2 AOKHow do we know things? We know things because we use a range of methods of inquiry that incorporate ways of knowing to help construct knowledge in different areas of knowledge (AOKs). The theory of knowledge course distinguishes between eight AOKs: • mathematics • natural sciences • human sciences • history • the arts • ethics • religious knowledge systems • indigenous knowledge systems
3 Knowledge frameworkWithin this knowledge framework, key features of each area are identified, as are specific terminology and concepts which shape that area of knowledge. The key historical developments that have influenced and shaped each area are identified, as well as the ways that each makes use of particular methodology. Finally, there is opportunity for reflection on the interaction between shared and personal knowledge in each area.Knowledge frameworks are a very effective device to compare and contrast areas of knowledge. The idea is that each AOK can be thought of, broadly speaking, as a coherent whole—a vast system with a rich inner structure. TOK aims to explore this structure and to understand just what it is that gives each AOK its particular character. It is also concerned with what these AOKs have in common. A useful strategy is to build a TOK course around comparing and contrasting the various AOKs, to look for features they have in common but also to highlight their differences and pinpoint what gives each its own characteristic flavor.
4 1. Scope/applications• What is the area of knowledge about? Subject matter might distinguish disciplines or fields that share some of the same methodology. • What practical problems can be solved through applying this knowledge? This is an important question because it reinforces the idea we mentioned earlier that knowledge can be seen as an attempt to solve a particular set of problems. • What makes this area of knowledge important? Any teacher worth his/her salts should be able to argue for the importance (or even the primary importance) of his/her subject.
5 1. Scope/applications• What are the current open questions in this area—important questions that are currently unanswered?It is useful for you to be confronted with two facts: that areas of knowledge are incomplete and that they are adapting to solve as-yet open questions.• Are there ethical considerations that limit the scope of inquiry? If so, what are they?You should be confronted with the possibility that there might be questions that might be unethical even to ask. Should researchers ask how to make a more effective landmine to maim more civilians per dollar, for example? (Brainstorm more examples?)
6 1. Scope/applicationsThis component attempts to explore the range of the specific AOK within the totality of human knowledge and how that knowledge is used. Scope refers to the definition of the AOK in terms of subject matter, and the form that an AOK takes depends critically upon the nature of the problems it is trying to answer. For example: • biology studies living organisms and is mainly concerned with how they function • mathematics is the study of quantity, space, shape and change • in engineering, however, precise numerical methods are a matter of life and death
7 1. Scope/applications• music might not seem concerned with solving practical problems at all but the composer has to solve the “musical engineering” problems of building a piece of music; it has to be a unified whole and yet at the same time there has to be some sort of inherent contrast there to provide tension and energy and, for the listener, interest. Exploration of the scope and applications of a particular AOK can lead to interesting discussions of the ethical considerations that have to be taken into account. Practitioners in a particular AOK might not be permitted to explore all the aspects that are of interest. There might be moral and ethical limits on the sort of investigations they undertake and experiments they perform.
8 2. Concepts/language• What role does language play in the accumulation of knowledge in this area? Knowledge can be shared over space and time. In order for this to happen it has to be transported and stored. This necessarily requires language. Precisely how this is achieved depends on the area of knowledge. Academic disciplines might answer this question in approximately the same way. Knowledge is transported and stored through the written word and other systems of symbols that do an equivalent job such as mathematical, chemical, musical or dance notation. BUT! the question becomes more interesting when we consider non-academic areas of knowledge such as indigenous knowledge systems, systems of religious knowledge or certain types of knowledge in the arts.
9 2. Concepts/language• What are the roles of the key concepts and key terms that provide the building blocks for knowledge in this area?(Write down the 5 big ideas in an HL subject you take. What concepts are required for these ideas to make sense? Try to write down the 5 big concepts to support these ideas.) This activity should help you understand how complex ideas within an area of knowledge are constructed out of concepts.
10 2. Concepts/language• What metaphors are appropriate to this area of knowledge? Metaphors play an important role in our understanding. (Explain)
11 2. Concepts/languageIt gives us a way to visualize complex our esoteric ideas in an everyday setting and hence enables us to find our way in an unfamiliar context. We can transfer our everyday intuitions and experience to the new situation and let the metaphor guide our thinking there. Like any analogy there are dangers. (Explain)
12 2. Concepts/languageWe might pursue the parallel too far and the everyday common sense intuitions and experience might not hold in the new situation. Light used to be thought of as being a bit like waves in water. But the analogy started to break down when physicists said: “OK what is the equivalent of the medium of water for light?” This turned out to be a bad question because Maxwell showed that the assumption that a wave had to have a transmission medium was necessary. Our intuitions are further confused in this example when quantum theory comes along and tells us that light is actually a particle (metaphor: ball). Now we have no common sense object to act as a metaphor: something that is both like a water wave and like a child’s ball. Our intuitions are left without a guide and our understanding suffers as a result.
13 2. Concepts/language• What is the role of convention in this area? (Define “convention”)
14 2. Concepts/language• What is the role of convention in this area? Convention is an arbitrary agreement that something is the case. Driving on the right hand side of the road is a convention. Language itself is one big set of conventions. Areas of knowledge use convention in order to make knowledge transportable—so convention is an important tool for producing shared knowledge. Without it we would have a multiplicity of little personal understandings.
15 2. Concepts/languageWe explored language earlier but there are conventions outside of language We explored language earlier but there are conventions outside of language. The arts are full of them and they come rather naturally. Students of art often draw pictures with horizontal perspective (horizontal parallel lines converging to a vanishing point) but without vertical perspective—this is not how the world appears but it is a convention we use in our representations. In music or theatre there are whole sets of performance conventions depending on the genre of the piece. In science there are conventions for experimental procedures and for publishing results, in film there are conventions with stock meanings. (Brainstorm more examples)
16 2. Concepts/languageAdvanced students (and their advanced teachers) might want to separate convention in the arts from convention in the sciences. It seems that convention in art is partly constitutive of the art form (just as rules of football are constitutive of a game of football—change the rules and you change the game) but this might not be true in science. What about comedy? Comedy link
17 2. Concepts/language PERSPECTIVE Convention in art. Horizontal lines tend towards a vanishing point (railway tracks) while vertical lines do not (telegraph poles) and remain parallel. This is not how the world appears but is rather a convention of our system of representation—in this case a perspective drawing.
18 2. Concepts/languageThis element explores the way in which language is used in the production of knowledge in each AOK. The key idea is that language does not just communicate pre-existing “non-verbal” knowledge but that, in many cases, the language used actually constitutes knowledge. Take language away and there is nothing left. One of the reasons for this is that the language names concepts—these are the building blocks for knowledge.
19 AOKs and produce different ways of thinking about the world. 2. Concepts/languageAn AOK is a system of relationships between its key concepts. Different building blocks build quite differentAOKs and produce different ways of thinking about the world.For example:• in physics key concepts include those of causation, energy and its conservation principle, field, chargeand so on• in visual arts we might be concerned with the color palette, texture, composition, movement,symbolism and technique• in music the central concepts might be melody, rhythm, harmony, tension, relaxation, texture and color.
20 2. Concepts/languageDiscussions of the concepts and language that shape an AOK can link well to discussions about shared knowledge. Language allows knowledge to be passed on to others and to be accumulated over time for future generations. This is what makes this sort of knowledge “shared knowledge”. The fact that it can be communicated between individuals across space and over time is important. A significant proportion of current knowledge is not new but has been passed down to us from the past or from other parts of the world.
21 3. Methodology• What are the methods or procedures used in this area and what is it about these methods that generates knowledge? It is important you do not just describe the methodology of a particular area of knowledge. You should also dig deeper and ask questions about why these particular methods work. • What are the roles of reason, emotion, sense perception, imagination, faith, memory, intuition in these procedures? To tackle this question you need to try to find glimpses of the traditional WOKs in the methods of inquiry of the areas of knowledge. (Discuss what this means) • What are the assumptions underlying these methods? • What counts as a fact in this area of knowledge? • What role do models play in this area of knowledge? • What ethical thinking constrains the methods used to gain knowledge?
22 3. Methodology• What are the assumptions underlying these methods? This question brings to light a cluster of important knowledge questions. In order for the methodology to produce knowledge, certain conditions have to be met. It is the nature of human knowledge that it is probably not possible to establish these assumptions without some sort of circularity.
23 3. MethodologyFor example, the natural sciences require that nature is uniform over time so that they can use repetition of experiment results as an indicator of reliability. But how can we decide if nature is uniform over time? The methods we might employ, such as experiment, only work if the assumption itself is true—they are themselves based on it. (Explain “circularity”)
24 3. Methodology• What counts as a fact in this area of knowledge? If we think of facts as being the raw material of knowledge—the foundations, let us say, then it is important to be able to identify what these could be in different areas of knowledge. In history facts might be historical documents, while in the natural sciences they might be the results of experiments. (What might they be in other AOKs?)
25 3. Methodology• What role do models play in this area of knowledge? Explanations probably aim to connect a complex thing to a set of simple things. In the natural sciences this might be an observed phenomenon and the simple things might be laws of nature. In the arts it might be understanding an artwork in terms of artistic or aesthetic principles. For example, a film might be understood in terms of its structure, its dramaturgy, its setting, its photography, its symbolism and its implicit psychology perhaps.
26 3. Methodology• What ethical thinking constrains the methods used to gain knowledge? Models can be found almost everywhere in the TOK course. (Explain what purpose models serve.)
27 3. MethodologyIt might be that a model is a good model of knowledge itself. (Identify the use of models in an area of knowledge and discuss its role.)
28 3. Methodology(Refer to “Modeling Spitfire and hangar”) The diagram shows how models help us to understand a complex and messy world. The blue vertical line divides the messy real world from the ideal world of the model. In a sense it is a vertical version of the horizontal division between the real world and TOK thinking. The three arrows represent the three stages of the modeling process. Each of these arrows gives rise to its own set of knowledge questions.
29 3. MethodologyOne of the most striking differences between the AOKs is the methods that they use. Examining and comparing the methodologies of the different AOKs begins with YOU being able to identify the specific methods or procedures used in an AOK, and exploring the assumptions that underlie those methods.
30 3. MethodologyAssumptions and values play an important part in the methodology that underpins the production of knowledge. Each AOK establishes certain things as being important and others less so—each has a set of values that underpin the knowledge that is produced. No AOK is value free—some methods are better than others, some facts are more reliable than others, some theoretical models give better understanding than others. Recognition of these values and how they affect the methodology that is used is crucial to understanding the character of the AOK.
31 3. MethodologyFor example, in the natural sciences, much knowledge comes about through testing hypotheses by experiment; this assumes that laboratory conditions accurately mimic what happens in the rest of the universe and that the world can be understood as a system of causes determining effects. One way to explore methodology is to examine the question of what counts as a fact in this particular AOK. Another way would be to examine the question of what counts as an explanation in this particular AOK.
32 3. MethodologyFor example: • in the natural sciences, much knowledge comes about through testing hypotheses by For example: • in history, an explanation might consist of an overarching theory giving plausible motivations to the various historical actors that joins up the isolated historical documents • in literature, the explanation of text might involve examination of its themes, motives and characterization through the literary devices employed.
33 3. MethodologyAnother way to explore methodology is to examine any constraints on the methods that can be used; for example, ethical constraints on experiments conducted in the human sciences.
34 4. Historical development This group of questions establishes how the current form of an area of knowledge depends on its past. It is an acknowledgement of the fact that knowledge is continually changing according to advances in methodology, interests and the types of problem it is designed to solve. This the place for reflection on the fact that the area of knowledge might have looked quite different if certain historical ‘accidents’ had not occurred.
35 4. Historical development • What is the significance of the key points in the historical development of this area of knowledge? This question seems on the surface to require a description of the main outline of the history of a subject. This in itself is a useful activity, of course, but in a TOK context the motivation is more subtle. The way in which we think about the world depends heavily on key moments in the past where our “conventional wisdom” about the area is formed.
36 4. Historical development • What is the significance of the key points in the historical development of this area of knowledge? T0 make epistemic progress it might be necessary to revisit these key moments and ask the question whether the direction taken then is a good one or whether it led us in the wrong direction. (Remember your Nobel Prize Winner presentations???) For example, in the 18th and 19th century big advances were made in economics that led us to consider the subject in terms of an overall cost benefit analysis.
37 4. Historical development Economics became an exercise in deciding whether certain policy decisions yielded the greatest net benefit (either from the point of view of the consumer, the producer, or government). Amartya Sen proposed a different where we look at the development of human capabilities instead. Perhaps some of the bigger economic disasters of the last 100 years could have been avoided if we had challenged these initial utilitarian or ‘profit driven’ ideas. (Brainstorm examples) • How has the history of this area led to its current form?
38 4. Historical development • How has the history of this area led to its current form? This question again looks like a request for description. It is intended to raise the awareness of the history of an area in the formation of present ideas. What is intended is that a connection is made between the answer to question #1 and YOUR current understanding of the area. This not only deepens YOUR knowledge but also gives YOU a set of examples that can be used in the TOK essay or presentation to support arguments suggesting that some areas of knowledge are perhaps more sensitive to cultural and historical factors than others.
39 4. Historical development •How would these questions be answered 100 years ago? (Examine the ways in which AOK have developed across all aspects of the framework: 1. Scope/applications 2. Concepts/language 3. Methodology )In the past the scope, interests and questions asked might have been different.
40 4. Historical development In the past the scope, interests and questions asked might have been different. The methods of inquiry might have been different for a number of reasons including technological change. This question is also designed as a quarry for examples.
41 4. Historical development • Is it conceptually possible that his AOK would look different if history were rerun? This is a difficult question. It asks you to understand that knowledge is a human attribute that is arrived at through human activities and is subject to all the complexities of human social life. If history were replayed these complexities might have been played out in different ways arriving at different-looking subject disciplines. Some AOK might be more prone to the contingency of human history than others and it is YOUR job to try to work out why this is. (Brainstorm examples)
42 4. Historical development In some cases YOU might decide that it is only a question of terminology that is subject to historical forces and that any differences would be cosmetic. YOU might decide that after human history is replayed chemistry would actually look the same (or at least be formulated in a functionally equivalent manner) because it is strongly answerable to an independent reality. But it is worth pointing out that even a tough realist student of the natural sciences would have to concede, for example, that the units of measurement we use are a result of 19th century European history and the concepts we use are largely developed in England in the 17th century.
43 4. Historical development AOKs are dynamic entities that change over time as conceptual developments and advances are made in methodology. This need not be seen as a problem but rather an advantage—our systems are flexible and capable of responding to developments. Knowledge can, therefore, be considered provisional.For example:• consider a Swedish school textbook in history from 1912: it is quite different in its idea of history from those used today; a physics textbook from 1912 seems to have much the same idea about physics but the content is likely to be different.
44 4. Historical development • an artwork or music might derive much of its meaning from the historical context in which it is produced and might even reference other earlier works. (Brainstorm examples)Tracking the rough historical development of an AOK is a valuable tool in TOK. It is tempting to speculate that if we re-ran the history of human knowledge then the AOKs might look quite different to their current form. How much of our knowledge depends on accidents of history? Are certain AOKs more susceptible to these historical factors than others? Even our systems of measurement (m, kg, s) are historically situated and so, of course, are the concepts and the language employed by subject disciplines. Interesting discussions can be had over why particular historical events and factors have had such an impact on the development of a particular AOK.
45 5. Links to Personal Knowledge This group of questions makes the important link between personal and shared knowledge. (Define each.) It is useful for getting YOU to think ‘what does this mean for me’? about results in a particular subject.
46 5. Links to Personal Knowledge • Why is this area significant to the individual? The purpose of this question is to explore exactly how one’s personal knowledge draws heavily upon shared knowledge. Moreover, it hints that our systems of value and significance are not just creative products of our imaginations operation independently of others but are refined and in some cases formed by contact with shared knowledge. Perhaps the lesson here is than we are far less original than we think.
47 5. Links to Personal Knowledge • What is the nature of the contribution of individuals to this area? You are encouraged to actually find concrete examples of individual contributions to shared knowledge to show how individual abilities can generate the initial impetus for innovation in an AOK. Of course the individual contribution then has to go through the validation procedures outlined in the ‘methodology’ part of the framework.
48 5. Links to Personal Knowledge • What responsibilities rest upon the individual knower by virtue of his or her knowledge in this area? Perhaps the access to shared knowledge brings personal responsibilities. (Brainstorm examples)
49 5. Links to Personal Knowledge It is conceivable that a doctor carries extra responsibilities through her training and could be obliged to act in situations that require her expertise. She might be called upon to attend to someone requiring assistance after an accident while off-duty while those without medical training might be exempt. There are a number of knowledge questions that are raised at this point. (Given the prior scenario, brainstorm some highly-effective KQ)
50 5. Links to Personal Knowledge To what extent might there be an obligation to use the access one has to shared knowledge for the common good? This is particularly complicated in the case of medical researchers working in a commercial environment on drugs to treat critical conditions such as AIDS.
51 5. Links to Personal Knowledge • What are the implications of this area of knowledge for one’s own individual perspective? Recall that those with access to a specific area of shared knowledge form a group. This group might possess a particular perspective on the world by virtue of this shared knowledge. This question explores in a concrete manner how personal perspectives might be formed or changed by access to shared knowledge. (Brainstorm examples)
52 5. Links to Personal Knowledge • What assumptions underlie the individual’s own approach to this knowledge? How the individual approaches shared knowledge might also depend a little on other factors particular to the individual. (Brainstorm examples)
53 5. Links to Personal Knowledge Factors may include biography, character, and membership to other groups. These factors are constitutive of personal perspective and it is important that the student explores ways in which these background assumptions can be brought to light. It is useful in doing TOK to be able to reflect on the contribution one’s personal perspectives make to one’s judgments and decision-making. (Ask yourself the following questions: “What are YOUR personal perspectives that contribute to your judgments and decision-making?”)
54 5. Links to Personal Knowledge There are links and interactions between shared and personal knowledge. Individuals contribute to shared knowledge. Their contributions have to go through whatever validation procedures are required by a particular discipline in order to be counted as “common” knowledge in that area. But shared knowledge also contributes to an individual’s own understanding of the world. This is one, but not the only, purpose of shared knowledge—that it enables individuals to make sense of the world.
55 5. Links to Personal Knowledge The nature of this interaction between shared and personal knowledge is the last component of the knowledge framework to be examined. It is important because it addresses the question “so what does this mean for me?” What impact do these AOKs have on our individual lives and the way in which we view the world? How does this area form or change our perspective?
56 YOUR TURN!Groups of 3: 1. Invent a new AOK. 2. Construct a knowledge framework. 3. Explain how each component of the framework supports the invented AOK.