110 shows that we have lots of non-propositional knowledge that we cannot easily articulate (is this intuition?). Discuss the possibility that intuition is ‘just’ subconscious processing; or is this just taking the metaphor of computing too far? Are we ‘just’ computers? 3. Do p111 - 112 exercise A – F (answers, teachers book p60). Our intuition in these physical cases seems very poor, in contrast to social intuition. Does this tell us anything about the differences between emotional/social knowledge and mathematical/scientific knowledge? Homework Task: Under what circumstances, and to what extent, should we rely on our intuition? Emotion Lesson 5: Learning Outcomes Students will re-visit the nature of emotions and understand the possible roles played by culture in shaping our emotional experiences. 1. Remind students about the initial task of categorizing emotions; now ask them to define it. This is difficult. Help out with the model top of page 117 (student book) and the powerpoint What is an emotion? Idea and assignment (TOK Portal, Emotions Page). E O Wilson’s definition may be scientifically accurate, but it like trying to explain the taste of whisky to someone who has never tasted alcohol. 2. The model top of page 117 is more helpful because it separated the rational, cognitive aspect of emotions with their unique ‘tastes’ – which we call qualia (interesting to note that qualia apply not just NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 26 Page 27 to emotions, but to other things too, like colours, smells, tastes). Read p117 and discuss questions p 118. 3. Question F is fascinating and a good one to explore with students from different cultures. Are our emotional lives dependent on our cultures? Asking residential kids to share experiences of living with people from different cultures can be interesting. Homework Task: What is the relationship between knowledge, emotion and judgment? (as on powerpoint shown in this lesson) Emotion Lesson 6: Learning Outcomes Students will understand that the humans sciences can now tell us a great deal about happiness. 1. Ask ‘What can science tell us about happiness?’ The answer may be little – this has traditionally been the province of philosophy and the arts, but there have been recent incursions into the field from psychologists too. This might, therefore, be a good place for a little diversion to review the scope and possibilities of science, before we formally look at the human sciences in DP2. 2. Question: Would winning a million dollars make you a much happier person in the long run? Would losing your legs in an accident make you a much less happy person in the long run? Ask students not just their answers, but how they know. And stress that this is an empirical question – we can find a lot of people who have one a million dollars, or lost their legs, and ask them. So this is within the realm of science. 3. Show What makes up happy? (TOK Portal, Emotions video page) 16 minutes. This is the brilliant Dan Gilbert on the 'hedonic errors' that are hardwired into our cognitive systems, and 'synthesised happiness' is the real thing. Witty, wise and an excellent bridge between the pastoral, academic and existential aspects of the course. Gilbert covers a lot of ground quickly, so it’s worth stopping the video at several points and discussing, and requiring students to take notes. Homework Task: What are the issues involved with knowing what will make us happy. Explain you points using examples from your own experience of things that you thought would make you very happy/sad. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 27 Page 28 Ethics Ethics is a code of values which guide our choices and actions and determine the purpose and course of our lives. Ayn Rand Significant Concept: There are a variety of approaches to knowledge in ethics, none of which are problem-free, but some of which are better than others, and individuals have a responsibility to make informed choices. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Introduction: Principles and sources of ethics The Role of Reason in Ethics I The Role of Reason in Ethics II Reason reappraised; room for emotion? What makes people evil? Ethics and cultural differences; objective or subjective? Ethics Lesson 1: Learning Outcomes Students will understand that there are a range of opinions about the principles which ought to govern ethical decision making, but that we all instinctively look for principles with universal application. 1. Two possible introductions: a. Give out An ethical problem (TOK portal, Ethics Page) and discuss (a possible solution is not particularly helpful). b. Use the Liar! Cards (TOK portal, Ethics Page) and ask students to place the cards on a continuum of ‘Not Wrong’ to ‘Wrong’ Either way, main point is not the answer, but asking students to identify the principles on which they are basing their judgements of what is the ‘right’ thing to do. We find students: a. Have an intuitive (emotional?) response b. Seek to justify our responses via reason Hence, Ethics is a great study of the reason/emotion distinction we have been considering. 2. So where do our principles come from? Discuss culture/parents/religion …. notions of ‘natural justice’, instinct? norms developed to ensure society functions? Or might they be ‘absolute’? Read p126 - 128 Homework Task: On the basis of p126 – 128, and what we have looked elsewhere in the course, do you think our ethical beliefs come from religion/God, reason, emotion, our culture, our families or ourselves? Where do you think our ethical beliefs should come from? NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 28 Page 29 Ethics Lesson 2: Learning Outcomes Students will understand the role of reason in ethics. 1. Case Study: Ask students about Abortion; see diagram p130 student book; also Abortion and Iraq (TOK portal Ethics page) on OHP as a logical syllogism/pyramid case study. Ask; is the logic valid? Are the premises true? (make sure you have read p130 -131 first) Whatever the discussion, the diagram should allow focus and debate rather than simply disagreement. As such, this is a helpful step towards pluralism as it gives a way of engaging with people of difference rather than simply arguing. The diagram this generates a great deal of clarity we can see where we have principles and where we need evidence but how do we justify our axioms? problems of language haven't we oversimplified? Isn't it really much more complex than this? What about rights to life? What about a woman's rights to control her body? and so on… 2. Do and discuss Exercise p129. 3. Students to construct ethical pyramids to argue that torture, or corporal punishment or capital punishment or promiscuity etc is wrong. Ethics Lesson 3: Learning Outcomes Students will further understand the role of reason in ethics. 1. Review the crucial idea that we can rationally debate in ethics. That means that we can examine differences to see if they are differences of principle, or of fact (you can use the examples p127): a. We can collect evidence we should do so b. Where we have principles, we should test them by seeing if these principles lead to unacceptable beliefs, or are inconsistent with other beliefs. Students to make brief notes in book on this distinction. 2. Remind students, from Abortion and Iraq (TOK portal, ethics page), that we sometimes ‘pretend’ to be reasoning when we are actually expressing an instinctive reaction. 3. Case Study: Homosexuality (TOK portal, ethics page). Apply the reasoning in point 1. Conclusion? 4. Propose that the way ethics works for us is that we tend to have a gut feeling about something and then try to justify it. [NB: unexpected link with Maths - spot a fact then identify beautiful/useful axioms for it!] Is this acceptable? Homework Task: What have you learnt about the role of reasoning in ethics? What have you learnt about your own ethical values? NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 29 Page 30 Ethics Lesson 4: Learning Outcomes Students will understand that reason has limits, and there is a need to take a broader view of ethical decisions. 1. Recap that we have seen the crucial importance of reason. Now offer the situation top p140 student book (don’t refer to text book yet) and ask students what factors they would need to consider. Hopefully they will come up with much of the list p140. 2. Discuss with them the fact that many of these factors are really about emotions and relationships; perhaps, therefore, some examination of these, rather than pure logic, would be in order. 3. Read the play p154,155, choosing students who read well to play the parts. What do we learn from these skits? Even thought Chris and Sam are ethically reasonable, they seem to miss the whole point of things. Again, we see that relationships and emotional attachments are a crucial part of ethical decisions. 4. Read p143 – 145 (possible 146 if class so inclined) and discuss the proper role of emotion in ethics. Homework Task: How do we balance the roles of reason and emotion in making ethical decisions? You might remember, from earlier, that the two are not necessarily opposed. Ethics Lesson 5: Learning Outcomes Students will understand that (ethical) behaviour is strongly influenced by group expectations and understand their consequent responsibility as individuals. 1. It is clear from many conflicts all over the world, and in our own personal experiences, that people do not, as a matter of fact, always do the ‘right thing’. Ask students why this is the case. One reason, of course, is that not everyone is educated. 2. Show Does education help us make better ethical decisions? (TOK Portal, Ethics page) and ask if this is right. Does education help? Discussion. Perhaps the point is that some education helps (hopefully, the sort we are giving the students) and some does not (authoritarian, following-rules type education). We will return to this point when we look at paradigms in DP2 3. Show (TED) What makes people evil (TOK Portal, Ethics Video page). In this at times graphic clip, Philip Zimbardo discusses the Milgram experiment, the Stanford Prison experiment and Abu Ghraib prison. He argues that the situation is a huge influence on our judgements and discusses the psychology of going against the crowd to do the right thing. Highly memorable; a vital video for education in the broadest and most important terms. Stop at points and discuss. Homework Task: Describe a time when you or someone you know went along with an ethically dubious decision because the group was doing so. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 30 Page 31 Ethics Lesson 6: Learning Outcomes Students will form their own views on the objectivity/subjectivity of ethical beliefs. Some classes may find these ideas difficult, but they are very important for our mission. 1. It is unlikely that the issue of relativism has been avoided so far. Can we find ways to objectively judge what is right and wrong? This is a fundamental and crucial question, central to personal and political life in the 21st century. Spend a few minutes with interesting cultural examples such as Chinese footbinding, female genital mutilation (circumcision?), slavery, apartheid etc. Can we say these are wrong, coming from a different culture? 2. Read the play p344 – 346, and ask students to summarise the strengths and weaknesses of the two positions. Discuss. Homework Task: What is your stance on ethical relativism? subjective? Are moral values objective or Ethics Lesson 7: Learning Outcomes Students will form their own views on the objectivity/subjectivity of ethical beliefs. 1. Watch ‘Objective Moral Values’ (TOK Portal, Ethics Videos page). This is quite difficult, so stop and discuss. There is an interesting article by Sam Harris, on the main Ethics page, which you might like to read beforehand. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 31 Page 32 Practice Essays Learning Outcome: Students will understand what makes a good essay, and practice writing one. You will need to photocopy resources and prepare carefully here. Best to take in the essays/resources and save them for next time – this saves a great deal of work. See TOK Portal Essay page for all resources. Practice Essays Lesson 1: Learning Outcomes Students will understand what makes a good essay, through an example and the criteria. 1. See the DP 1 Teachers section of the TOK Portal Essay Page. Give out Example essay cut up and require students to order it. Alternatively, simply give out the essay with line numbers and go through some nitty-gritty detail as per commentary; ask students to write a 100 word abstract. 2. Identify what makes good essay: Intro, Conclusion, Transitions and Signposting, Examples. 3. Give out Essay Criteria and explain/discuss in context of the essay. 4. Give out Titles; discuss. Homework Task: Read and ponder titles. Choose a title. Practice Essays Lesson 2: Learning Outcomes Students will consider the titles, and develop a plan for their essay. 1. Remind students that we are not looking for platitudes. Mention the fact that we should be looking for multiple/nuanced views – that is, the answers are not justy ‘Yes’ or ‘No’; show some example from portal (Multiple/nuanced views – TOK Portal Essay page). 2. Get students into groups to discuss possible approaches to the title – the overarching narrative/theme for the essay - and to develop mind maps with the ideas that radiate from this central idea. 3. Give out Essay Planning Sheet. Homework Task: Complete Essay planning sheet. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 32 Page 33 Practice Essays Lesson 3: Learning Outcomes Students will deepen their understanding of the process through peer – marking of the plan 1. Students read and comment on each other’s plans in pairs. It’s important you give some thought as to the pairs here, for maximum benefit to both students. Also important to provide some structure for the activity: a. Recap Intro, Conclusion, Transitions and Signposting, Examples. b. Students swap plans; A reads B’s and vice versa. c. A tells B what he understands the plan to be, and offers 2 good points and 2 points for improvement. Discussion. d. B tells A what he understands the plan to be, and offers 2 good points and 2 points for improvement. Discussion. Practice Essays Lesson 4: Learning Outcomes Students will deepen their understanding of the process through peer – marking of the essay. When students have handed in their essays to you, they should also bring a clean copy to class. You can then have a peer-marking exercise where each student grades the essay according to the criteria. This is more much designed to help the student doing the marking than the one receiving feedback. 1. Each student marks another student’s essay, and offers suggestions. 2. You give each student your comments and grades, so that the marking student can see how close he or she was to your score. 3. Essays and teacher’s comments returned to writers. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 33 Page 34 Human Sciences Significant Concept: Knowledge in the Human Sciences has the scientific method in common with the Natural Sciences, but the ‘human’ element creates some additional issues. Overview: Lesson 1 Lesson 2, 3 Lesson 4 Lesson 5 What are the human sciences? What do they try to do? Data Collection and interpretation Prescription/Description: Beijing Olympics. Nature/Nurture :Can we do science on humans? Human Sciences Lesson 1: Learning Outcomes By considering the extent to which ‘human sciences’ are possible, students will better understand the nature, scope and ambition of the human sciences. 1. Light a candle on top of a cupcake in the middle of the room. Say ‘When the candle goes out, you can eat the cake’ but do not answer further questions. After a while, and several ignored questions, someone will come and blow out the candle and eat the cake. Ask ‘why did the candle go out?’ and write the responses on the board. These might vary from a. There was not enough heat in the flame to support combustion b. The wind on the flame blew it out etc to c. Daniel is a rebel (Daniel being the student who blew it out) d. Daniel loves cakes etc On the board, elicit the crucial distinction between natural (a and b) and human (c and d) sciences. The latter is about how humans are motivated and how they behave, the former is not. 2. Read list p157,158 as an example of claims in the human sciences. Discuss points B – F about the nature of ‘laws’ - what does this word mean here? Is it the same as in the natural sciences, or in legal matters? Can we break the laws of human sciences? 3. If you can pull it off, at this point turn over a piece of paper with Daniel’s name on it that you clearly wrote before the lesson. This is a striking thing that students will remember – it looks like magic but in fact it raises ideas of free will and of human uniqueness. It’s not as hard as it sounds – if you know the class well you can usually get it right. You can certainly predict some students who will not be the ones to blow the candle out. 4. To follow this up, see Fun exercise: Are you predictable? And Using Maths to decide on relationships and marriage (TOK Portal Human Sciences Page). Discuss with students. Homework Task: To what extent can the scientific method be successfully applied to humans? Give specific examples in your answer. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 34 Page 35 Human Sciences Lesson 2, 3: Learning Outcomes Students will understand the problems with collecting data in the human sciences but that these can sometimes be overcome. Scientific explanation is based on data; this must be collected. There are complications in collecting data on humans. 1. We are easily swayed by the words people use, and how they ask questions. Watch Questionnaires clip (TOK Portal, Human Science Videos page; text available in teacher book p66). Is opinion being elicited or created? Questionnaires may tell us as much about the writer’s opinion as they do about public opinion. Writing neutral questions is a good deal harder than it sounds – see student book p160; there are very different answers to the questions – but which question is better? 2. We are prone to being influenced by irrelevant factors, and sometimes even by factors we are not conscious of. Watch Ad Agency and Manipulating people (TOK Portal, Human Science Videos page). What do we learn from these? 3. However, these problems can sometimes be overcome by clever experimental design. Read p 161, 162 and discuss. 4. Of course, science has a whole methodology designed to overcome biases. Ask How do test a drug? Discuss the idea of control groups How do we allow for placebos? Discuss the idea of double blind trials. Now of course we might think that drug testing is natural science – but there is a social science element too; the whole point is that the double blind trials are meant to eliminate the problem of placebo, expectation etc. In a crude sense, good methodology can (at least partially) eliminate the human from human science. Show Esther Dufflo randomised trials to answer soc sci question 14 minute TED talk (Hum Sci video portal page) stopping to discuss at various points. Homework Task: See article Are you subconsciously racist or sexist? (TOK Portal, Human Sciences page) and try a test here - http://implicit.harvard.edu/implicit/ . You have to shoot white/black/male/female - and it seems we are quicker to shoot the other race/gender to ourselves. So this generates data; what does it tell us? Is the methodology good? There is the suggestion that many people are subconsciously racist or sexist. Do you agree? What issues are raised here? Human Sciences Lesson 4: Learning Outcomes Students will understand the positive/normative distinction, and how normative values are often hard to escape. 1. Show the Positive and Normative statements powerpoint (TOK Portal, Human Science page) and ask what distinction is being illustrated (link to TED video in previous lesson should be easy). The economists, at last, should all be able to explain – but make sure everyone gets it. 2. Ask if this distinction appears in Natural Sciences. It does not seem to. But what about Human NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 35 Page 36 Sciences? Consider, for example, the question related to the recent Beijing Olympics - ‘which country did best?’ What sort of question is this? Is this description or prescription? 3. See top table at Beijing Olympics – who did best? (TOK portal, Human Science page). This seems to be positive, not normative, in that it simply presents numbers, but the alternative tables all have a lot going for them too. The common 3-2-1 scheme, which ranks the USA at the top is common, but is it the correct and only valid scheme? Would an Olympic athlete say that 3 bronzes = 1 gold? I doubt it. The other tables are also plausible. A problem of language is raised - what does 'best' mean - does it map to the 'real world' like a positive attribute such as length or does it exist solely in the minds of humans, like normative qualities such as ‘importance’? The moral is that it is often difficult to separate the descriptive and prescriptive elements. So perhaps we can characterise Human Sciences as prescribing as well as describing – unlike natural sciences. 4. Ask students about the IBDP; the way that the 45 points are distributed between HL, SL, TOK, CAS, EE. Is this a normative or a positive measure? Homework Task: Read article on Testing p182 – 184. In light of what you have learnt and read on this topic, what do you think of an educational model which gives a number to students? Human Sciences Lesson 5: Learning Outcomes Students will understand the debate around the extent to which the scientific methods can be used on humans through the context of the nature/nurture debate. 1. Ask students if they like the idea that science will ‘explain’ them. Do they think that this will be popular idea? Would it be good to find that some races are naturally less intelligent than others? This will be the entry to nature/nuture and the political dimension of human sciences. 2. Read student book p172-173. Discuss the points made. 3. Watch (TED) Nature or Nurture? (TOK portal, Human Science videos page), stopping to discuss and explain. Pinker links the human sciences to Arts, Politics and Ethics. Not the most exciting delivery, but broad ranging, incisive and important stuff. Homework Task: Read p175 – 180. No writing required. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 36 Page 37 History Significant Concept: Historical Knowledge is an interpretation made on the basis of available evidence, which may be partial, contradictory or unavailable. Even though there are often differences between historians, there are often agreements over these interpretations. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 What is History? Introduction Problem of facts Problem of interpretation History and Science History Lesson 1: Learning Outcomes Students will understand the distinction between history and historiography, and understand that there are problems of fact and problems of interpretations. We have seen that Human Sciences may want to be descriptive, but are often prescriptive. Touch on problems of language and the built-in values of eg democracy, dictator. Ask students for their own examples. Ask 'Are all descriptions prescriptive,?' 1. Give students ten minutes to write a summary of their week so far. Divide the classes into three and each third is to write for a different audience – but don’t let them know this (ie write this instruction down on paper - don’t say it out loud). some to write to their parents, others to their chosen universities, others for their own diaries Read out a few pieces; use the similarities/differences to draw out the important points (esp. that their description was prescriptive in as much that it implicitly said what should be important and recorded); and ask: What did you leave out? (selection - link to empiricism, paradigms and science) On what basis did you exclude/include details? What makes something important? Note that the writing of the pieces mirrors writing of sources; the reading and interpretation of sources mirrors the work of the Historian. 2 So the point is an obvious one – we write for different audiences. See Why do historians write? (TOK Portal, History Videos page). Make the distinction between history and historiography (history is what happened; historiography is what historians write and believe about what happened) and point out that 'history' can sometimes mean either (problem of language). We are looking at historiography. 3 Handout the History Continuum and ask students to place the first set of statements on the continuum where they think they should go (save the second set if spare time later on) NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 37 Page 38 4 5 Discuss: a. what kinds of statement provided the most certainty? generally those which gave a date, event etc something easy to check - positive statements, in vocab of social sciences b. what is the problem / unsatisfactory with the statements that are most certain? They don’t really give any meaning, just isolated events the building blocks of history – not history itself. The accuracy of such facts is presumed of the historian. c. What kinds of statement give lesser certainty? a. those to do with interpretation e.g. those focusing on why? e.g. those focusing on the consequences of an event, since both involve some kind of judgement to establish meaning from the facts. Ie normative statements in vocab of social sciences b. those for which we have no evidence e.g. ‘William not drinking’ c. those where evidence about the past presents contradictory information e.g. ‘Richard murdered the princes’. d. Which statements are most uncertain? If William drank no alcohol, will probably never be able to find this out! We need evidence (like science) e. How far down the ‘uncertain’ end of the continuum have you put statements like: ‘Nelson Mandela’s moral authority was crucial to the dismantling of apartheid.’ and ‘Tom Mboya’s murder in 1969 was a devastating blow to Kenyan stability at the time.’? Probably not right at the very end, since there are FACTS to back up such views, not totally random interpretation. Overall: History struggles to provide absolute certainty. Mainly because of: a. Problems with the facts themselves b. Problems of interpretation c. But this does not mean History is completely subjective; it is rooted in the facts too. ‘The relation between the historian and his facts is one of equality, of give and take…the historian is engaged on a continuous process of moulding his facts to his interpretation and his interpretation to his facts…History is a continuous process of interaction between the historian and his facts.’ E. H. Carr What is History, 1963 pp. 29-30. History Lesson 2: Learning Outcomes Students will understand that there are issues around the ‘facts’ of history. Refer to the previous lesson which established that one of the difficulties preventing History being able to provide absolute certainty was problems with the facts themselves e.g. contradictory evidence existing about the same event or insufficient evidence. 1 Students in groups to list 8 items in which to put into a time capsule which will be opened by historians in 3008 in order to give them a sense of 2008. Aim to provide useful information. Discussion: listen to objects placed in time capsules and record some on the board. For a few of the capsules generate some conclusions that the historian in 3008 might reach as a result of the objects inside e.g. the technology, entertainments, lifestyle available in 2008 etc. What would they not be able to find out from the evidence in the capsule? e.g. types of food, education system etc. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 38 Page 39 Are there any misleading conclusions that they might draw? e.g. that there was no___ ?; that ___? was particularly important (but actually it was just important to the person that designed the capsule), About what an object might be used for? 2 What problems does this exercise show might face historians in their study of (any) past? the problem of lack of evidence (history is not the study of the past, but of the past which survives) leading to misinterpretations of the past.\ the problem that the author (creator) of the source’s preferences / views will influence the facts presented and this will be misleading, although they are not necessarily deliberately lying (although could be – can they provide an example when this might be?). For example, Medieval Times very religious – probably so, but perhaps we have an exaggerated view of this since the only people that made records were monks! 3 What information do you think the historian finding your time capsule would like you to have recorded on a plaque to help him draw the most useful conclusions from the evidence you have included? What would he like to know about you to stop him drawing too many false conclusions? WHO: useful because if I knew it was from an 11 year old pupil it would help me understand it showed teenage interests but not necessarily those of adults and babies. WHEN: 2008 and not another date (is something written at the time that an event occurred always more useful?) WHERE: Africa, important since might be very different in UK or Australia – different culture, socio-economic situation and climate. WHY: Personal box? School box, box with friends, did you intend it to be discovered? Might this have affected what you put inside it? Overall: any piece of information (source) from the past is useful but it has limitations and can be misleading, so don’t necessarily believe all of it at face value. Therefore by going through an evaluative process like this for the ‘facts’ that the historian uses to construct his account, it is more likely to reach the truth. This exercise focused on selectivity of evidence rather than deliberate distortion, but the historian also needs to be aware of this and can use the same process procedure to evaluate them e.g. photos of Trotsky manipulated by Stalin. Homework Task: Read p190 -194. What are the issues related to determining the facts of history? History Lesson 3: Learning Outcomes Students will understand that even once we have the ‘facts’ of history, there are issues around their interpretation. In addition to the problem of facts to the historian (limited number / too many facts, contradictory, selective in message, deliberately biased), there exists the problem of interpretation. One of the major issues with which history is concerned is the explanation of cause. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 39 Page 40 1. Handout article on Carr’s crash (TOK Portal, History page) 2. Spider diagram on board – What issues arise when we consider historical interpretations? Possible causes are clear drunk driver impaired sense of judgement (Jones MAINLY to blame) brakes defective why were the brakes defective Jones not maintaining, the garage for servicing badly? The blind corner; going too fast; a fault in the road Robinson not looking as he goes out into the road? The person who invited Jones to the party* The person who served Jones drinks at the party* Jones’ girlfriend dumping him so he drunk too much* Robinson’s addiction to smoking and desire for cigarettes* The person who smoked Robinson’s last cigarette leaving him with the need to get more* So the task is to focus on the issues arising not the factors themselves: All things connected We have free-will (?) What seems important to us depends to some extent on us (alcohol); though we would hope we make progress in this respect All interpretations by definition ignore some parts; we cannot collect all data We make many assumptions Perhaps the language of a description is important Are the causes marked* perfectly logical and true?Yes: if Robinson hadn’t been a smoker he would not have been killed. But we might say they are not really causes… how far do you go back, for example, the scenario of: For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail. (can we create a similar example for eg WWII?) As they consider this task, students can refer to textbook p197 -198 Might like to look p204 for a light hearted approach to an historical incident. End of lesson: Discuss the way we spent last lesson on facts; this lesson on interpretation; in fact perhaps we have seen these re not as distinct as we would like. This is a difficult idea; try to link to the class discussion. Homework Task: To what extent can we distinguish between facts and interpretations in History? Or in science? (hard, but good prep for next lesson) NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 40 Page 41 History Lesson 4: Learning Outcomes Students will understand the similarities and differences between history and science. Science and history both share a sense of looking at evidence and coming up with theories. Are they, then, the same? Can the scientific method by applied to History? 1. Students to fill in (a) venn diagram(s) showing the aspects common / unique to the disciplines of History and Science. Depending on your interests, we can do Two circle venn diagram, History and Science Three circle venn diagram, History and Natural Sciences, Human Sciences Of course if might be that some students argue that one circle is totally inside another…. Possible issues might include: History deals with the unique and particular; science with the general and universal. But historians do seek to generalise. History cannot make accurate predictions about the future, history doesn’t repeat itself – partly because the participants are aware of history and consciously try to avoid certain things; science makes accurate predictions about the future. The historian influences his data perhaps more than a scientist influences his data (but even the sciences has some influence over his evidence) i.e. interpretation although present in both is stronger in history. The evidence both use may be incomplete / more discovered later / overwhelmingly large. Do both scientist and historian have a moral responsibility? Both require evidence to substantiate claims In history multiple interpretations are possible and fruitful but in science less so. B Both methodologies involve observation and interpretation. 2. Students to read page 205 – 207, and to add/amend their venn diagrams in light of this. 3. Interesting to note that in some traditions (eg continental European), History is a Human Science. It is not in the British tradition because in history experimentation by controlling variables is not possible. This is both interesting in its own right, mirroring the interpretation aspect of history, but also critiquing the TOK diagram (TOK Portal, Introductory page) is a good activity. The issue of oral histories can be addressed here too. Africa has an oral rather than written tradition. To what extent does this make a difference? NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 41 Page 42 Presentations Objective: Students will plan and perform good presentations. Students should come to class for all these lessons; it is important that we spend time assisting students. Students should not simply be sent to work in the library. These lessons can be spread over a few weeks. Practice Presentations Lesson 1: Learning Outcomes Students will understand what makes a good knowledge issue, the structure of presentations and the criteria. 1. Explain the Presentation Structure (TOK Portal, Presentation page) 2. Explain the Marking Criteria (TOK Portal, Presentation page) 3. Go through the Defining Knowledge Issues either on cards or powerpoint (TOK Portal, Presentation page) 4. Explain practicalities - pairs, 15 minutes required. 5. Students to work on their Real-life situations and KI. 6. Handout the Handout with important details (TOK Portal, Presentation page) Homework Task: Choose a RLS and identify KI. Practice Presentations Lesson 2: Learning Outcomes By choosing their own real-life situation, students will better understand the process of extracting a knowledge issue and begin planning their own presentations. 1. Watch a good presentation and discuss with reference to the criteria. 2. Students to work on planning the presentations and identifying and sharpening their KIs. Discussion with teachers. Homework Task: Students to work on presentations. Practice Presentations Lesson 3: Learning Outcomes Students will develop and prepare their presentations. 1. Go over good and bad presentation powerpoints (TOK Portal, Presentation page), to stress the structure and focus of a good presentation. Homework Task: Students to work on presentations. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 42 Page 43 Perception Significant Concept: The practical and theoretical problems of perception mean that we can perhaps distinguish between how well our senses allow us to function, and whether or not they ‘tell us the truth’. Overview: This module is centered around the Overview PowerPoint, which uses many examples and graphics and which provides a structure and progression through what are quite difficult ideas. The module starts with practical problems, goes on to philosophical problems and can take between 3 and 4 lessons, depending on class discussions. Below is an estimate. This is a tricky topic the first few times you teach it. If you are new to this, do think it through carefully, and read the notes at the bottom of each of the PowerPoint slides for a steer (or of course, ask for assistance if you need it!) Perception Lesson 1: Learning Outcomes Students will understand that human perception is not the only method of perception and that we ‘construct’ our empirical world in some (debatable) sense. Perception Lesson 2: Learning Outcomes Students will understand that we have a range of biological/cultural/linguistic influences on our empirical knowledge. Perception Lesson 3: Learning Outcomes Students will understand that the constructed nature of our sensory knowledge calls into questions what we mean by ‘real’ or ‘true’. Perception Lesson 4: Learning Outcomes Students will understand that ideas around Perception can have important practical consequences. 1. Presentation and Puzzle: Police Line Ups (TOK Portal, Perception page). 2. Watch and discuss Flicker 1, Flicker 2, Gradual 1, Gradual 2, Continuity 1, Continuity 2 These effects show how our brains assume things about stability and change in the world - for good reasons (see Beau Lotto). Watch carefully! NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 43 Page 44 Paradigms and Culture Significant Concept: Knowledge is to a great degree shaped by paradigms and culture; while we cannot escape this, awareness of the fact should serve to mitigate some of the intellectual and moral dangers that result. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 What is a paradigm? (misshapen hunk, missippi) Role of reason (incident in store, 9 dots) Culture as a Paradigm Nacirema ; influences on ourselves Derren Brown Milgram; authority Grand Paradigms (Buzz, Known Universe) Paradigms Lesson 1: Learning Outcomes Students will understand that all knowledge comes from a perspective, and when we might call a perspective a paradigm. 1. Click on What do you see? And choose Mr Nasty 1 and the Mr Nasty 2 (TOK Portal, paradigms page) and ask students to describe the man - suggest that from the first perspective he is a 'baddie'; from the second perspective he is a 'goodie'. Ask students to try and 'zoom out' again so he becomes a 'goodie' again... and then a 'baddie' and so on. And then find another perspective where the whole concept of goodie/baddie is not applicable, where he is something else like an actor in a film, or a clay model. Stress that nothing about the man changes, just our perspective, and hence our 'knowledge' about him. As he changes from goodie to baddie and back, we change our perspective. But as we find him to be an actor or a clay model, and the categories of goodie/baddie no longer apply, we are changing our paradigm – the whole platform in which we make our judgements shifts. 2. Define paradigm: - a mental construction which we use to filter and interpret information and classify knowledge. Give some examples of paradigms (student book textbox page 233), and ask students for their own examples of times they did a perceptual flip (eg accuse someone of stealing only to realise that they were returning the object) - this can be very entertaining. The example that I use from my own experience is seeing, in a department store, someone who looked familiar. I was surreptitiously watching him study some shirts - after a moment I moved away and only then realised that it was my reflection in a mirror. I might be inclined to say that I really did see someone else for a few seconds. 3. Why are paradigms important? Show Calvin and Hobbes (TOK Portal, paradigms page) and discuss. 4. Read Life on the Mississippi (Student book page233 - 235) discuss idea of paradigms being mutually exclusive; discuss questions at end of the article NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 44 Page 45 Homework Task: Answer question A student book p235. Try to link your answer to what you learn about perception. Also answer C and E. Paradigms Lesson 2: Learning Outcomes Students will understand the role of reason in forming paradigms. 1. How do paradigms affect what we think? Refer back to exercise done in DP1 'Incident in the Store' exercise (student book p82, answers teacher book p47). Most students make lots of errors in this exercise, and we can now revisit why that’s the case. Discussing with students the reasoning process that lead to faulty conclusions (student book p235 - 237). This is best done on the board via discussion not via the book. Of course there are many stereotypes and media images that help form what I have called 'the robbery paradigm' (diagram in student book p236). 2. Read student book p239 – 240. Ask who should be set free. The answer depends on one’s paradigm of prison. Is there a ‘correct’ paradigm (see student book p236 q1)? Paradigms Lesson 3: Learning Outcomes Students will understand the role played by culture in determining our paradigms. Culture is a paradigm par excellence; from birth we are brought up to believe certain norms; let us try to see if we can say how important they are, and identify some things that we take for granted. 1. Project Statements (TOK Portal, paradigms page) and discuss if they are true or not. It will quickly emerge there are cultural differences – but then we can touch on the equally uncomfortable possibilities that (a) either all cultural views are equally valid, or (b) some cultural views are better than others. As we shall see, this is a central issue here, and one that links very tightly to issues around pluralism. 2. It might be helpful to ask students working in pairs/small groups to divide up the list into: Things that are not culturally universal but should be Things that are considered to be culturally universal but should not be 3. Use the Presentation: Culture (TOK Portal, paradigms page) to drive home what we mean by culture and introduce some key terms (this powerpoint needs some updating and Kenya-isation – any ideas gratefully accepted). Enculturation : A partly conscious and partly unconscious learning experience whereby the older generation invites, induces and compels the younger generation to adopt traditional ways of thinking and behaving' (Weak) Ethnocentrism: The point of view that one's way of life is to be preferred to all others. This is a perfectly tenable position, but there is a danger that it becomes: (Strong) Ethnocentrism: The point of view that one's own group is the universal norm, and all others should be scaled and rated with reference to it. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 45 Page 46 Cultural Relativism: A theory or philosophy which argues that truth, beauty and morality are not absolute, but are dependent on the culture in which they exist. In other words, one culture's notion of truth is valid only relative to that culture; a second culture's notion of truth could be quite different and yet still be valid relative to that second culture. There are obvious problems and indeed dangers of both strong ethnocentrism and cultural relativism. History and indeed the modern world is full of cases where zealots and bigots judge the world by their own perverse standards and often end up murdering them. On the other hand, for us to condemn this and act to stop it (which we must, mustn't we?) we are open to the same charges of imposing our cultural norms on other cultures. Are we not just hypocrites if we require everyone to be cultural relativists, because we are effectively then not being relativist ourselves (this is the general problem of relativism in a cultural guise)? Homework Task: Journal entry: Can we justify judging other cultures by our own standards? If so, how? If not, does that mean that ‘anything goes’ Paradigms Lesson 4: Learning Outcomes Students will understand how our paradigms means that seeing ourselves as others might see us is very difficult to do I have used this activity successfully in other countries, but it may be culturally referenced itself. All feedback appreciated. 1. Body Rituals of the Nacirema (student book p256, instructions teacher book p96). This is an excellent activity. Make sure that students read it in silence, and that no-one calls out and ruins it for everyone else. You may need to spend some time going through the article identifying the different aspects. Then ask students to write their own version of a ‘common’ event, seen through the eyes of an outsider. Once students have written their own 'bizarre' story you can ask them to read them out and see who can guess them. In my experience this usually takes a lesson but if there is more time then to prepare for the next lesson ask students how much they are influenced by the surrounding (big or small) cultures; ask how pliable how likely to 'follow' they are. Paradigms Lesson 5: Learning Outcomes Students will understand role of authority in shaping our paradigms. 1. Ask students how much they are influenced by the surrounding (big or small) cultures; ask how pliable how likely to 'follow' they are. Use Power of Situation video or Milgram’s Experiment (TOK Portal, paradigms videos page) - which draw on very powerful psychology experiments to explore the extent to which we follow the roles demanded of us in various situations. It is absolutely fascinating. We can conclude that the social context (which we might identify with culture) can affect what we believe is right/wrong, what we are prepared to do, and even what we can perceive. 2. Follow up with the Powerpoint: Authority (TOK Portal, paradigms page). Discuss. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 46 Page 47 3. Ask students when they have every followed due to social pressure. difference? Might education make a Paradigms Lesson 6: Learning Outcomes Students will understand the historical changes of paradigm, and the implications for our ethical, scientific, religious and self-knowledge. The content of this lesson follows student book p241-245 closely. Important to read teacher book p90 too. It will be much more interesting to use the suggestions below, however, than simply to read the book. It would be vital, however, that you are very familiar with the ideas. Note that the book refers to a classical paradigm an enlightenment paradigm and a modern paradigm whereas the slides refer to a classical paradigm, a modern paradigm and a post-modern paradigm. The names don’t really matter; the point is that there are three paradigms. 1. Show Presentation: The Grand paradigms (TOK Portal, paradigms page). The transition between paradigms is interesting– each paradigm seems to contain thing that lead to the next. Shakespeare seems to have managed to echo different paradigms at different times. 2. Discussion should not focus on which paradigm is ‘better’, but the basis on which we choose our paradigms (bottom p90 teacher book). NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 47 Page 48 Language Significant Concept: That language is not a neutral medium of transmission of knowledge but that it shapes our knowledge (and possibly even what we can know) in powerful ways. Overview: Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Language issues; not a neutral medium; language and values Language and Meaning 1(including translation) Language and Meaning 2 (including translation) Language and Thought Language and Human Cognition Language Lesson 1: Learning Outcomes Students will understand that language is not a neutral medium but a powerful transmitter of values; perhaps a paradigm in itself. 1. Stimulus: Surgeon riddle p104 teacher’s book. Worth some detailed analysis – see p104 – 106 for ideas. Stimulus: Look up black and white in a dictionary (online is easy) and see the moral aspects of definitions. Stimulus: Mad dogs and Englishmen (student book p266). Obvious point is that language contains values. 2. Brainstorm value-laden words – usually some good discussion about gender, class, tribe comes up. 3. Is all language value laden? Read ‘There was Once’ (student book p268). Maybe best acted out by a male teacher and a black girl. In a sense, merely by talking about something one is giving it more value than the things not mentioned. So….? Homework Task: Find an example of value-laden language which pretends not to be (politicians?) Language Lesson 2: Learning Outcomes Students will understand that the meaning of words is not transparent but depends on a whole range of factors, many of which are sometimes not consciously understood. We have already seen, from the batchelor example in DP 1(student book p86) that we seem to know more than we can say. Let’s explore this a bit more (it follows well from values). NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 48 Page 49 1. Stimulus: Time flies like an arrow – see student book p276 question B and the teacher’s book p108. Stimulus: Riddles – see student book p275 (answers teacher book bottom p109) – these are more about words than anything else. The meaning of the words, in the contexts, is either ambiguous or in some way problematic. The idea is that meaning is subtle and difficult. 2. Go through student book p276 question A (see teacher book p106) and discuss the meaning of ‘truth’ and ‘law’. These are very difficult to define. 3. Read p276 an 277 and discuss the issues. Language Lesson 3: Learning Outcomes Students will understand that the meaning of words is not transparent but depends on a whole range of factors, many of which are sometimes not consciously understood. 1. Stimulus: Read p278 – middle 279. Discuss what ‘I love you’ means in the various languages spoke by the class. The problem is that meanings do not always carry across languages; what we know about words cannot be applied elsewhere. Thus or knowledge is to some extent linguistically limited. 2. Previewing the next lesson, ask students how they think in different languages; are somethings easier to say? Are some meanings easier to convey? 3. The points on p280, 281 are, I think, profound. Students should read and then do a think-pairshare activity whereby they explain the key points to each other, and then have some discussion. Language Lesson 4: Learning Outcomes Students will understand that language is linked with thought in some way, and may arguably determine what we can think. 1. Stimulus: Read George Orwell p271. Is he right? If meaning is so difficult to grasp, can we limit thought by limiting language? See Teacher’s book p106 for a discussion of how to deal with the issue. 2. Referring to the previous lesson, it’s interesting to note that some languages have different vocabularies. Here are some amusing examples: Portuguese geram unbearably cute. Italian terrano big fat lazy person from the South Japanese Tsugi-giri trying out a sword on passer – by Japanese Madogiwazoku window gazers (office workers who sit at desks with little to do) Farsi Nakhur A camel that won’t give milk until it’s nostrils are tickled. NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 49 Page 50 Japanese Italian Baku-shan Slampadato A woman who looks better from behind. One who is excessively tanned from a sunlamp. See also the Neologisms (TOK Portal, language page). But does this really tell us much? The fact that we immediately grasp the ideas suggests that the lack of words is hardly a limiting factor. And of course even within out own languages, we have lots of words missing - see p273. 3. Ask students to make up their own new words. That this is difficult to do does suggest that there may be some effect on thought. 4. Read p285 – 287 which takes a different angle on meaning. Discuss. I think the ‘corriearklet’ on p273 is a case similar to the triangle – having the word really does make our experience different – to that extent language does affect thought for sure. Language Lesson 5: Learning Outcomes Students will understand that language can provide a tool for understanding human cognition. This is an optional lesson for able classes! Two clips that you must watch beforehand so you have thought about where to pause and discuss what’s being said. The point is that we can understand ourselves and our cognition through examining the way we use language. Quite a profound thought. 1. See and discuss language reflects thought and structure and then Pinker on languages and human nature (TOK Portal, language video clips). NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 50 Page 51 Assessed Essays Objective: Students will prepare and write good essays. Students should come to class for all essay-writing lessons; it is important that we structure the lessons so that students are seeing good essays and learning how to write them for half the lesson at least. Students should not simply be sent to work in the library. Note each lesson here needs photocopying preparation. I recommend lessons 1 and 2 be done early in process, 3 midway, and 4 towards the end, possibly even after the draft essays have been handed back. These lessons are best not done one after the other; the essay should be done over an extended period, including the Christmas break. Essays Lesson 1: Learning Outcomes Students will better understand, holistically, what makes an excellent essay; also the essay criteria. 1. Students to read Excellent Essay 1 (see Here1 on TOK Portal Essay page), and to review four features of makes an excellent essay – focus on KI, Examples, Introduction, Conclusion. Discuss. 2. Hand out titles and criteria; remind students of the DP1 experience; these are not easy essays to do. Remind students that we are not looking for platitudes. Mention the fact that we should be looking for multiple/nuanced views – that is, the answers are not justy ‘Yes’ or ‘No’; show some example from portal (Multiple/nuanced views – TOK Portal Essay page). 3. Give out Essay Planning Sheet. Get students into groups to discuss possible approaches to the title – the overarching narrative/theme for the essay - and to develop mind maps with the ideas that radiate from this central idea. Homework Task: Complete Essay planning sheet. Essays Lesson 2: Learning Outcomes Students will better understand what makes an excellent focus on knowledge issues. 1. Print and handout the Knowledge Issues sheet (see Knowledge Issues on TOK Portal Essay page). Students to read the example and discuss, then teacher to go through and highlight what makes a good focus in KI. Ensure the students get some notes here. 2. Work on essays. Homework Task: Work on Essays NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 51 Page 52 Essays Lesson 3: Learning Outcomes Students will better understand what makes an excellent example. 1. Print and handout the Examples sheet (see Examples on TOK Portal Essay page). Students to read the example and discuss, then teacher to go through and highlight what makes for good examples. Ensure the students get some notes here. 2. Work on essays. Homework Task: Work on Essays Essays Lesson 4: Learning Outcomes Students will better understand what makes an excellent introduction. 1. Print and handout the Introductions sheet (see Examples on TOK Portal Essay page). Students to read the example and discuss, then teacher to go through and highlight what makes for good introductions. Ensure the students get some notes here. 2. Work on essays. Homework Task: Work on Essays Essays Lesson 5: Learning Outcomes Students will better understand what makes an excellent conclusion. 1. Print and handout the Conclusions sheet (see Conclusions on TOK Portal Essay page). Students to read the example and discuss, then teacher to go through and highlight what makes for good conclusions. Ensure the students get some notes here. 2. Work on essays. Homework Task: Work on Essays NSA: Theory of Knowledge Teaching Plans NB These lessons are for 50 minute lessons – adapt! Page 52