Lessons from Around the World - Wikispaces · PDF filePreface Conceived at a TOK meeting at Arden House in New York State in 1993, the project to provide examples of TOK lessons to

Theory ofKnowledge

Lessons from Around the World

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Teacher Support Material—Theory of Knowledge Lessons from Around the World

Lessons 1–10, August 2000Lessons 11–20, November 2000

The International Baccalaureate Organization wishes to acknowledge the help of the following teachersand assessors in the production of this document:

Sue Bastian, former chief assessor, New YorkEileen Dombrowski, deputy chief assessor, UWC Pacific/ Lester Pearson

Bill Frere, teacher, Trinity College Preparatory HS, IllinoisLucia Harvilchuck, assistant assessor/ teacher, Pensacola HS, Florida

Julian Kitching, assistant assessor/ teacher, SOS-Hermann Gmeiner IC, GhanaJohn Mackenzie, former chief assessor/ teacher, The Grange School, Chile

Dennis Oberg, assistant assessor/ teacher, Antwerp IS, BelgiumUlf Persson, teacher, Hvitfeldska Gymnasiet, Sweden

Pat Prather, assistant assessor/ teacher, Rancho Buena Vista HS, CaliforniaLena Rotenberg, deputy chief assessor, Washington DC

Manjula Salomon, assistant assessor/ teacher, Jakarta IS, IndonesiaMatthew Thompson, teacher, UWC Atlantic College, Wales

David Wilkinson, teacher, UWC India/ Mahindra, IndiaAyman Zanoun, assistant assessor/ teacher, Amman Baccalaureate School, Jordan.

© International Baccalaureate Organization 2000

International Baccalaureate OrganizationRoute des Morillons 151218 Grand-Saconnex

GenevaSWITZERLAND

Preface

Conceived at a TOK meeting at Arden House in New York State in 1993, the project to provideexamples of TOK lessons to practising teachers is now coming to fruition. The first ten lessons werepublished in August 2000 as the first instalment of Lessons from A round the World. Lessons 11–20 are afurther instalment.

Teachers are encouraged to treat these lessons as working documents. Put aside those which you mayconsider inappropriate for this year’s class, amend and improve on those which you think have potential,and use some just as they are. Dovetail them with your own schemes of work and supplement them withmaterial which you may have accumulated yourself, or obtained from students or from workshops.

If you think it useful, arrange the lessons according to the ways of knowing and areas of knowledge in theTOK guide, or arrange them chronologically according to the sequence in which you engage yourstudents in the course. Each lesson contains a section linking it to other areas of TOK.

We are deeply indebted to the teachers and assessors, listed on the inside front cover, who have workedso hard to make this project a reality. Further lessons are in final draft form.

Contents

Julian KitchingNumbers and NumeralsLesson 13

Dennis ObergIs Math for Real? (a TOK Quizfor Mathematical Knowledge)

Lesson 12

Manjula SalomonRoutes of MathematicalKnowledge

Lesson 11

Julian KitchingThinking LogicallyLesson 10

Eileen DombrowskiThe Map is not the Territory Lesson 9

Sue BastianNothingness Lesson 8

Ulf PerssonWords and not Words: anLesson 7

Eileen DombrowskiLanguage and SymbolismLesson 6

Julian KitchingThe Power of NamesLesson 5

John MackenzieExercises on Meaning Lesson 4

Sue BastianLetters from an Indian Judge to anEnglish Gentlewoman

Lesson 3

Eileen DombrowskiDoes it Matter if what we Believe is True?

Lesson 2

Matthew ThompsonWhat Good are Schools?Lesson 1

AUTHORTITLELESSON

Julian KitchingWebs of ExplanationLesson 20

Dennis ObergThe Growth of ScientificKnowledge

Lesson 19

Julian KitchingScientific Claims: an AfricanPerspective

Lesson 18

John MackenzieOne Person’s Hypothesis isAnother Person’s Dogma…

Lesson 17

David WilkinsonWhy was Thales Wrong?Lesson 16

Matthew ThompsonMyths and Fairy TalesLesson 15

Bill FrereA Show of Hands Lesson 14

AUTHORTITLELESSON

Lesson 1: What Good are Schools?

Cont ex tThe curriculum in every system of education reflects our different ideals of the human person, ofour communities and of our understanding of knowledge.This lesson could form a useful introduction to TOK by offering a wider context of reflectionon the total curriculum. It could also provide a conclusion to the course, giving the students anopportunity to revise and synthesize their learning. Altogether, it offers students ownership of theTOK course.

Aim s To identify the ideals or criteria of excellence in individuals and society. To consider the nature of sound evidence.

To analyse critically the components of educational systems. To link the power and process of education to the above-mentioned criteria, and to

consider the kinds of knowledge that are valued.

Class Managem ent The student handout (from Benjamin Franklin) should be copied and distributed to the class

ahead of time. This is useful as a stimulus. Probably, two 45 minute lessons are required. One lesson will give students time to discuss

and record their findings. In the second lesson they will report on and analyse their task.

The level of education being considered may or may not be restricted to the DiplomaProgramme.

Foc us Ac t iv i t yDivide the class into two or three groups. Tell them that they have been elected to the positionof Minister of Education in their country and that they have been given the task of devising thebest possible educational curriculum for the nation. They should be given only twopreconditions.

1 Their aim must be to produce the best individuals and the best society possible.2 They must impart only knowledge and beliefs which are based on sound evidence.

Teacher Support Material—Theory of Knowledge Lessons from Around the World © IBO, August 2000 Lesson 1—page 1

St udent HandoutA useful passage is the following from Benjamin Franklin’s Remarks concerning the Savages of North A merica.It is an appealing story, in which many relevant issues are raised to stir students to thought: issues of valuejudgments, cultural context, definitions of knowledge, applicability of knowledge.

At the treaty of Lancaster in Pennsylvania, anno 1744, between the government of Virginia and the SixNations, the commissioners from Virginia acquainted the Indians [Native Americans] by a speech, thatthere was at Williamsburg a College with a fund for educating Indian youth; and if the Chiefs of the SixNations would send down half a dozen of their sons to that college, the government would take care thatthey be well provided for, and instructed in all the learning of the White People.

The Indians’ spokesman replied:

“We know that you highly esteem the kind of learning taught in those colleges, and that the maintenanceof our young men, while with you, would be very expensive to you. We are convinced, therefore, that youmean to do us good by your proposal and we thank you heartily.

“But you, who are wise, must know that different nations have different conceptions of things; and you willnot therefore take it amiss, if our ideas of this kind of education happen not to be the same with yours. Wehave had some experience of it; several of our young people were formerly brought up at the colleges ofthe Northern Provinces; they were instructed in all your sciences; but, when they came back to us, theywere bad runners, ignorant of every means of living in the woods, unable to bear either cold or hunger,knew neither how to build a cabin, take a deer, nor kill an enemy, spoke our language imperfectly, weretherefore neither fit for hunters, warriors nor counsellors; they were totally good for nothing.

“We are however not the less obligated by your kind offer, though we decline accepting it, and to showour grateful sense of it, if the gentlemen of Virginia will send us a dozen of their sons, we will take care oftheir education, instruct them in all we know, and make men of them.”



Disc ussion Quest ionsAny of the following discussion questions could be extended into a written assignment. What are the aims of the education system and the institution of which you are a part? What,

through the aims, are you expected to know?

What are the ideals of the society that have determined those aims? Where did those ideals come from? On what grounds are they justified?

What conflicts can arise from those ideals?

Teac her Not esDiscussion can be extended to wider contexts by offering the students categories of choice.

What choices are faced when these ideals (and the conflicts that arise between them) inpractice influence the nature of the curriculum? Some considerations may be:Theoretical versus practical

Sciences versus arts/ humanities What status should be given to

moral/ ethical education community service

political education physical education and sports

arts education and sports? How is it decided which of the so-called great works of science, art, literature and morality

are worthy to be passed on in your school or college?

Discussion can be stimulated and extended by introducing regional, religious, cultural and otherconsiderations.The IBO ideals and the Diploma Programme curriculum can be critically analysed as ade-briefing exercise.

Link s t o Ot her Areas of TOKUsing the IBO ideals and curriculum as the basic material for this lesson gives it a lasting andholistic frame of reference for the student.

From Ot her Tim es and Plac esThe handout may easily be replaced by other suitable pieces such as ones by Confucius or HsunTzu, or by Koranic principles or by Australian Aborigine ideals.



Quot at ion

Do not judge a man until you have walked ten leagues in his moccasins. Proverb

Referenc esFranklin, B, Remarks concerning the Savages of North A mericaBruner, J, The Culture of Education, (1997) Harvard University Press, ISBN 0674179536

Freedman, JO, Idealism and Liberal Education, (1996) University of Michigan Press, ISBN0472106929Toffler, A, The Third Wave, (1991) Bantam Books, ISBN 0553246984

The TOK Guide (1999) IBO DR17



Lesson 2: Does it Matter if what weBelieve is True?

Cont ex tThis lesson works well as one of the opening classes for the TOK course.

Aim s To give an initial thrust of purpose to TOK by considering the consequences of belief.

To introduce an approach to reading critically. To introduce truth tests as applicable to everyday thinking.

Class Managem ent Keep articles short and read them together in class. The Harem Hell article included as a studenthandout could be used. The lesson requires one hour of discussion time, not necessarilydistributed evenly across articles. The follow-up discussion needs roughly half an hour.

Foc us Ac t iv i t yGive each student photocopies of three short articles, chosen with a range of credibility.

An absurd newspaper article, to provoke disbelief, eg tabloid articles such as Elvis on Moon orSunbather Bursts into Flames on Beach.

A newspaper article which mixes facts and values, especially in treating negatively a culturalor national group, such as a US treatment of Arab terrorism, or an Islamic treatment of USdecadence.

An article which is more dependable, but is still selective and interpretative, such as a passagefrom a history or science textbook.

Read the articles together and discuss each one in turn.


Disc ussion Quest ions

Cent ra l Quest ions1 Do you believe this article? Why, or why not? 2 Does it matter if what you believe is true?

All other questions are preliminary questions towards a fuller consideration of these two.

Prel im inary Quest ions Are you familiar with the newspaper, the journal, or the author from which the articles are

taken? If so, do you consider the source to be reliable? Why, or why not?

Are there any features of visual presentation which incline you to accept or reject before youeven read the article (eg size of headlines and typeface, accompanying photographs oradvertisements)?

Are there any features of the language used which influence your judgment (eg sensationalphrasing, value-laden language, use of statistics, direct quotation of experts)?

Does the article seem plausible—that is, does it make sense in terms of what you alreadyknow?

Does the article present any evidence that could be checked or tested?

If you are wrong in your judgment—rejecting something that is true or accepting somethingthat is false—does it matter? Is your own mind or conception of reality damaged? Is anyonehurt? What are the possible consequences of false beliefs about other national, cultural orreligious groups?

Fol low -up Disc ussionAfter the students have discussed the articles using their own vocabulary and critical response toyour questions, introduce the following general approach to assessing the credibility of thearticles. The approach should summarize points already discussed and provide a framework tobe used at other points in the course.

The Three Ss: Sourc e, St a t em ent s , Se l f

1 Sourc e: What are the characteristics of a reliable source? What are the characteristics of anunreliable source? Does an apparently reliable source necessarily give true statements?(Consider: reputation, qualifications, accountability.)

2 St a t em ent s : What clues to reliability are provided by the text itself? What clues tounreliability are provided by the text itself?

3 Se l f : What inclination to accept or reject what you read do you notice in yourself? Are youmore inclined to read critically if something does not fit your beliefs?

Similarly, point out to students that they have used, without realizing it, philosophical tests fortruth. If this lesson is used as an opening to the course, introduce the tests lightly, to be picked upin many other contexts later. Does it make sense? Is it plausible? Does it hang together?

The Coherence Test evaluates the truth of each new statement in the context of the bodyof statements already accepted as true. It involves looking within the text, analytically, andseeking rational consistency.

Lesson 2: Does it Matter if what we Believe is True?


Where is the evidence?The Correspondence Test evaluates the truth of a statement on the evidence. It involveslooking outward, and checking or testing.

What difference does it make? So what?The Pragmatic Test evaluates the truth of a statement on the basis of its usefulness—theworkability of predictions based on it, or the practicality of its consequences. (You may wishto distinguish between practically useful, as in science, and psychologically useful, as in thebenefit of believing self-flattering statements. The latter is not a convincing test for truth!)

You may wish to round off the lesson with a discussion of an ethical dimension to belief—that valuingthe truth and seeking to avoid harmful consequences are moral values significant in TOK discussions.

Link s t o Ot her Areas of TOKAssessment of credibility is relevant to all areas of TOK.

From Ot her Tim es and Plac esThere is room for discussing national or cultural or historical points of view throughout thelesson, depending on the discussion provoked by your choice of articles.

Quot at ions

One who learns without thinking is lost; one who thinks without learning is in great danger. Confucius

Human beings are never more frightening than when they are convinced beyond doubt thatthey are right.

Laurens van der Post, on Apartheid

Referenc esA sample article, Harem Hell, is attached.

Quest ions How is the article written? Does it seem reliable?

Exactly where does the action in this article take place? Is it geographically specific? Who is reported as doing the actions? Arabs? Moslems? Specific nationalities? Nomads or

urban dwellers?

When do these practices take place? (Islam forbade the burying of babies, a practicereported as carried on ‘until recently’. When did Islam begin?)

What claims are made about women’s lives? Are all the examples given accurate? Howmight you check? Are they all shocking?

So what? Does it matter whether or not you believe the claims in this article? Does it matterif you frequently encounter similar attitudes?



St udent Handout



Lesson 3: Letters from an Indian Judgeto an English Gentlewoman

Cont ex tThis lesson is useful after the introduction of the course. It shows that knowledge claims may beheavily reliant on culture and social perspective. Because the lesson has wide application it may bereferred to throughout the course.The lesson could also serve to consider the multiple meanings of the word culture, so relevant indiscussions of knowledge, and to consider the differences between members of any designatedgroup. Causes of cultural cohesion or bias can arise from a combination of geography, ethnicity,gender, academic training and many other factors.

Aim s To consider knowledge within a cultural context. To expand the concept of culture beyond the categories of race, language and nationality.

To account for the variety of knowledge claims. To note the power of belief systems.

Class Managem ent This lesson is easily done in 45 minutes, with a reading aloud of the handout in class followed bya discussion.


Foc us Ac t iv i t y

St udent Handout

‘Now I can tell you a little more of some of my work up here, which may perhaps be of interest to you. Andfirst and most formidable of all, behold our local Snake.

He dwells in a cleft up here on the mountainside, in a large fissure that was caused by an earthquake.For I must tell you, this part of the world is very prone to earthquakes and for this reason, very sensibly, nobrick building must be of more than three feet high. After that your edifices must all be composed of woodor of plaster and laths so that he who gets fallen upon by his house in an earthquake is not fallen upon toomuch.

Now you and I may have our private ideas as to the causes of earthquakes, but that makes no differenceto the small unlettered man in the country about here, because, you see, he knows. And what he knows isthat the earthquakes come because the Snake has been allowed to get angry and then through the earthhe goes, and confides his troubles to the spirits that sit within the earth and then the spirits get angry aswell, and then, pouf, down come all our houses upon our heads.

The small man in the village knows this, just as he knows that anything we may say to him to the contraryproves only our ignorance or that we have some private axe to grind. Do not suppose that it is ever by itsRulers and enlightened men a country is really governed. It is by the small men in the villages, who know.

Another thing the small man knows is just how to placate this angry Snake. The way it is done is asfollows. Once yearly you must make chapattis [bread] mixed with the best of flour and ghee [butter], allwelded together with human blood. It is useless trying to palm off goat’s blood upon this very intelligentSnake. He knows what he wants.’

Excerpt from Letters from an Indian Judge to an English Gentlewoman

Lesson 3: Letters from an Indian Judge to an English Gentlewoman


Teac her Not esAfter reading the handout aloud, the class breaks into two groups. One group establishes step bystep the knowledge claims of the small man based on the evidence. The other group establishesthe knowledge claims of the judge. Each group presents their claims to the other, looking forstrengths and weaknesses.

Disc ussion Quest ions Ask students to offer knowledge claims that they think are culture-specific, from either their ownculture or others they know about. These knowledge claims could come from personalexperience, or from literature and films.

Observe whether students tend to use culture as a generic term, assuming a homogeneous group.A trifocal way of understanding people may be useful in considering culture and the variety ofknowledge claims. Each person can be seen to be: a member of a species, and therefore alike

a member of a group, and therefore having a number of names an individual, and therefore unique.

With these questions in mind, ask students to give several attributes of each category tothemselves, and to construct a situation where things go wrong because people use the wrongcategory for the situation.

Link s t o Ot her Areas of TOKThis lesson is clearly relevant to Knowers and Knowing, Ways of Knowing, and many of theLinking Questions in the TOK Guide. In its discussion of the role of culture it also connects morespecifically with general patterns observed in the human sciences and with the role of definitionin language. The claims generated are also relevant to evidence and reasoning, especially in thelight of what counts as a good reason around the world.

Quot at ions

Much learning does not teach understanding. Heraclitus

The only reality is that which the mind constructs and the only truth is the mind’s coherencewith itself.

Tejedor Cesar

A wise man proportions his belief to the evidence. David Hume

Referenc esOlen, J, Persons and Their World, (1983) McGraw Hill College Div, ISBN 0075543117 (especiallychapters 15 and 16)

Lesson 3: Letters from an Indian Judge to an English Gentlewoman


Lesson 4: Exercises on Meaning

Cont ex tSharing meanings and using categories seem to be important human abilities. How we do thesethings seems relevant to a consideration of language, as a way of knowing. The view that students often seem to hold is that categories correspond to natural kinds that existout there in the world, on which we hang labels (words) when we recognize them. According tothis view, the objects that make up this natural kind, whether it be birds or tables, are a part ofthis category because they share a common property or feature. Because we recognize thisfeature, so the reasoning goes, we are able to group them together and name them.

This view of meaning can easily be shown to be faulty in various ways. The first of these is to saythat even if one could categorize tables in this way, we would have serious problems doing thesame with freedom or good or any number of concepts of that sort. The complexity ofcategorization should be illustrated by the activities.

Aim s To examine the meaning(s) of words and our knowledge of these meanings.

To highlight the importance of categorization in the construction of knowledge.

Class Managem ent These activities could take up one or two 45-minute lessons. Discussion in small groups,followed by a plenary, would be appropriate. At other points in the TOK course there shouldbe sufficient opportunity to return to the issues raised.

Foc us Ac t iv i t yDefine the word good. It might help to provide some statements to stimulate discussion. He is a good man.

She is a good athlete. There are a good many liars in this outfit.

Are you good for a few dollars? The common good.

This activity can be repeated with other generic words, such as true. He was true to his word.

She is a true friend. Everything he told us was true.

That arrow flies true.

Teacher Support Material—Theory of Knowledge Lessons from Around the World - © IBO, August 2000 Lesson 4—page 1

Disc ussion Quest ions Do we need to know a definition of a word, in order to understand its meaning? Is knowing how to use a word similar to knowing how to walk or swim; that is, could it be

viewed as a skill?

Do words have meanings or do we give them meanings? What do people mean when they claim that young people no longer use language properly?

Students may quickly fix on a variety of uses (the moral good versus the good used inwinetasting, for example). It is also possible to narrow the discussion by asking for a singledefinition of good when describing human action only (the moral dimension). The likelihood isthat students will be unable to provide an answer to everyone’s satisfaction. If they object to thechoice of word, arguing that it is too abstract, try them out on Wittgenstein’s defining game.These are words that they use successfully every day, and so they are competent users of theseterms and yet they are unable to define them. Does this mean, as Socrates would have it, thatthey have no idea of what they are saying? (This is the metaphysical view so eloquently portrayedin Plato’s dialogues, where Socrates goads prominent Athenians, requiring them to define keyconcepts which they are prone to use as if they were experts on the subject, such as beauty,justice, virtue, and when they are unable to do so, concludes that no one knows anything. Onecannot improve on Hubert Dreyfus’s quip that someone should have suspected that this was nota good starting point for Western philosophy.)An alternative view, that could emerge when these questions are considered, is the meaning as useview. Here words take on meaning as ways in which we use the term (often in varied andspecialized contexts), which need not respond to any one underlying paradigm or model.

Link s t o Ot her Areas of TOKMost of the concepts in the programme can lend themselves to the question of whether theycould be considered a language, and therefore the question of meanings becomes relevant. (AsDennet has recently pointed out in his Darwin’s Dangerous Idea (Simon and Schuster, 1995, p.371)it sometimes seems as if the highest praise we can bestow on a phenomenon we are studying isthe claim that its complexities entitle it to be called a language.) Might meanings work verydifferently in different types of language? For example, does the word truth always mean thesame thing, or is it applied in the same circumstances, in all the areas of knowledge covered byTOK? The same could be asked in relation to evidence, or justification. This is central toTOK. How much of what is going on when we apply such words is common, and how muchis particular, to different areas of knowledge?For example, in a discussion of what science is, should we include social research and analysis? Isthere one common feature typical of all those practices we call science? Or do we use it indifferent ways, some of which make it easier to accommodate social studies than others? Thesame applies to the discussion of art, or of good actions, or indeed the word language itself.

How we actually categorize is not an entirely resolved question. This lesson can focus attentionon the extent to which we are passive describers, registering the world about us, or activeinterpreters of our surroundings (the or is not of the either/ or variety).



From Ot her Tim es and Plac es Use of the word good in Australian English? (I’m good = I’m well) Use of these words in the past. For example, between the 15th and 18th centuries the word

presently meant immediately. It still does in British English, but means currently in AmericanEnglish. Words are not static, but shift meaning with time, place, culture and purpose.

Quot at ions

Definitions are like belts—the shorter they are, the more elastic they need to be. Steven Toumlin

Language is by its very nature a communal thing; that is, it expresses never the exact thingbut a compromise—that which is common to you, me and everybody.

Thomas Ernest Hulme

Meanings receive their dignity from words instead of giving it to them. Pascal

Ours is a Copious Language, and Trying to Strangers. Mr Podsnap in Dickens’s Our Mutual Friend

Referenc esHayakawa, AR & SI, Language in Thought and A ction, (1991) Harcourt Brace, ISBN 0156482401Keller, H, The Story of My Life, (1999) Demco Media, ISBN 0606159983

Kolak, D & Martin, R, Wisdom Without A nswers, (1998) Wadsworth Publishing Co, ISBN053425974X



Lesson 5: The Power of Names

Cont ex tNames are often considered to be the most straightforward aspect of language—words simplyas labels for things. Because of the apparent simplicity of names, this is a good starting point forthe investigation of the nature of language. This lesson considers examples of names for places and people in order to show how theword-as-label model is inadequate in itself—how even apparently simple names embody wholeranges of connotation, abstraction and generalization, and thus illustrate wider aspects of thephenomenon of language as a whole.

The lesson is effective as an introduction to the work on language and thought, because it raisesmany points which can be addressed later.

Aim s To investigate the nature and power of names in language and their levels of meaning.

To consider the cultural and historical context of language.

Class Managem ent Students will need access to atlases, both present day and historical. Other reference sources ofAfrican history would also be useful. It may be necessary for students to investigate the historyand meanings of their own names in advance.

This lesson lends itself to group work for the geographical part, and individual work for thecollection of personal names.Timing will depend on whether the gathering of all the information is to be a class activity or apreparatory one (with students bringing the results of their research to the lesson). Either isfeasible. The structure of the lesson is open and any part of the content outlined may besufficient to stimulate the discussion.

Foc us Ac t iv i t yConsider a current political map of Africa. Consult a historical atlas and note changes in thenames of countries, particularly since the start of the European colonialist period. Try also todiscover the origins of some current names for African countries.Make a list of the personal names of members of the class. Exchange information with otherclass members about their personal names. Do any of these names have known meanings, otherthan simply referring to the person in question?

Amongst the Akans of Ghana, each individual receives a name (in addition to others) whichcorresponds to the day of the week on which he/ she was born (see chart below). Does anythingsimilar happen in other parts of the world?



Teac her Not esBy conducting this lesson with a minimum of technical vocabulary, the students can begin todiscover for themselves the intricacies and complexities of language. 1 Examples of changes might be:

Rhodesia to Zimbabwe Gold Coast to Ghana Upper Volta to Burkina FasoNyasaland to Malawi Dahomey to BeninMany present-day names refer to historical territories quite different from those inexistence now. Often, they were great empires, such as Ghana, Benin, Mali.

Some present day names have quite simple derivations: Liberia, meaning freedom Sierra Leone, meaning land of lions (Portuguese meaning thunder as lions roar) Tanzania is a combination of Tanganyika and Zanzibar.

2 In Africa biblical names such as Solomon, Moses and Emmanuel are common. In LatinAmerica, Jesus, María and Angelo are often chosen.

3 Compare the Akan practice of giving a baby a name corresponding to the day of the week,with the Monday’s Child rhyme in English (see student handout).

If names of countries are simply convenient ways of referring to particular geographicalareas, then why have the names changed? List some specific examples to illustrate youranswers.

Why is it perhaps particularly pertinent to look at African names in this connection? How arehistory and language intertwined?

What names denote may change historically (eg Germany, Yugoslavia), but what theyconnote also changes in other, not necessarily related, ways. For example, a person’s namemay have some meaning other than the trivial sense of being a label, but what is therelationship between that name and the person concerned?

Different cultures employ different names. To what extent do they correspond to oneanother in meaning?

Names refer to people and places we can point to, but they must also refer to images ofthese people and places in our minds. What are the different layers of meaning in names? Tryto identify them, separating the different levels. Can we distinguish between theinformation-bearing and affective aspects of connotation?

If more than one individual shares the same name, what does that mean? Is this the same asthe use of the word table, for instance?

Personal names go in and out of fashion. How, if at all, can this be related to their meanings?How are language and taste related?

To what extent is a personal name a reflection of, for example, religion, social class,nationality?



Fol low -up There is an Akan taboo which proscribes the mention of the word snake after dark. People

will sometimes refer to snakes by some other term during this time. Is there anything to belearned here? What is the relationship between a word and the thing it denotes?

Why is Shakespeare’s Macbeth sometimes called the Scottish play?

In Germany, there is an official list of names from which the name of a baby must bechosen. Why would such a list exist?

In the Akan language, as in all others, there are only a certain number of colours which havenames. How does this compare in different languages? What might these differences mean?

Consider the names for describing relatives (father, aunt, cousin, et cetera) in different languages.Are there any differences in the way this is done in different countries or cultures? Consider theelaborate kinship terminology of the Akans (see chart below) and compare this with your ownexperience. Why do kinship terminologies differ in structure from one society to another?

Relat ed Quest ions What do we mean when we talk about meaning? Can we distinguish between different kinds

of meaning, such as the literal versus the symbolic, the dictionary definition of a term versusits everyday use?

What is meant by definition? Can names be defined? What are the different functions of language?

Are words simply labels for things, or are they tools with which we investigate the world? What problems are encountered in translating words and meanings from one language into

another?

Is it possible plausibly to argue that people who speak different languages live in differentworlds? What exactly would this mean?

Quot at ions

When I use a word, Humpty Dumpty said, in rather a scornful tone, it means what I chooseit to mean—neither more nor less.

Lewis Carroll

What’s in a name? That which we call a rose by any other name would smell as sweet.Shakespeare

Language is like fixed rails upon which all our thought must run. Past TOK examination paper

If language be not in accordance with the truth of things, affairs cannot be carried on tosuccess.

Confucius

A child when it begins to speak, learns what it is that it knows. John Hall Wheelock



Referenc esChomsky, N, Language and Responsibility, (1998) New Press, ISBN 1565844750Farb, P, Word Play: What Happens When People Talk, (1993) Vintage Books, ISBN 0679734082

Hayakawa, AR & SI, Language in Thought and A ction, (1991) Harcourt Brace, ISBN 0156482401Spuhla, JN, The Evolution of Man’s Capacity for Culture, (1959) Wayne St University



St udent Handout

Mo=mother; Fa=father; Si=sister; Br=brother; Wi=wife; Hu=husband; Da=daughter;So=son.

Key:

child/maleSoBa barimaSonchild/femaleDaBa baaDaughter

feminine father/child/maleFaSiSoSiwaa ba barimaCousinfeminine father/child/femaleFaSiDaSiwaa ba baaCousinmother’s brother/child/maleMoBrSoWofa ba barimaCousinmother’s brother/child/femaleMoBrDaWofa ba baaCousinfather/child/maleFaBrSoAgya ba barimaCousinfather/child/femaleFaBrDaAgya ba baaCousinmother/child/maleMoSiSoEnna ba barimaCousinmother/child/femaleMoSiDaEnna ba baaCousin

SiHuAkontaBrother-in-lawBrWiYereSister-in-law

sibling/maleBrNua barimaBrothersibling/femaleSiNua baaSister

person with right to collect propertyMoBrWofaUnclefatherFaBrAgyaUnclefatherFaSiSiwaaAuntmotherMoSiEnnaAunt

FaAgyaFatherMoEnnaMother

MoFaNana barimaGrandfatherFaFaNana barimaGrandfatherFaMoNana baaGrandmotherMoMoNana baaGrandmother

MeaningRelationTwiEnglish

The following chart shows how the Akan use an elaborate system of names in order to identify withprecision the relationships between family members. The far left column shows the generally used termsin English; the next column the terms in Twi (an Akan language); the third column specifies torelationship (key below) and the right hand column outlines (if appropriate) the literal meanings of theTwi words.

Additional Information Concerning Akan Kinship Terminology



Example: MoSiDa indicates a person’s mother’s sister’s daughter, a relation normallyexpressed in English simply, and precisely, as ‘cousin’.



Specific information was collected in collaboration with Michael Djan, SOS Hermann-GmeinerInternational College, Ghana

AmaKwameMemendaSaturday

Afua/EfuaKofiFiedaFriday

Aba/YaaKwaw/YawYawodaThursday

Akua/EkuaKwekuWulkudaWednesday

Abena/ArabaKobinaBenadaTuesday

AdjoaKodjo/kojiDwodaMonday

EsiKwesiKwesidaSunday

Female NameMale NameDay (Fanti)Day (English)

Akan Names



Lesson 6: Language and Symbolism

Cont ex tThis lesson is useful in raising distinctions between the strengths of body language and thestrengths of language symbolism in communication. It can also help make distinctions betweensigns and symbols. It includes a game which leads to discussion on the capacity of language tocommunicate what physical gestures cannot.

Aim s To examine the symbolic nature of language.

To investigate the use of language for abstraction through an introductory game of charades.

Class Managem ent This lesson takes 40 to 50 minutes, though the discussion questions can occupy more time. Theclass is divided into small groups to play the game first, and then brought back together fordiscussion.

Cards such as those which follow must be prepared in advance. They are only suggestions.Those written by teachers referring to situations to which their own students can relate would bemore effective. You will need one pair of cards per group.Have all the card As in one colour, and all the card Bs in another colour. You should mark eachcard clearly on the back as A1, B1, A2, B2, and so on, so that it is possible to move cards fromgroup to group for a second round of the game and still keep track of what each group isdoing.

Foc us Ac t iv i t yDivide the class into groups of four to six students and disperse them in the classroom. Thendivide each group in half. Give the first half of the group a card A, on which is written a description of a situation whichthey must act out for the second half—without using any words. The second half of the groupmust guess as accurately as possible what is being communicated, with the goal of being able toreproduce verbally the description on the card without having seen it.

Then give the second half of the group the equivalent card B, for them to act out in turn.The TOK twist to this game of charades is that the cards are in pairs. The A cards describeconcrete objects, physical actions, and emotions, all of which are fairly easy to enact. The B cardsshift to greater level of detail, abstract ideas, connection in time, space, or consequence, and otherrelationships such as addition, contrast, and exception.

Be prepared for indignant wails from students on first reading a card B.


St udent Handout

You have just had a serious conversationwith your parents about going to university

You have just had a serious conversationwith your parents about whether you should

You have just received a phone call fromyour mother who tells you that your brotherhas just won a huge scholarship to studyastrophysics at a top university in England,beginning next autumn.

You have just received a phone call fromyour mother who tells you that the familypet dog has died.

A friend comes to you, very excited,because he/she has just been hired to writea feature article for the regional newspaperon a project on which he/she will beassisting an art expert who restores oldpaintings and establishes their authenticity.

A friend comes to you, very excited,because he/she has just won a huge prizein a lottery and wants you to come alongand celebrate.

Although your marks in mathematics arenot very good, you enjoy the challenge ofstudying mathematics, because you findthe intellectual rigour satisfying andconsider the subject to be fundamental tosuccess in other areas such as economicsor engineering.

You find mathematics very difficult. Youhave studied hard for a test, but your markis still bad and you feel extremelydiscouraged.

You are in love with someone, but refuse totake your emotions seriously, because youregard love as a destructive force whichcan undermine good judgment and leadcouples into hasty and ill-fated marriageswhich can end only in divorce.

You are in love with someone, but all yourefforts to attract his/her attention fail, andyou are left with a broken heart.

CARD BCARD A



after your Diploma Programme studies, orwhether you should work and save for ayear first in order not to build up a debt fromthe very beginning of what will probably beseveral years of higher education.

go to university after your DiplomaProgramme studies.

CARD BCARD A



Disc ussion Quest ions What, on the cards, was easy to act out? What was difficult? Why? Are there some things forwhich body gestures and expressions are more effective than words? Are there some things forwhich words are more effective in communication? What is a symbol? What is the relationship between a word and that to which it refers?

Is body language natural, or is it learned? How might body language vary across cultures—in theextent to which it is used for communication, and in the significance given to gestures? Possibleexamples for discussion are: one’s sense of personal space, the use of eye contact, gestures foryes and no, for come here, for flirtation, for aggression or insult. How might the accompanyingbody language affect the meaning of utterances?Is sign language for the deaf more accurately considered to be body language or a symbolicsystem?

What effect does the existence of our symbol system of language have on knowledge?

Link s t o Ot her Areas of TOK How does language compare with other symbolic forms of communication such as

painting, dance, music and mathematics? Would it be possible to place all these forms in arange or spectrum according to any of the following qualities: precise–evocative;rational–emotional; representational–abstract; specific–general?

Is knowledge restricted to claims made in language? Can a look or gesture communicateknowledge?

How does the anthropologist or other practitioner of the human sciences gain knowledge ofan individual or culture? How might the context of body language be significant in methodsof observation and interview?

From Ot her Tim es and Plac esA discussion of the variability of body language around the world, both in its acceptability and itsspecific gestures, places language in its cultural context.

Referenc esAxtell, RE (ed.), Do’s and Taboos A round the World, (1993) John Wiley and Sons, ISBN0471595284

Farb, P, Word Play: What Happens When People Talk, (1993) Vintage Books, ISBN 0679734082



Lesson 7: Words and not Words: anExercise in Describing and Listening

Cont ex tBecause this lesson is designed to show how difficult it is to express even a simple idea in such away that the receiver will properly understand it, it is best used at the beginning of the course oras a refresher at other appropriate times. Students are encouraged to consider whether all sortsof knowledge can be communicated in words.

Aim s To consider the relationship between perception and language.

To develop an awareness of problems involved in communicating ideas and knowledge.

Class Managem entThe class should be divided into groups of five or six students. Each group should appoint aleader.

In advance of the lesson, teachers will need to make a copy of Picture A and Picture B for eachof the student leaders. All the other students, the followers, will require two pieces of graph(squared) paper each.One hour of class time should be allowed for the completion of the two activities. Additionaltime will most likely be required for group discussion and reflection.

Foc us Ac t iv i t yThe lesson consists of two different activities, A and B. They may be taken in any order. Duringactivities A and B, the followers are required to listen attentively to the leaders’ instructions anddraw a series of figures on the graph paper. After activities A and B are completed, the teacher, astudent or a group of students could award marks to the pictures completed by the followers.Once activities A and B are completed, results can be discussed as a class.


St udent Handout

Lesson 7: Words and not Words: an Exercise in Describing and Listening


Activity A

One student is appointed the leader. The rest of the group are followers. The leader describes Picture Averbally. The followers are to listen and, without collaboration, attempt to draw the picture, with the sameshape, the same size and the same orientation, on their graph paper. There should be no other

communication other than the leader’s description. No questions are allowed from the followers.

Picture A

Activity B

This activity is similar toactivity A: anotherpicture such as the onebelow should be used,but the followers arenow allowed to ask foradditional information.

A

B

Disc ussion Quest ions Compare the process of the verbal transfer of knowledge, as done in activities A and B,

with the transfer of knowledge between teacher and student in a school lesson. Whatsimilarities and differences exist?

Compare the process found in activities A and B with the process of a student acquiringknowledge by reading a text. What similarities and differences are there?

By what means can our ideas and opinions be made more clear to others in a conversationor when writing?

What is the difference between information and knowledge?

Relat ed Quest ions If language works according to sets of rules and conventions, how much scope do we have

as individuals to break the rules, to challenge conventions, to be creative? Are vagueness and ambiguity shortcomings of language that must be eliminated in the

interest of knowledge, or can they be also viewed as positive aspects of language?

From Ot her Tim es and Plac esFrom the writings of Benjamin Whorf (1897–1941) we learn that:The categories and types that we isolate from the world of phenomena we do not find there because they stare everyobserver in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to beorganised by our minds—and this means largely by the linguistic system in our minds.

From this he concludes his principle of linguistic relativity. . . which holds that all observers are not led by the same physical evidence to the same picture of the universe,unless their linguistic backgrounds are similar.

This allows for a different view of one’s relationship to reality, and to the role of language in thisrelationship. After all, the linguistic distinctions that we use so frequently lead us to believe that theworld is really made up of all those things that I talk about all day. This may be why our languagehas all the terms that it does—so we can refer to this huge variety of things out there.

Quot a t ion

The crucial point to be considered in a study of language behaviour is the relationship betweenlanguage and reality, between words and not words. Except as we understand this relationship,we run the grave risk of straining the delicate connection between words and facts, ofpermitting our words to go wild, and so of creating for ourselves fabrications of fantasy anddelusion.

Wendell Johnson

Referenc esFarb, P, Word Play: What Happens When People Talk, (1993) Vintage Books, ISBN 0679734082Minsky, M, The Society of Mind, (1988) Simon and Schuster, ISBN 0671657135



Hayakawa, AR & SI, Language in Thought and A ction, (1991) Harcourt Brace, ISBN 0156482401



Lesson 8: Nothingness

Cont ex tOne of the central functions of language is to express thought. However, identifying otherfunctions of language is important so that the power of language can be assessed. If language isonly a tool by which we express our thoughts, then we may command it and use it for our ownends. If, however, language is not only a tool but is also a shaper, forming thought, identity andmemory, then we may be commanded by it. Among other things, then, the knowledge we haveis dependent to some extent upon it and we may not be as free as we assume we are.This lesson belongs to a consideration of language, after the introductory material has beenpresented. It is fairly sophisticated, but beginning students have responded well to its inherentdrama.

Aim s To discuss the fundamental nature of language and its role in all knowledge systems. To consider linguistic determinism in human life and to question, therefore, claims of free

will.

To consider whether or not language creates, clarifies, or obscures what is true.

Class Managem ent This lesson is based on the reading of a single poem. It is divided into two different groupsessions with reports back to a full class and a discussion as a result of those reports. The lessonusually requires 100 minutes to complete and can easily be done over two consecutive classsessions.

Group Session IDivide the class into groups of three and ask each group to complete the following tasks (allow20 minutes).

One student should read the poem out loud to the other two. The repetition of thepoem may serve to dramatize the fear in the poem.

Choose a recorder or spokesperson. Write down in one sentence the central knowledge claim of the poem.

Cite as much evidence as possible for that claim from the poem itself. Summarize what life seems to be with language and what it seems to be without it.

Write down any experiences, anecdotes or memories students have, that are similar tothe contents of the poem or support the central claim of the poem.

Ask students to rejoin the whole class and give each group a chance to present its insights andexamples (allow 30 minutes).


Group Session I IAs the general discussion wanes, have students count off in numbers, 1–5. Assign knowledgesystems to each number:1 The arts

2 History3 Human sciences

4 Natural sciences5 Mathematics

Have each group prepare a brief report for the whole class on the particular way(s) this poemwould be true or not true for the discipline the group represents (allow 20 minutes).Ask students to balance theoretical, abstract conclusions with specific cases drawn particularlyfrom their Diploma Programme subjects.

Once again, ask students to rejoin the whole class and compare their central findings (allow 30minutes).


Nothingness

I woke up at night and my language was gone No sign of language no writing no alphabet

nor symbol nor word in any tongue and raw was my fear—like the terror perhaps

of a man flung from a treetop far above the ground a shipwrecked person on a tide-engulfed sandbank

a pilot whose parachute would not open or the fear of a stone in a bottomless pit

and the fright was unvoiced unlettered unuttered and inarticulate O how inarticulate

and I was alone in the dark a non-I in the all-pervading gloom

with no grasp no leaning point everything stripped of everything

and the sound was speechless and voiceless and I was naught and nothing

without even a gibbet to hang onto without a single peg to hang onto

and I no longer knew who or what I was and I was no more

Aharon Amir, translated from the Hebrew by Abraham Birman



Disc ussion Quest ions What are some feasible working definitions of language? Why does the poem take place at night in close proximity to sleep and dreams?

How might it be among our worst nightmares to wake up and find language gone? Orhow, on the other hand, might it turn out to be heaven on earth, or a dream come true, towake up and be forever unencumbered by language?

How accurate is the contention at the close of the poem that the absence of languageamounts to annihilation?

If languages are systems of symbols, how can we be sure that the symbol represents thething for which it stands?

If language rests on symbols, how can it be the thing itself, that is our identity, ourconsciousness, our life?

If one takes the symbol away, does not the thing itself remain? If we lose the symbol, what is it that we have lost if not the thing for which the symbol

stands?

What is it in human life that having the symbol seems to supply us with? To what extent is every kind of human knowledge dependent upon having a symbol system

through and within which it can be formulated?

How does language resemble other things or people to whom we grant power? Can it be said that language is one of the several instances in human life in which we create

something, forget we have made it, and yield to it maximum authority? What other instances,if any, are there in which we do this?

Identify several different kinds of language. Are any more effective than others in changingnothing to something?

One definition of a miracle is the bringing of something out of nothing. Considering the titleof the poem, can language be considered a miracle? Are there any instances or stories thatdepict language not as a miracle but as a curse? Which position seems to be the stronger?

How can we be sure that something we coax out of nothing through language is anything atall?

Are there any advantages to entering the nothingness and forfeiting the language that seemsto anchor us in something?

Having once acquired a language, is it ever possible for us really to stop talking? Once wetake on a language, can we ever really lose it?

Rather than language, what would you prefer as the basis for knowledge, reality, personalidentity?

If you were to write a poem about the absence of language, would fear be the dominantemotion you would emphasize or would you stress some other emotion?

The poem implies that we are dead the minute we lose language. In what way(s) is this claimtrue? How could it be justified? How valid would it be to claim that we are dead the minutewe begin to speak?

How might nothingness, especially linguistic nothingness, be among the most substantialstates on earth?



Link s t o Ot her Areas of TOKThe lesson centres on language, with links to perception and emotion in the TOK guide and, ingroup session II, to areas of knowledge. It is also relevant to the linking questions aboutinterpretation and truth.

From Ot her Tim es and Plac es Hinduism, Buddhism and Christianity each have traditions which encourage the loss of

speech. Studying these pursuits of silence and the practitioners of such pursuits offerscounter-arguments to the ideas of this poem.

Biblical and mythological stories also both affirm and deny the central importance oflanguage in human life.

The life of Helen Keller provides a wonderful, specific case of language as miracle.

The account of Samuel Johnson as he describes waking in the night unable to speak becauseof a stroke is a wonderful case of facing linguistic impairment without fear.

Quot at ions

We live not on things, but on the meaning of things. Antoine de Saint-Exupéry

Words form the thread on which we string our experiences. Aldous Huxley

All human thought comes into existence by grasping the meaning and mastering the use oflanguage.

Polanyi



Lesson 9: The Map is not the Territory

Cont ex tThis lesson is effective following discussions of the capacity of language to map the worldsymbolically. When Alfred Korzybski declared that the map is not the territory he was referringto language, whose representation of the world is not to be confused with reality itself.

Aim s To consider the nature of symbolism and conventions for representing the world.

To recognize assumptions that may arise from past structures of power.

Class Managem ent Two hours are required. First allow the class to take a good look at wall maps of the world.Raise questions of projections and centring. The following should emerge.

A flat map is a distortion of a sphere, and a wall map is inevitably a simplification of theworld’s detail.

Particular representations carry hidden assumptions and values.

Maps, like languages and theoretical models, are conceptual tools.The teacher should take on primarily a questioning role, with students doing their own analysis.However, the teacher may wish to introduce passages for reading, or give historical background.

Foc us Ac t iv i t y1 Display a minimum of three wall maps of the world that differ in their projections and their

placement of particular regions in their centre. Ideal maps are a Mercator projection centredon Europe, a Peters equal-area projection, and a map which appears to be upside-down,with south at the top. Also valuable are maps which centre on the United States, with Indiarepeated at both sides of the maps to allow the symmetry, any Asian or Middle Easternmaps with their own areas at the centre, and satellite pictures of the earth from space.

2 Have ready, on handouts or overheads, a few examples of conceptual maps, in which thesize or shape of the countries is determined not by geographical size, but by other criteriasuch as population, trade balance, or incidence of a disease.

3 Have ready, on handouts or overheads, maps which are supplemented with graphics—pictures of nature or recreation (from tourist brochures), bold concentric circles for indicationof ripple impact, arrows for movement of armies (from a history text or newspaper).

Use these visual examples to raise questions about conceptual schemes which influencerepresentation. Each category raises slightly different questions.


Having established that maps are not simply perceptual records, move to overt conceptual mapsto raise questions of statistics, and then to maps embellished with graphics, to consider the finedistinction between clarification and persuasion.


Part 1: Geographic al and Pol i t ic a l Wor ld Maps Which wall map looks to you most natural? Why? As you look at all three of them, do they

suggest different things to you?

Which region is in the centre? Why? Which region appears largest? How much is Scandinavia or Australia affected by the

projection? Which map takes as its goal the showing of regions according to their relativesize?

Is it necessary for north to be at the top? What distinguishes north from south when there isno up or down in space? If the poles are determined by the earth’s rotation, what thendivides east from west?

Is the prime meridian placed by geographical necessity—or by a decision that could beotherwise? Do we have associations other than geographical designations with west, east,north and south?

Are borders part of nature? Are they visible if the world is viewed from space? What doborders and naming represent on a world map?

Part 2: Conc ept ual Maps When the size and shape of countries on the map represent not their geography, but another

concept, what is the difference between a map and a pictorial graph? Why use a world map?

How do we know that the statistics behind the representation are accurate? What is thesource of the statistics? How are the terms defined? What is the significance of samplingtechniques— representative samples, adequate samples?

Part 3: Graphic Enhanc em ent of Maps To what extent do symbols drawn from elsewhere combine with maps solely for purposes

of clarification? How do arrows or concentric circles help us to visualize movement acrossspace? Can those graphics be drawn differently to imply benefit or menace?

Can colour on a map create an emotional impact? What do you associate with countriescoloured red? If a country coloured white is surrounded by countries coloured black, doesthe colour distinction carry any emotional impact?

Why include pictures on a map? What non-geographical ideas are being conveyed?

Link s t o Ot her Areas of TOKApart from obvious connections with symbolism, this lesson can raise discussions of valuejudgments, contrasting conceptual schemes around the world, the legacy of history in ourknowledge of today, and the association of knowledge with power.



From Ot her Tim es and Plac esAn examination of our maps of the world is an examination of our conceptions of the worldand our place in it; this lesson should bring out shifting perspectives. In considering the waymaps can be conceptual tools—or tools of power—it is fruitful to bring in whatever historyseems relevant to the particular group of students. For example, you could consider associationof the Mercator projection with European imperialism, ways in which European powersinfluenced reality by drawing from afar borders in Africa, why the Kenya / Tanzania border isdiverted around Kilimanjaro, map-based land claims which exclude aboriginal concepts of landas something which cannot be owned, maps which play for sympathy for an encircled country(for example, Israel in the Arab world), or the use of maps in combination with technology tofix a wartime target without face-to-face contact with the enemy.

Quot at ion

The map is not the territory. Alfred Korzybski

Referenc esHarley, JB, ‘Maps, Knowledge, and Power’, The Iconography of Landscape: Essays on the SymbolicRepresentation, Design and Use of Past Environments (Cambridge Studies in Historical Geography), ed.Denis Cosgrove and Stephen Daniels, (1994) Cambridge University Press, ISBN 0521389151

Monmonier, M, How to Lie with Maps, (1996) University of Chicago Press, ISBN 0226534219Introduction only.Shohat, E & Stam, R, Unthinking Eurocentrism, (1994) Routledge, ISBN 0415063256

Wood, D, The Power of Maps, (1992) The Guildford Press, ISBN 0898624932Kidron, M & Segal, R, The State of the World A tlas, fifth edition, (1995) Penguin, ISBN0140252045. Recommended for conceptual maps.

Peters equal-area projection wall map available from the Friendship Press, P.O. Box 37844,Cincinnati, Ohio 45222, USA



Maps made it easy for Euro-pean states to carve up Africa andother heathen lands, to lay claimto land and resources, and toignore existing social and politicalstructures… That maps drawn upby diplomats and generalsbecame a political reality lends anunintended irony to the aphorismthat ‘the pen is mightier than thesword.’

Monmonier, How to Lie withMaps, Univ. of Chigago 1991.

Map Knowledge:A Pragmatic Approach

Aboriginal maps can only beproperly read or understood by theinitiated, since some of theinformation they contain is secret.This secrecy concerns the ways inwhich the map is linked to the wholebody of knowledge that constitutesAboriginal culture. For Aborigines, theacquisition of knowledge is a slowritualized process of becoming initiatedin the power-knowledge network,essentially a process open only tothose who have passed through theearlier stages. By contrast, the Westernknowledge system has the appearanceof being open to all, in that nothing issecret… In the Western tradition theway to imbue a claim with authority is toattempt to eradicate all signs of its local,contingent, social and individualproduction.

In the light of these considerations weshould perhaps recognize that all maps,and indeed all representations, can berelated to experience and instead ofrating them in terms of accuracy orscienticity we should consider only their‘workability’—how successful they arein achieving the aims for which theywere drawn.

David Turnbull in Wood, The Power ofMaps, Guildford Press, 1992.

Map KnowledgeSo how do we know the earth is round? We know the earth is round because

(almost) everybody says it’s round, because in geography class our teacherstell us it is round, because it is round on map after map… Ultimately, the mappresents us with the reality we know as differentiated from the reality we see andhear and feel. The map doesn’t let us see anything, but it does let us know whatothers have seen or found out or discovered, others often living but more oftendead, the things they learned piled up layer on top of layer so that to study eventhe simplest-looking map is to peer back through ages of cultural acquisition.

Denis Wood, The Power of Maps, Guildford Press, 1992.

CARTOGRAPHY: KNOWLEDGE & POWERCartography, whatever other cultural significance may have been attached

to it, was always a ‘science of princes’. In the Islamic world, it was the caliphsin the period of classical Arab geography, the Sultans in the Ottoman Empire,and the Mogul emperors in India who are known to have patronisedmap-making and to have used maps for military, political, religious, andpropaganda purposes. In ancient China, detailed terrestrial maps werelikewise made expressly in accordance with the policies of the rulers ofsuccessive dynasties and served as bureaucratic and military tools and asspatial emblems of imperial destiny. In early modern Europe, from Italy to theNetherlands and from Scandinavia to Portugal, absolute monarchs andstatesmen were everywhere aware of the value of maps in defence andwarfare, in internal administration linked to the growth of centralisedgovernment, and as territorial propaganda in the legitimation of nationalidentities… With national topographic surveys in Europe from the eighteenthcentury onwards, cartography’s role in the transaction of power relation usuallyfavoured social elites.

JB Harley, ‘Maps, Knowledge, and Power’, The Iconography of Landscape, Cambridge 1994.

Eurocentrism, like Renaissance perspectives in painting, envisions theworld from a single privileged point. It maps the world in a cartography thatcentralizes and augments Europe while literally ‘belittling’ Africa. The‘East’ is divided into ‘near’, ‘Middle’, and ‘Far’, making Europe the arbiterof spatial evaluation, just as the establishment of Greenwich Mean Timeproduces England as the regulating center of temporal measurement.Eurocentrism bifurcates the world into the ‘West and the Rest’ andorganizes everyday language into binaristic hierarchies implicitly flatteringto Europe: our ‘nations’, their ‘tribes’; our ‘religions’, their ‘superstitions’;our ‘culture’, their ‘folklore’; our ‘art’, their ‘artifacts ’; our ‘demonstrations’,their ‘riots’; our ‘defense’, their ‘terrorism’.

Ella Shohat and Robert Stam, Unthinking Eurocentrism, Routledge 1994.

St udent Handout



Lesson 10: Thinking Logically?

Cont ex tThis lesson can be done after a consideration of the nature of reasoning, or before looking atfallacies. It links into work on scientific methodology.

Aim To investigate the extent to which logical thinking is influenced by the subject matter.

Class Managem entThis lesson can be completed in 40 minutes, or longer if necessary.In advance of the lesson, photocopy the two Logic Tests overleaf. You will need one copy ofthe two tests for each student. Students may be given the two problems at the same time (on thesame sheet of paper), or one following the other.

Ask the students to work out and write down their answers without collaborating, and then toreport them back to the whole class. Compile a list of votes for each card on the blackboard.Overwhelmingly, students fail to identify the 7 as one of the correct responses in Logic Test 1.Explain to the class why 7 is correct (this card is capable of falsifying the rule) and why 2 iswrong (this card is irrelevant to the rule).

Students normally identify the correct answers for Logic Test 2.Discussion can then proceed as to why, given that the two problems are formally identical, one isso much easier to solve correctly than the other. Reference can be made to the importance ofform and content in logical reasoning, and how this may affect the building of knowledge.



St udent Handout

Logic Test 1

You are presented with the following rule:Every card with a vowel on one side has an even number on the reverse side.

These are the cards.

U G 7 2

Logic Test 2

You are a barperson in a night-club. The club has the following rule:Every person drinking alcohol must be over 20 years of age.

These are the four situations.

Persondrinking beer

Persondrinking

lemonade

Person aged19 years

Person aged21 years

Lesson 10: Thinking Logically


Disc ussion Quest ions Compare your answers for the two examples given. Justify your choices. The two examples are formally identical (that is, their underlying structure is the same), yet

many people do not choose the same answers. Why not?

Might this difference reflect something about human thinking in general? Why is it easier tospot the correct answers in the second example?

One view of the nature of science is that scientific activity is primarily about generatinghypotheses and then trying to falsify them. What might these examples have to do with this?

Link s t o Ot her Areas of TOK What is fallacious reasoning? Why are fallacies so often persuasive and plausible? Why is mathematics, as a school subject, so difficult for many students at the advanced

levels?

From Ot her Tim es and Plac es In what way, if any, might good reasons vary across cultures? Is there knowledge beyond the categories of logic? If so, what are its foundations?

If arguments in ordinary life are not formally set out so as to exhibit clearly their formalstructure of premises and conclusions, how can this structure be identified?

Quot at ions

The paradox is now fully established that the utmost abstractions are the true weapon withwhich to control our thought of concrete fact.

A N Whitehead

If a man can play the true logician, and have as well judgement as invention, he may do greatmatters.

Francis Bacon

It is not therefore the object of logic to determine whether conclusions be true or false; butwhether what are asserted to be conclusions are conclusions.

A de Morgan



Referenc esThe examples given here are adapted from tests devised by Peter Wason of University College,London. Most authors refer to them as Wason Tests. The following four books all refer to themin somewhat differing contexts.Plotkin, H, Darwin Machines and the Nature of Knowledge, (1997) Harvard University Press, ISBN0674192818

Wolpert, L, The Unnatural Nature of Science, (1994) Harvard University Press, ISBN 0674929810Ridley, M, The Red Queen, (1995) Penguin, ISBN 0140245480

Gardner, H, The Mind’s New Science—A History of the Cognitive Revolution, (1987) Basic Books, ISBN0465046355Note: Plotkin’s book includes a résumé of the research of L Cosmides in taking this workfurther, into what Cosmides calls the logic of social exchange. The TOK teacher could perhapsinvestigate the relevance of this statement.



Lesson 11: Routes of MathematicalKnowledge

Cont ex tThere is a tendency in many TOK discussions to perceive the rational as Western and thenon-rational as belonging to the non-Western. Most students tend to think of knowledge systems as being fully formed and sprung upon them.This lesson allows the student to explore the development of a system of knowledge.

Students also assume that knowledge systems are pure, and that they have a life of their own. Asassessment questions sometimes ask students if knowledge can be affected by culture or otherinfluences, this lesson reveals that knowledge systems like mathematics and logic can respond topolitical, economic and cultural influences, by offering the dual perspectives of Asian andEuropean politics.

Aim s To follow the development of both Asian and European frameworks for mathematical

knowledge, and to explore the possibility of a common heritage.

To reveal the stages of formation in a system of knowledge. To challenge the assumption that rationalism is a Western product.

Class Managem ent This activity might involve a visit to the library, followed by the return to the classroom. Abouthalf an hour could be spent creating a timeline and making a web of exchanges of knowledge.The rest of the lesson or part of the next can be spent in discussion of the questions.


St ep OneGive each student an index card with one of the following research topics on it. Send thestudents to the library to research (date and place) their topic for about 20 minutes. Anencyclopaedia will be the best source of reference as there is insufficient time for extensiveresearch.

Teacher Support Material—Theory of Knowledge Lessons from Around the World © IBO, November 2000 Lesson 11—page 1

Suggest ed Researc h I t em s

Infinity Zero Calculus

Trigonometry Geometry Probability

Algorithm Chaos Theory Ramanujan

Euclid Omar Khayyam Decimal system

Algebra Pythagoras’ Theorem Abacus

St ep Tw oEach student should describe his/ her findings and place the topic on a timeline on theboard—so creating the periods of knowledge development and points of transference.

St ep ThreeExamine the completed timeline. Discuss the origins of each topic and any interdevelopment.

Disc ussion Quest ions Conventional division of the mathematical history timeline separates into periods: earliest times toancient Babylonia and Egypt, the Greek contribution, the Far-Eastern and Semitic, and theEuropean from the Renaissance onwards.1 Can mathematical knowledge be called the most international of all systems of knowledge?

2 Does Western mathematical theory diverge from Eastern mathematical theory? Explain youranswer.

3 The development of mathematical knowledge is often illustrated by a tree diagram (that is,roots labelled as arithmetic, the trunk labelled as calculus). Mathematical scholars often selectthe banyan tree as the best tree for such an illustration. Why might this be so?

4 Why is the vast Asian learning in mathematics so little known in the rest of the world?5 Asian students are expected to do well in mathematics. What is the basis of this expectation?

6 What assumptions are challenged by the brief research the students did?7 Is mathematics invented or discovered?

Link s t o Ot her Areas of TOK What is the role of inductive and deductive reasoning in mathematical knowledge? What is the connection between mathematics and logic?

How do you explain the impact of culture or politics on mathematical knowledge? What is mathematical truth?

Are the conclusions of mathematics concerned with truth or validity?

Lesson 11: Routes of Mathematical Knowledge


From Ot her Tim es and Plac es Pythagoras (or his school) is recognized for the theorem relating the lengths of the sides of a

right-angled triangle (that the square on the hypotenuse of a right-angled triangle is equal tothe sum of the squares on the other two sides). It should be noted, however, that this wasknown in China some 400 years before Pythagoras. It is thought that Pythagoras’ discoverywas independent of the claim of the Chinese. This example, along with others (Newton andLeibnitz are given credit for their independent discoveries of calculus during the nineteenthcentury) supports the argument that mathematics more or less exists in nature and is waitingto be discovered.

Enrichment was provided unexpectedly in this class when a Ghanaian student researchedoracle bones as a means of mathematical measure and told us their purpose. Students fromother cultures—such as Korean and Japanese and Latin American—might wish to investigatetheir own culture’s contribution to mathematical knowledge.

Quot at ion

When a flower brings forth a blossom with six-fold symmetry, is it doing mathematics? from ‘A Physicist Looks at Mathematics’, Philip J Davis & Reuben Hersh

Referenc esDavis, PJ & Hersh, R, The Mathematical Experience, (1999) Mariner Books, ISBN 0395929687McLeish, J, Number, (1992) Flamingo, ISBN 0006544843

Joseph, GG, The Crest of the Peacock, (1991) Penguin, ISBN 0140125299

Lesson 11: Routes of Mathematical Knowledge


Lesson 12: Is Math for Real? (a TOK Quiz for Mathematical Knowledge)

Cont ex tThis lesson serves as an introduction to a unit on mathematical knowledge. It could be presentedat any time during the TOK course, but is best given after a unit on reasoning.

Aim s To reflect on the nature and formation of mathematical knowledge.

To develop arguments for and against various issues surrounding the formation ofmathematical knowledge.

Class Managem entThe lesson requires one 40–60 minute period for a class of 12 to 20 students, divided intogroups of three. Each member of the group should receive a copy of the quiz and be allowed15–20 minutes to complete it and discuss the how and why of their answers within the group.

Members of each group are encouraged to compare and contrast their answers with those ofother members in the group. At least 20 minutes should be allowed for class discussion. One can normally expect a fairamount of class interaction with arguments and counter-arguments being presented. Becausesome questions tend to result in rather predictable answers, the teacher, as the discussion leader,must be prepared with supporting examples in mind.

Foc us Ac t iv i t yThe following two pages comprise the quiz. A copy should be given to each student.


St udent Handout



A TOK Quiz for Mathematical KnowledgeCircle the letter(s) of the appropriate answer(s) for each of the following. Discuss these answerswith the people in your group and prepare to give supporting arguments for your selections.

1 Mathematics is a subject about:

A logical thinkingB illogical thinking

C things that exist in natureD things that do not really exist at all

E things that are certainF things that are not certain.

2 Problems in mathematics can best be solved by using:

A clever tricksB experiments

C computersD graphic calculators

E trial and errorF investigations

G discussionH the answers in the back of the textbook.

3 Mathematics is a subject that should be studied by:

A people who are interested in itB engineers and other people who want to apply it

C people who are challenged by itD people who want to become better thinkers

E people who are intrigued by its aesthetic qualitiesF people who want to become better artists

G people who want to improve their overall academic performanceH people who want to improve their college entrance exams

I all Diploma Programme candidates



4 Which of the following best describes mathematics?

A a body of knowledgeB a practical tool

C a cornerstone of philosophyD the perfection of the logical method

E the key to understanding natureF an intellectual game

G an aesthetic experience.

5 One plus one is:A always equal to two

B sometimes equal to twoC never equal to two

D too philosophical to think about.

6 Parallel lines:6 never intersect

7 always intersect8 do not exist.

7 Which of the following quotations best captures the essence of mathematics?

A A mathematician is a blind man in a dark room looking for a black cat which isn’tthere.

Charles Darwin

B Pure math is a game. It’s fun to play. We play it for its own sake. It’s more fun thanapplying it. Most of the math that I teach is never used by anyone. Ever.

Ted Williams, Prep School Mathematics Teacher

C If you ask your mother for one fried egg for breakfast and she gives you two fried eggs andyou eat both of them, who is better in arithmetic, you or your mother?

Carl Sandburg

D Mathematics is a game played according to certain simple rules with meaningless marks on

Disc ussion Quest ions Comments for the teacher’s use:1 Do any mathematical statements seem illogical at first glance? Why, for example, do we say

¾ + ½ = ¾ % 2?

It will be difficult to associate all aspects of mathematics with natural phenomena. Tryfinding in a natural setting.1 i- =

Mathematics is not the total solution that some people claim it to be. It has been found(Gödel’s Incompleteness Theorem) that any system of logic (mathematics included) will byits very nature be incomplete. That is to say, certain questions will be unanswerable. Considerthe following paradox:

If the Barber of Seville shaves all men in Seville who do not shave themselves, then whoshaves the Barber?

Can we apply this question to the formation of mathematical knowledge? For example, ismathematical knowledge formed in some experimental manner?

2 What is the basis of the formation of mathematical knowledge?3–4Who is interested in mathematical knowledge and why?

May mathematicians consider theorems like Euclid’s or other mathematical proofs to beworks of art?Why must all Diploma Programme candidates take mathematics? Perhaps justificationcomes with the choice of answers for question 4, most of which come from a descriptionof mathematics by Morris Kline.

5 Is A the obvious answer here? After all, Bertrand Russell took 362 pages in Principia Mathematica to prove that 1 + 1 = 2.And we can certainly think of examples of nature from the very simple to the complexwhere the meaning of ‘to add’ does not function in the usual mathematical sense. Consider,for example: What is the sum of one drop of water with another drop of water? Thisexample may seem trivial, but it must not be quickly dismissed. The branch of mathematicsknown as Chaos Theory was developed only when mathematicians were able to see that1 + 1 does not always equal 2 in the natural world (see The Meaning of ‘To A dd’: TheMathematical Experience, by Davis and Hersh).

6 Students are often surprised to learn that all three answers may be correct, as they tend tolive in some sort of Euclidean world. See notes in ‘From Other Times and Places’.

7 The real issue in this question is one of truth. What kind of truth are we talking about?

Link s t o Ot her Areas of TOK How does the formation of mathematical knowledge differ from that of scientific

knowledge and historical knowledge? What role does logic play in the formation of mathematical knowledge?

How does mathematical proof compare to proofs in other forms of knowledge? What is the value of acquiring mathematical knowledge?



From Ot her Tim es and Plac esMost of the geometry taught in schools is based upon the work Euclid undertook over 2000years ago. However, in the early nineteenth century brilliant mathematicians altered the work ofEuclid and formed geometries that gave rise to mathematical knowledge seemingly contrary tothat of Euclid. The two mathematicians who formed these non-Euclidean geometries wereRiemann and Lobachevsky. Examples of different conclusions reached by the three geometriesinclude:

more than 180°less than 180°equal to 180°The sum of the angles ofa triangle are…

do not existalways intersectdo not intersectParallel lines…

RiemannianLobachevskianEuclidean

Riemann and Lobachevsky came to these different conclusions by falsifying Euclid’s 5thpostulate (through any point on a plane there is one and only one line parallel to a given line).When this postulate was replaced with other postulates, the entire system of axioms remainedconsistent, and eventually gave rise to different conclusions. This example shows that how wedescribe the world mathematically is not necessarily dictated by nature.

Quot at ions

Mathematics may be defined as the subject in which we never know what we are talkingabout, nor whether what we are saying is true. Bertrand Russell

The most distinct and beautiful statements of any truth must take at last the mathematical form.Henry David Thoreau

How can it be that mathematics, being after all a product of human thought independent ofexperience, is so admirably adapted to the objects of reality?

Albert Einstein

Referenc esDavis, PJ & Hersh, R, The Mathematical Experience, (1999) Mariner Books, ISBN 0395929687

Eves, HW, A n Introduction to the History of Mathematics, 6th edition, (1990) College Pub, ISBN0030295580Kline, M, Mathematics in Western Culture, (1965) Oxford University Press, ISBN 019500714X

Russell, B, Principia Mathematica, (1997) Cambridge University Press, ISBN 0521626064



Lesson 13: Numbers and Numerals

Cont ex tMost of us are so familiar with the system of numerals we use that it is hard for us to appreciatecertain features of that very system. In order to highlight these features, this lesson asks studentsto design their own system of numerals. In this way, shortcomings and ambiguities in what theycreate can demonstrate more clearly the necessary characteristics of an effective system forrepresentation and manipulation of numbers.As numbers are so fundamental to mathematics, this lesson could serve as an introduction to thatarea of knowledge in the Theory of Knowledge guide.

Aim s To distinguish between numbers and the symbols which represent them. To make evident some of the assumptions embedded in our use of numerals.

To recreate and highlight some of the great leaps forward in number representationthroughout the history of mathematics.

Class Managem ent Divide the class into small groups. Hand out some paper for rough work. Provide atransparency and markers so that each group can present its scheme to the class.

It is important to allow sufficient time for sharing of students’ work across groups since it is herethat the lesson’s aims can largely be fulfilled. Suggested time allocations are: 30 minutes for devising a system

30 minutes for presenting the systems to the other groups 20 minutes for summing up.

One copy of the following focus activity and discussion questions should be given to eachgroup.The student handout Numeral Systems from Different Parts of the World provided with thislesson plan could serve as a follow-up homework assignment to be discussed in the next session.


Foc us Ac t iv i t yGive the students the following task:1 To invent a series of symbols to represent numbers.

These symbols should not be the same as any numeral system known to them.The number of different symbols and how they may be combined with one another (ifat all) is entirely their choice.

2 To explain their numeral system to another group of students.To show their audience how to represent:

Three Forty-five

Twenty One hundred and seventeen

3 Devise a series of problems for other students to solve, using their system of symbols.

Disc ussion Quest ions What is the advantage of employing place value?

Why does the number system which we generally use have base 10? What is the advantage of having a numeral for zero?

Is there a difference between zero and nothing?

Teac her Not esA set of assumptions will probably manifest itself. These assumptions generally involve thefollowing concepts.

Place Value: the meaning of a given symbol changes according to its position in thenumeral sequence representing the number.

Base 10: the value of a given symbol increases tenfold for every single shift of position tothe left.

Zero: students often omit a symbol for zero in their initial scheme, but invent one when itsdesirability becomes clear.

Link s t o Ot her Areas of TOK Can we think of mathematics as a language? Which features of language does it possess?

Look closely at the following quotation. Do you agree with it?

N umbers constitute the only universal language. Nathaniel West

Many words refer to objects or classes of objects in the world (that is, they have adenotation). What do numerals denote or refer to?



From Ot her Tim es and Plac es

Hom ew ork Assignm entConsider the information supplied on the handout Numeral Systems from Different Parts of theWorld.Prepare responses to these questions.

How many symbols are needed in each system? Does the system use a base? If so, what is it?

Does it employ place value? Does it use a zero?

Where exactly did each of these civilizations exist? What do the dates associated with the development of each number system suggest?

Quot at ions

One, two, buckle my shoe; three, four, knock at the door. Nursery Rhyme

Philosophy is written in this grand book, the universe, which stands continually open to ourgaze. But the book cannot be understood unless one first learns to comprehend the languageand read the letters in which it is composed. It is written in the language of mathematics.

Galileo

Referenc esMcLeish, J, Number, (1991) Flamingo, ISBN 0006544843Joseph, GG, The Crest of the Peacock, (1991) Penguin, ISBN 0140125299



St udent Handout

Num era l Sys t em s f rom Di f fe rent Par t s o f t he Wor ld



Lesson 14: A Show of Hands

Cont ex tThis lesson can be used as an introduction to TOK work on perception, since it addresses thefollowing questions. How far do we trust and rely on our sensory perceptions?

How does our knowledge change when our perceptions are shown to be wrong?

Aim s To examine the nature and reliability of knowledge gained by perception.

To examine the relationship between perception, knowledge and belief.

Class Managem entStudents should not be forewarned of this activity. Total time should involve no more than30–40 minutes including 5–10 minutes to photocopy hands and retrieve the copy. The remaining25–30 minutes should be used for class discussion.

Foc us Ac t iv i t yTake the class to an available photocopier. Have the students remove all rings and bracelets.Photocopy the right hand of every student. Work out some method of identifying (only for theteacher) which copy belongs to which student. Move back to the classroom. Lay out the copies on desks in a random order and allow thestudents five minutes to identify and retrieve their hand.

Lead the class in a discussion of what led them to think that they had identified the correct handas their own. Reserve the correct identification until after students have had some time to explainwhy they feel they have identified their own hand. Reveal the correct and incorrect choices, thendiscuss how their perception was correct or faulty.

Disc ussion Quest ions How did you form your hypothesis about which copy was yours and which ones were not? What factors influenced your final decision?

Was your final choice a matter of picking what was left after eliminating all the obviouslyincorrect, or was a different process at work?

What different types of perception were involved in your choice?

What types of evidence were involved in your choice? If you picked incorrectly, how and why was your knowledge false? Is there such a thing as

false knowledge?


What does this exercise suggest about the knowledge gained from perception? How reliableis it? Is something more than perception necessary for knowledge to be gained?

Link s t o Ot her Areas of TOK

Perc ept ion In which areas of knowledge is perception essential for the acquisition of that knowledge?

Is there such a thing as knowledge which is independent of perception? If so, what sort ofknowledge would it be?

K now ers and K now ing What, if anything, is the difference between believing and knowing?

The Ar t s What kinds of accurate and informative statements do images convey?

From Ot her Tim es and Plac esPlato’s Cave (c350BCE) examines the question of image and reality—what is real and what ismerely a shadow of what is real. Well-known visually ambiguous illustrations, by Escher, forexample, could be used to reinforce the aims of the lesson.

As technology and multimedia become more prevalent in education and in students’ lives, willthere be a parallel increase in relying on graphical information to make judgments?

Quot at ions

To know and yet think we do not know is the highest attainment. Not to know and yet thinkwe do know is a disease.

Lao-Tzu

All human knowledge is uncertain, inexact and partial. Bertrand Russell

He walked toward the sheets of flame. They did not bite his flesh, they caressed him andflooded him without heat or combustion. With relief, with humiliation, with terror, heunderstood that he also was an illusion, that someone else was dreaming him.

Jorge Luis Borges

Referenc esAbel, R, Man is the Measure (Chapter 3 and 4), (1997) Free Press, ISBN 068483636X

Discovering Psychology Series, Film 7, Sensation and PerceptionNational Geographic Video, The Invisible World

Gaarder, J, Sophie’s World, (1996) Boulevard (Mass Market), ISBN 0425152251





Lesson 15: Myths and Fairy Tales

Cont ex tMany students regard myths and fairy tales as sources of purely fictional entertainment. Yet theyhave been and still are an important source of knowledge and understanding.Students should consider the ways in which myths and fairy tales might be understood as part ofhistory, psychology, religion and, of course, the use of myth as a pejorative term to indicatefalsehood. What sort of understanding is provided by myths? What truths, if any, do they containand if they contain truths, how can they be verified? How much of what we think to beknowledge or reasonable belief today might, on closer analysis, turn out to have been myth (inthe pejorative sense)?

When we realize and reflect upon the universal importance and presence of myths in humancivilization, we can be brought to realize the deep human need for qualitative maps of reality tocomplement the purely quantitative maps of reality provided by the physical sciences. We mightalso realize the equally dangerous consequences of neglecting the quantitative maps of reality.Students may be brought to realize that our knowledge and understanding requires a sensitivebalance between the powers of imagination and those of reason—that upsetting the balance canlead either on the one hand to impersonal, inhuman forms of understanding and knowledge or,on the other, to the equally oppressive tyranny of fiction and fantasy.

Aim s To analyse the nature of myths and fairy tales as sources of knowledge and understanding

about ourselves and our environment.

To compare the knowledge and understanding which can be gained from these sources withscientific knowledge and understanding.

Class Managem ent Teachers need only familiarize themselves with a few myths and fairy tales and bring examples into their class. If further research is required they could turn to writings by Bruno Bettleheim, CarlJung and Joseph Campbell.

Foc us Ac t iv i t yAsk the students to collect together as many myths and/ or fairy tales as they can and bring themto the next lesson. Try to resist requests for further clarification of the task, because it is to behoped that there will be a variety of interpretations as to what a myth and what a fairy tale is,which will be reflected when the material is presented. This can form a starting point for adiscussion of their nature and epistemological status.Ensure that you bring your own selection of myths and fairy tales from your own and othercultures. You may wish to bring some writings on myths and fairy tales to stimulate some morediscussion.


Disc ussion Quest ions 1 What is a myth?

You may wish to point out the etymological origin of the English word “myth”, namelyfrom the Greek “mythos” meaning a speech/ utterance/ word in the sense of a story. Thiscontrasts with “logos”, meaning “word” in the sense of rational discourse, discussion,argument. Myths, in one sense, are concerned with storytelling, giving meaning, purpose,value and direction to our lives (that is, qualitative forms of understanding and knowledge).This contrasts with the sciences, which are not normally concerned with questions of humanor divine purpose or value judgement, but are rather seen as providing only quantitativemaps of reality. These assumptions can, of course, be challenged.

2 Can myths provide a way of understanding (ourselves and our world) that is complementaryto that provided by logic, science, social science and religion (with which myths are sointimately connected)? Myths are often concerned with explaining the origins of features of our landscape. Theexplanation might give an account of how, for example, a mountain, rock or river acquiredthe features it now possesses. Or myths might relate to features of animals, such as the clawsof a lion, the stripes of a tiger, or the spots of a leopard. Or they might relate to humancharacteristics—such as the origin of a race, nation or tribe. Or they might relate tometaphysical and ontological concerns such as why humans are so powerful and destructive.What explains the origin of our propensity for good and evil? What is the origin of moralprinciples? Why is there suffering? Why is happiness so fleeting?

Myths and fairy tales have provided answers which are characteristically anthropomorphic.They provide answers that are stories. Can they be regarded as true or valid in any sense,now that the sciences (both physical and social) have come to dominate all our acceptedmeans of understanding and explaining?

3 To what degree is it possible and desirable to arrive at explanations and knowledge of ourworld that are free of all human value judgements and perspectives? Can science ever bevalue-free and totally objective?

4 What are the comparative roles of reason and imagination in science and in myths and fairytales?

Link s t o Ot her Areas of TOKMyths and fairy tales can be linked to many elements of TOK. Do myths, for example, containtheir own logic? How can we define a mythological use of language; and how are mythologicaland religious forms of language related?

Myths and fairy tales provide potential sources of understanding and knowledge of ourenvironment which may or may not be compatible with those provided by the sciences. Thesame could be said of our understanding of ourselves. In some human sciences, such as psychology, myths and fairy tales have assumed greatimportance: for example, in Freudian and Jungian psychoanalysis as the archetypes of theunconscious. In the study of history, myths and mythological language play a major role.



From Ot her Tim es and Plac esModern Myths: what myths (in the sense of stories that are assumed to be true, but have little orno evidence or reasonable justification to support them) are there today in society? Possibleexamples may include the popularity of the supernatural, phenomena such as fortune telling andpsychic powers, also the fascination with UFOs and crop circles, and modern mythologies suchas the Star Wars trilogy and Star Trek in many Western countries. This fascination could berelated to a human reaction against the cold, impersonal, rational picture of reality presented bythe physical sciences, with UFOs replacing visitations by gods to compensate for our loneliness ina meaningless universe devoid of purpose.Another example of modern mythology might be the rise in popularity of New Age religionsand the revival of talk of Mother Earth (a delicate, creative, female life force) in response toenvironmental concerns and the destructive effects of understanding the earth in purelymechanical, materialistic, scientific terms. Again, this concerns the difference between qualitativeand quantitative forms of knowledge and understanding.

There are many possibilities for classroom activities, from discussions to debates to dramaticrepresentations of myths. Could one say that myth and the arts are closely intertwined, where oneis re-enacting a story or a drama, weaving together meaning and purpose, in contrast to science,which appears unable to articulate understanding into drama and appears unable to givedirection and purpose to human knowledge?

Quot at ion

Fairy tales or fairy land is nothing but the sunny country of common sense . . . the world isa wild, startling and delightful place which could have been otherwise . . . fairy tales providea certain way of looking at life: certain things are necessary (in the sense that it cannot beimagined otherwise) in nature. There is no necessary law saying that eggs must turn intobirds or that fruit falls in Autumn. The explanation of such events is magic, just like theanswer to the question why do mice turn into horses in Cinderella.

… Nature is best explained by fairy book terms: ‘charm’, ‘spell’, ‘enchantment’ (rather than‘laws’, ‘necessity’, ‘tendency’ et cetera), for they express the arbitrariness of the facts of natureand their mystery. A tree grows fruit because it is a magic tree; water runs downhill becauseit is bewitched, et cetera.

… This elementary wonder, however, is not mere fancy derived from the fairy tales; on thecontrary, all the fire of the fairy tales is derived from this . . . This is proved by the fact thatwhen we are very young children we do not need fairy tales. Mere life is interesting enough.

… Nursery tales only echo an almost pre-natal leap of interest and amazement. These talessay that apples were golden only to refresh the forgotten moment when we found that theywere green. They make rivers run with wine only to make us remember, for one wildmoment, that they run with water.’

Orthodoxy, GK Chesterton

Referenc eBettelheim, B, The Uses of Enchantment, (1989) Vintage Books, ISBN 0679723935



Lesson 16: Why was Thales Wrong?

Cont ex tThis lesson can be used as an introduction to the problems of knowledge in the natural sciences.Thales (c624–c545BCE) was a Greek philosopher, mathematician and astronomer. He was oneof the Seven Sages named by Plato, and according to Aristotle was the founder of physicalscience.

Aim To exemplify the test of a scientific hypothesis.

Class Managem entOne week in advance of the lesson students should be asked to spend some time observing thenight sky. In particular, they should note the pattern of the stars on two occasions on the sameevening, making the second observation about two hours after the first.

The lesson will take 40 to 60 minutes, including the initial 15 minute presentation by the teacher.An OHP and screen will be required, and the transparencies (Thales OHPs 1, 2 and 3), includedwith this lesson.

Foc us Ac t iv i t yBegin the lesson by discussing how the pattern of the stars appears to move in great circles(OHP 1). Continue by describing Thales’s explanation of this phenomenon (OHP 2). The keyfeatures are as follows. The bowl of the sky which holds in the waters which surround the land.

The eternal fires which burn outside the sphere. The windows through which the fires are glimpsed. The little fires are the stars.

The God who turns the bowl carrying the stars and so causes the nightly rotation of thepattern of the stars.

Disc ussion Quest ionsMost of the discussion will be directed by student answers to the question “Why was Thaleswrong?” The discussion might proceed as follows.

The little windows will let in water as the sphere turns below the horizon. Be unfair andpoint out that portholes do not leak.

A God turning a handle is not science. What other mechanism could there be? Does itmatter?


What about the sun or moon? Point out that Thales is attempting to explain the movementof the stars, not objects very different in appearance.

What about the little fires in the sky? Do they all move in the same way?

Why do the planets not follow this pattern? The Greeks called them planetes, or wanderers(OHP 3).

Was Thales wrong because his explanation did not fit the facts?

Are you sure he was wrong?

Link s t o Ot her Areas of TOK Are disciplines other than cosmology equally susceptible to extraordinary knowledge claims?

From Ot her Tim es and Plac es Thales’s explanation is an example of a hypothesis which was a product of its time. How

does this compare with other explanations offered in the past? Can you identify historical examples of seemingly wild claims later being substantiated?

Can you think of contemporary explanations of natural phenomena which might beridiculed in the distant future?

Quot at ion

It is a capital mistake to theorize before one has data. Arthur Conan Doyle, The Memoirs of Sherlock Holmes

Referenc esKoestler, A The Sleepwalkers (1959) Penguin Books



Thales: OHP 1

Pole Star

Why does the night sky do what it does?

A first observation

The pattern of stars appears to rotate to the right. The pattern remains thesame with all of the individual stars appearing to make a circular movementaround the pole star.



Thales: OHP 2

The bowl is turned nightly, carrying the pattern of little fires in great circlesaround the axis. The stars are glimpses of the eternal fire seen through little‘windows’ in the bowl of night and day.



BURNING OUTSIDETHE BOWL

BOWL ISTURNED NIGHTLY

E

ETERNAL FIRES

Thales: OHP 3

Not all of the little fires move in great circles. A small number loop back onthemselves. The Greeks called them planetes, or wanderers.



Lesson 17: One Person’s Hypothesis isAnother Person’s Dogma…

Cont ex tMany students think of hypotheses as belonging only to science, but the idea of educatedguessing and testing belongs to nearly all ways of knowing. Students should consider the numberof ways in which belief might be understood. Check to see if the term initially carries onlyreligious connotations. This lesson can be helpful almost anywhere in the course.

Aim To examine how hypotheses, and the beliefs that underlie them, are formed.

Class Managem entThe lesson could be managed in one class period of 50 minutes, but two would be preferable. Prepare multiple copies of the student handout.

Divide the class into groups of no more than four students. Distribute the handout and allow theclass time to read it. Depending on the total number of students, discussion can be a whole classdebate, or as parallel debates.

Foc us Ac t iv i t yRefer to the student handout.

How is t he Ac t iv i t y In t roduc ed?Simply say that students will discuss and debate a position they may find difficult or unusual, andthat they should defend their hypothesis until such time as another group gives them irrefutableproof that they are wrong.Assign each group a hypothesis (A or B or C). Instruct them to imagine all the possible reasonsthey could give in defence of their hypothesis.

Teac her Not esStudents may need some advice as to possible strategies to defend their position. For instance,group A could add to their hypothesis the theory that there are nocturnal and diurnal propertiesthat explain why night and day have this effect, but that also explain the behaviour whenanomalies occur, such as fire making it rise at night, and cold water making it drop in the daytime. This makes their position almost impregnable. C should be asked to remember that theirspirits are capricious, which destroys any attempt to subvert their hypothesis with the systematicbehaviour of the thermometer… And so on…


St udent Handout

The Three MartiansThree Martians, A, B and C, were crossing the Great Victoria Desert when they came upon anobject (a thermometer) which had possibly been lost by an explorer.Having observed it for a few days, they realize that there is something inside it (the column ofmercury) which at different times can be seen to be in different positions.

They discuss the possible reasons for such strange behaviour.A proposes the hypothesis that the behaviour is related to the time of day. This would explain

why at night the column drops, and why it rises during the day.

B suggests that the reason must be heat and cold, which also would explain why it drops at nightand rises during the day.

C says that both A and B are wrong. The real reason for the movement lies in the nature of theenclosed substance that is animated by invisible spirits who adopt a capricious behaviour whenimprisoned. These spirits make the substance rise or fall whenever they feel like it. This wouldexplain what both the other hypotheses have explained; moreover, it would explain anyvariation, at any time and under any circumstances.

Lesson 17: One Person’s Hypothesis is Another Person’s Dogma…


Disc ussion Quest ions How is each hypothesis formed? How do they differ? Why do they differ if all three are

Martians? What are the roles of intuition, prejudice, inductive and deductive thinking in forming the

hypotheses?

What assumptions or beliefs are behind each hypothesis? How do these beliefs affect thequestions the Martians will ask?

What are the virtues of each hypothesis?

How would you test each hypothesis? How would the Martians test the hypotheses? What would count as evidence against each hypothesis? Of what, in fact, would you have to

convince each person?

Suppose you agree with B. Could you help her convince A and C that their hypotheses arefalse? Of what, in fact, would you have to convince C?

What are the requirements of any hypothesis in science?

What is the demarcation, if any, between scientific and pseudo-scientific knowledge claims?

Addi t iona l Quest ions

Depending on the level of the students, the following more sophisticated questions can be raised.

Do you experience the learning of scientific knowledge in school as resting on foundationalbeliefs about the natural world?

Can we think of any knowledge claim that does not make a foundational or basicassumption even though it may not be apparent?

If all our claims to knowledge are built upon basic beliefs about reality, how can we everchange our point of view? Does innovation come about from those who are aware thatbehind all our interpretations are assumptions that both allow knowledge and hinder it?

From Ot her Tim es and Plac esPlato’s student Aristotle explained gravity (the phenomenon of falling objects, if you like) bysaying that things sought their natural place in the universe. This was also the reason for flamesrising as they aspired to be with the sun. What a beautiful idea compared to our present views onthis. What view of the world allows for this notion of things that seek or aspire to besomewhere else? Are there no beliefs lying behind the notion of the force of gravity, or ofcurved space?

That previously held beliefs are the basis of our claims about the world can already be found inHume’s Critique of Induction. It might be worth a teacher exploring questions in relation to thePrinciple of Uniformity, or the Principle of Causality.Teachers might want to explore further the work of Kwasi Winedu, University of Ghana, fordifferences and similarities between traditional and scientific societies in forming and testinghypotheses.



Link s t o Ot her Areas of TOKNearly all areas of TOK are touched by this exercise. In language, the various meanings of belief should be noted. For instance, the phrase “I

believe” does not carry an identical meaning in the context of “I believe in God” to its use inthe context of “I believe in honesty”.

In reason, could we have argument at all without premises? If we did not have basic beliefs,would we not be caught in an infinite regression?

In the human sciences, do different cultural beliefs lead to different values and hypothesesfor explaining behaviour?

In history, students might try to find areas where hypotheses are formed and tested in wayssimilar to or different from those identified for the focus lesson. How do beliefs about thepast influence enquiry in ways perhaps not realized by the scholar?

The arts do not make claims in quite the same way, but do schools of painting or literaturehave basic tenets that guide their activity?

In ethics, there is fertile ground for discussion of beliefs underlying moral action. Forinstance, are beliefs about what is of value central to forming a code of morality?

Quot at ions

The great tragedy of Science—the slaying of a beautiful hypothesis by an ugly fact.TH Huxley

Man is a credulous animal and must believe in something; in the absence of good groundsfor belief, he will be satisfied with bad ones.

Bertrand Russell

Referenc esOlen, J, Persons and Their World, (1983) McGraw Hill College Div, ISBN 0075543117

Miller, M, Introduction to Logic, Living Logic, (1978)Anderson, WT, Reality Isn’t What It Used To Be, (1992) Harper Collins, ISBN 0062500171



Lesson 18: Scientific Claims: an AfricanPerspective

Cont ex tCertain knowledge claims are reliably supported by scientific activity. On the other hand, certaintraditional beliefs are justified in a less rigorous manner, although there are similarities in the waysin which each claim might have come into existence: repeated observation, generalization,inspired ideas, or prediction and explanation. Given these similarities between the origin of scientific claims and these other traditional beliefs,how do we know what counts as science?

By the subject matter? By the nature of the explanation? By the theory or law involved?

By the proofs? Or just by belief?

Aim To investigate what constitutes a scientific knowledge claim and whether such claims can be

differentiated from other sorts of claims.

Class Managem ent The activity could be completed in about one and a half hours.

This activity lends itself well to work in small groups. It might be advisable to mix themembership of each group so as to spread the science-inclined students and any particularnational or cultural groups. On the other hand, concentrating such differences in particulargroups may enrich a subsequent discussion between groups.Encourage students beforehand to bring examples of taboos or superstitions to the class.

Foc us Ac t iv i t yWhich of the following can be regarded as scientific claims?1 During the first seven days after birth, it is dangerous to expose a child to the outdoors or to

strangers.

2 When a man and a woman both have sickle-cell anaemia, it is dangerous for them to havechildren.

3 Singing while bathing is dangerous.

4 Bringing bundles of firewood from the farm into the village is dangerous.


5 Smoking cigarettes is dangerous.6 Cutting a tree in the forest without performing certain rites is dangerous.

7 Fishing on Tuesdays is dangerous.8 A live, non-insulated electric wire is dangerous to touch.

9 Pounding fufu after dark is dangerous.10 Driving after drinking alcohol is dangerous.

Teac her Not es1 In Ghana, infants are not displayed to the public or indeed officially named until

(traditionally) eight days after birth. This takes place at an outdooring ceremony. Variousexplanations are concerned with high infant mortality rates in the past, or with the infant’ssusceptibility to infection. Thus there may be a social or a biological basis, or both, orsomething else—symbolic?

2 Sickle-cell anaemia is a genetically transmitted blood disorder particularly prevalent insub-Saharan Africa. When two carriers (that is, having sickle-cell anaemia), each possessingonly one copy of the faulty gene (and thus not seriously affected) have children, the chancesof any one child having full sickle cell anaemia is 25%. The carrier condition confers extraresistance to malaria, and this is the reason for the high incidence of the gene in this part ofthe world.

3 This is an old Akan taboo from Ghana, possibly related to the toxicity of the soap used inthe past.

4 Tied bundles of firewood could conceal weapons, or could provide a route for snakes toenter the village undetected.

5 No note required.6 There may possibly be some connection with the conservation of forests, especially given the

importance of a stock of plant species for herbal medicinal purposes.

7 The Ga of southern Ghana do not fish on Tuesdays—origins in conservation or socialcohesion . . .?

8 As 5.

9 Fufu is a Ghanaian food preparation consisting of ground cassava, yam, cocoyam orplantain which is pounded into a starchy paste, shaped into gelatinous balls and served with aspicy soup containing fish or meat. Pounding after dark would require artificial lightingwhich might attract insects into the mixture. Alternatively, a lack of light would prevent thepeople involved from seeing what was happening to the dough. Also, pounding fufu is anoisy activity…

10 As 5 and 8.

Disc ussion Quest ions Consider each of the claims given. Suggest how each of them could have come into

existence. In each case, what sorts of thinking processes and types of reasoning might havebeen involved? Observation, generalization, application of generalizations, inspiration…

Compare your answers for the different claims. Are there aspects of the thinking processesinvolved which are common to most or all of them? If so, what are they?

Lesson 18: Scientific Claims: an African Perspective


Is it possible to construct very different, but equally believable, routes by which these claimscould come into existence? Compare different claims here. What problems are there insuggesting their possible origins?

Which of the claims do you regard as being scientific? Justify your answers. Do you have asingle criterion for distinguishing the scientific from the non-scientific? Or is it necessary touse several criteria? Has the distinction more to do with method or content or result, orsomething else?

If a claim works in everyday life, is there any need for further explanation? Does it matterwhat kind of explanation is provided?

To what extent is each of us as an individual justified in believing each of these claims?

Why do non-scientific beliefs persist in groups of people familiar with scientific explanation? Explanations for taboos are often given in supernatural terms. Is it possible to reconcile

natural and supernatural explanations?

If science and taboos are both about laws, then how, if at all, do these types of laws differ? Is this attempt to rationalize beliefs always justified? Are there beliefs which arose in quite

non-rational ways? If so, how?

Link s t o Ot her Areas of TOK Does knowledge always require that good reasons be provided? In what way, if any, might the phrase “good reasons” vary across cultures?

What is meant by the scientific method? How is this method traditionally described in sciencetextbooks? Is this depiction an accurate model of scientific activity or could it be adistortion?

How does the social context affect the questions and results of the scientific enterprise?

What is the demarcation between scientific and pseudo-scientific knowledge claims? In the context of attempting to explain and predict human behaviour, what sort of approach

would be most effective? A scientific approach? An approach based on cultural beliefs?

To what extent is it necessary that a person’s beliefs are consistent?

From Ot her Tim es and Plac es List some superstitions or other beliefs from your own background. What sort of claims are

these? How do they compare with the examples here?

Traditional beliefs are sometimes criticized on the basis that they do not explain things.Consider Newton’s Law of Universal Gravitation. What is and what is not explained here?Is there a difference between science and medicine in terms of the explanations they aim ator provide?

Quot at ions



Science is facts; just as houses are made of stones, so is science made of facts; but a pile ofstones is not a house and a collection of facts is not necessarily science.

Henri Poincaré

Science is nothing but trained and organized common sense. TH Huxley

Referenc esChalmers, AF, What Is This Thing Called Science?, (1999) Hackett Pub Co, ISBN 0872204529Wolpert, L, The Unnatural Nature of Science, (1994) Harvard University Press, ISBN 0674929810

Feynman, RP, The Character of Physical Law, (1994) Modern Library, ISBN 0679601279Appleyard, B, Understanding the Present—Science and the Soul of Modern Man, (1992) Picador, ISBN0330320130

Wiredu, K, Gyekye, K, et al, Person and Community—Ghanaian Philosophical Studies I, (1992) TheCouncil for Research in Values and Philosophy, ISBN 1565180046Gyekye, K, A n Essay on A frican Philosophical Thought—The A kan Conceptual Scheme, (1995) TempleUniversity Press, ISBN 1566393809



Lesson 19: The Growth of ScientificKnowledge

Cont ex tThis lesson is best used when the class has already devoted some time to the topic of scientificknowledge, during which several examples of scientific claims, drawn especially fromexperimental science studies, are established.

Aim s To consider the nature of the growth of knowledge in the natural sciences.

To develop argument(s) for a particular growth explanation (either presented or created) aswell as arguments against other explanations (either presented or created).

To compare the growth of scientific knowledge with the growth of knowledge in otherareas of the TOK programme.

To consider the several ways in which the term “growth” might be used, and how these, inturn, might influence the conclusions we reach about knowledge.

Class Managem ent The lesson usually requires 40–60 minutes. The class is best divided into groups of three or fourstudents. Each member of the group should receive a copy of the student handout, containingthe instructions and The Growth of Scientific Knowledge: A n A nalysis by Six Scientists.

Each group should be allowed 15–20 minutes to discuss the various interpretations given withthe graphs or to create a graph that better represents the growth of knowledge. Each groupmust give reasons in support of their selection as well as reasons why other interpretations werenot selected.An open discussion should then follow, in which each group’s findings and conclusions areconsidered. An abundance of arguments and counter arguments is a good sign.

Foc us Ac t iv i t yThe following three pages (one page of instructions and two pages of graphs) should be copiedfor each student.


St udent Handout

Lesson 19: The Growth of Scientific Knowledge


The Growth of Scientific Knowledge

InstructionsEach of you has been given a set of graphic interpretations put forward by six different scientistsconcerning the growth of scientific knowledge.

1 Carefully study each of the interpretations given by the scientists.2 Discuss these different interpretations with your group and select the one that you find

appropriate. If you find that none of the six ideas is appropriate, and you would like topresent another idea, then clearly illustrate or define your interpretation.

3 Make a brief note of the argument in support of your selection. List at least one reason foreach of the other interpretations as to why it has been rejected. Do not hesitate to use supportexamples from your own experience of science or from your study of science in the DiplomaProgramme.

4 Select a group leader who can communicate your selection and rationale to the rest of theclass.

In approximately 20 minutes we will reassemble to discuss results from each of the differentgroups.

The Grow t h o f Sc ient i f i c K now ledge: An Analys is by Six Sc ient is t s

Six distinguished scientists have met to discuss to what extent scientific knowledge can be said to grow.When asked to produce graphs representing the accumulation of knowledge (K) versus time (T), thescientists replied as follows.Scientist A demonstrated that the growth of scientific knowledge has occurred simply in a linear way asshown below.

K

T

A

Scientist B showed that knowledge claims have not grown in straight linear fashion but curvilinearly.Note that the curve represents a rapid growth of knowledge claims in the earlier days, while moremodern claims appear to occur less and less frequently.

K

T

B

Scientist C stated that she agreed with Scientist B’s curvilinear interpretation but that she disagreed withthe way the curve had been drawn. Scientist C stated that the most rapid growth has occurred not at thebeginning of recorded knowledge but rather at the end, as shown below.

K

T

C

Scientist D stated that the growth of scientific knowledge claims has come not in a strictly linear fashionnor in a curvilinear way but rather in a piece-wise linear manner. He argued that the steps or breakpoints in the curve represent major discoveries (eg electricity, laws of motion, atomic energy).

D

K

T



Scientist E agreed with the spurt growth of knowledge described by Scientist D, but added yet anotherpoint to consider. She stated that once a major claim of knowledge has come to light, other prior claimsmay be falsified. Therefore we see that after a major stair-step jump, we have a slight drop off in totalclaims still considered to be true.

E

K

T

Scientist F had to disagree with all others. He stated that the growth of scientific knowledge is allrelative to what we know at a particular time. He asserted that science has actually raised more questionsthan it has answered. Indeed his curved graph shows a decrease in knowledge (that is, relative to theamount of knowledge that humans actually thought they knew at a particular time).

K

T

F



Disc ussion Quest ions What are the different meanings of the phrase “to grow”, and how do the implications

change with its changing meanings? What are the different causes of the growth of scientific knowledge?

What are the factors that limit or contribute to the stagnation or decline of knowledge in thenatural sciences?

What are some of the factors that influence the problems or questions that scientists decideto work on?

Does the element of chance play a role in the accumulation of scientific knowledge? Does and/ or should a scientist’s gender or culture or personal beliefs influence his/ her

judgements as to what is or is not scientific knowledge or worthy of scientific investigation?

What role do different kinds of logic play in the growth of scientific knowledge? Do notions of science appear to be becoming more complex as time goes by, or do ideas

appear to be reducing to a simpler form? How would one assess such an issue?

What is the notion of a paradigm shift, particularly as it is presented by Thomas Kuhn in hisStructures of Scientific Revolution?

Link s t o Ot her Areas of TOK Does the word “growth” predispose us to certain conclusions about knowledge?

How do other forms of knowledge such as mathematics, ethics, history, and the arts,compare to science on this issue of growth?

Compare the accumulation of knowledge in an individual with the accumulation ofknowledge in a knowledge system. What can be said about each individual’s accumulation ofknowledge? What are the factors that contribute to the differences in the accumulatedknowledge among individuals? Have these factors been identified in this lesson ascomponents of growth in scientific knowledge?

In terms of political judgements, how do political issues, such as government subsidies ordefence needs, contribute to activities in science?

In terms of ethical judgements, how does the urgency of a problem or the moral worth of aproblem contribute to or detract from scientific endeavours?

To what extent are scientific activities driven by economic considerations?

From Ot her Tim es and Plac es What do the efforts to achieve cold fusion imply about the way science grows?

What does Fleming’s discovery of penicillin imply about the nature of scientific growth? What does the debate surrounding Darwin’s Theory of Evolution contribute to the growth of

scientific knowledge?

What do the experiences of Copernicus and Galileo suggest about the nature of scientificchange?



Quot at ions

Science is not a system of certain, or well-established, statements; nor is it a system whichsteadily advances towards a state of finality.

Karl Popper

Even if the open windows of science at first make us shiver after the cosy indoor warmth oftraditional humanising myths, in the end the fresh air brings vigour, and the great spaces havea splendour of their own.

Bertrand Russell

Referenc esBarrow, JD, Theories of Everything, (1991) Clarendon Press, ISBN 0198539282Collins, H & Pinch, T, The Golem: what you should know about science, (1998) Cambridge UniversityPress, ISBN 0521645506

Chalmers, AF, What Is This Thing Called Science? (1999) Hackett Publishing Co, ISBN 0872204529Abel, R, Man is the Measure, (1997) Free Press, ISBN 068483636X



Lesson 20: Webs of Explanation

Cont ex tExplanations in various disciplines often seem to rely on what is known from other disciplines.This lesson investigates how different subjects are related in terms of such explanations. In thisway, the extent to which knowledge can be regarded as a continuum can be discussed. Thelesson is best used after the mid-point of the course.

Aim To investigate the relationships between different forms of knowledge by focusing on

explanations.

Class Managem entHand out copies of the statements sheet (in the focus activity) to the entire class. Ask the studentsto classify the statements according to the two questions at the foot of the sheet.



St udent Handout

Statements

1 Organic remains turn into oil because high pressure and heat prevent organisms from utilizingthese remains.

2 The behaviour of subatomic particles can be described by mathematical functions.

3 Human qualities such as aggression and charisma are the result of the way that the human brainworks.

4 Ions behave as they do largely because of an imbalance of protons and electrons (that is, theyare charged particles).

5 Country X invaded country Y because X’s leader is aggressive and charismatic.6 There are oil deposits under country Y because abundant plant and animal remains in that area

were crushed under pressure at high temperatures for millions of years.

7 Country X invaded country Y because country Y has large reserves of oil.8 The brain works largely because of the movements of sodium and potassium ions through

brain cell membranes.

Question A To what extent does each of these statements belong in a particular subjectdiscipline?

Question B How can these statements be ordered in a sensible sequence?



Disc ussion Quest ions Are the boundaries of disciplines fixed or changeable? Could we create a different set of

disciplines which would partition knowledge in a different way? Do you think the traditional boundaries between disciplines are ‘natural’? Are they helpful to us?

Are there disciplines which rely largely on explanations from another discipline? To what extent is it possible to seal off a discipline from other disciplines?

Is it possible to string together a number of statements so that one statement can beexplained by another statement far removed from it?

Is everything ultimately explicable in terms of subatomic particles? If not, why not? If so,what would this mean?

Is there a distinct border between the human sciences and the natural sciences? Or is theresimply a continuum?

Is it possible to produce an ordered hierarchy of disciplines? If so, on what basis?



Teac her Not esOne diagram often constructed by students is illustrated below. Clearly, this is not the onlyoption. The main three issues highlighted by this scheme are:1 alternative frameworks of explanation for history

2 a reductive sequence for the natural sciences which may or may not include psychology3 the relationship of mathematics to the other subject disciplines.

PSYCHOLOGY

HISTORY

GEOGRAPHY

CHEMISTRY

BIOLOGY

PHYSICS

MATHEMATICS

HISTORY

HUMAN SCIENCES

NATURAL SCIENCES

MATHEMATICS

Areas of Knowledge



Link s t o Ot her Areas of TOK In what way, if any, should the methods of the natural sciences be exemplars for the social

sciences? Can human knowledge be confined to what the natural sciences discover? What other

important enquiries are not covered by the natural sciences?

Are causes and reasons both required for full historical understanding? Why is mathematics so important to the physical sciences?

From Ot her Tim es and Plac esIt is instructive to examine the ways in which disciplines have been partitioned in the past, forexample, ‘natural history’ and ‘natural philosophy’. Why are these categories no longer favoured?The English use of the word ‘science’ is quite different from that in Germanic and Scandinavianlanguages, for example, where its meaning is more inclusive.

In modern times, a number of new interdisciplinary subjects have gained prominence, such asbiochemistry, geophysics, art history and economic history. Why?

Quot at ions

God may have separated the heavens from the earth. He did not separate Astronomy fromMarine Biology.

Jonathan Levy

The historian makes a distinction between what may be called the outside and the inside ofan event… When a scientist says “Why did that piece of litmus paper turn pink?” he means“on what kinds of occasions do pieces of litmus paper turn pink?” (… the outside of theevent). When a historian asks “Why did Brutus stab Caesar?” he means “What did Brutusthink which made him decide to stab Caesar?” (… the inside of an event).

RB Collingwood

The human brain craves understanding. It cannot understand without simplifying; that is,without reducing things to a common element. However, all simplifications are arbitrary andlead us to drift insensibly away from reality.

Lecomte du Nouy

Referenc esRyan, A, The Philosophy of the Social Sciences, (1976) Macmillan, ISBN 0333109724

Searle, J, Minds, Brains and Science, (1986) Harvard University Press, ISBN 0674576330Casti, J, Searching for Certainty, (1991) Abacus, ISBN 0349104557



Documents

Lessons from Around the World - Wikispaces · PDF filePreface Conceived at a TOK meeting at Arden House in New York State in 1993, the project to provide examples of TOK lessons to