Tok Maths Essay

When we are to think of the two subjects art and mathematics, the first impression we get is the difference in the two subjects. It is a natural phenomenon for us to believe that that these two subjects are very different from each other not only in their area of study but also in its use in our current society. A large part of mathematics bases its fundamentals on logical reasoning. Thus, it is widely used in many areas of study such as physics and economics.  On the other hand, art is largely based upon creativity and is used widely for entertainment as a form of expression. Despite these seemingly distinct differences, a through look at the two subjects show clear similarities and differences between the two areas of knowledge.

The questions we should ask when we think of Math as one of the areas of knowledge, we should ask ourselves if math is something men made or something that men has discovered from nature. Although the two answers may differ in depending on the type of group you support (Platonist and the formalist), the two questions without doubt are some of the fundamental questions asked in the areas of mathematics. like the mathematics, there are several questions we need to ask when we look at art. These following questions are what defines art, what makes art great and finally, who has the right to judge art. This just like math is a very controversial topic as different individuals have different perspectives upon the definition of art. For example, some people consider nature itself to be art whereas some people believe that art needs to be something intentionally made by an individual. In addition to the controversial question these two areas have, both areas of knowledge use numerous symbols. In math, there are numerous Latin and Greek letters used to express the equation. In the case of art, artists use colours and texture to express their emotions towards a certain topic. For example if the tone of the colour is dark, may change the overall mood of the painting or the art work.

Although there are numerous differences in math and art, the most noticeable difference between the two is its basis. The numerous theories in mathematics are something of concrete idea meaning that they are unlikely to change over centuries. For example the Pythagoras theory, is a theory that existed millenniums ago. And yet, it still remains one of the most basic aspects in trigonometry of math. In contrast, art is something very subjective. Meaning that different individuals may have different interpretations on the same art work. Moreover, there are numerous mediums used to make an art work.

In conclusion, the aforementioned explanations show that art and math despite being contrasting subjects have many differences and similarities.

 

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How to Structure a Theory of Knowledge Essay

The following structure is a very good, step-by-step method you can use on any ToK essay to get very high marks. 

Here are the main things to keep in mind when you're using this method:

    1. Your #1 priority is answering the prescribed title. If you somehow follow this method, but don't answer the question you won't score well. So make sure you keep linking back to the question as you go. 
    2. Try to use original, interesting evidence. 

(I have a full a lot of helpful advice, tutorials, evidence videos in my online ToK course, which you're welcome to join if you like. Or, if you just need some TOK Notes you can get those here.)

And I've also made a help page (similar to this) for the TOK presentation, here.

Okay here we go...

The structure on this page will give you a strong foundation for your essay and then we're going to make your essay as insightful as possible.

First, choose your PT and KQ

Before you can begin your real/final essay, you’ll want to look at the Prescribed Title (something like: “What is it about mathematics and science that makes them so convincing?” and think about it.

Get some of your initial ideas down on paper.

Second, choose 1 WOK and 2 AOKs

Now, take your prescribed title and choose two AOKs to explore it with (here are my notes: Mathematics, Human sciences, Natural Sciences, the Arts, Ethics, Indigenous Knowledge Systems, Religious Knowledge Systems, or History). Or you can use WOKs: (again here are my notes: Emotion, Faith, Sense perception, Reason,  Imagination, Intuition,  Language, Memory). Then you can explore these aspects in your essay.

I normally recommend exploring just  2 AoK's in the main body of your essay and then include a few insights into WOKs around the edges (more on this in a bit).

The essay contains two body sections (or "developments"). Each body section will look at a certain area of knowledge or way of knowing.

To explore the question we chose above, it's pretty easy to choose our AOKs because they are actually listed in the question. We'll be using  Mathematics and Natural Science. 

The courtroom analogy

The TOK essay is about knowledge (how we come to know things). It helps to think of the essay as though you're showing the most interesting bits of a conversation between two smart people, about how we know things. 

Or you could think about it like presenting two sides of an argument, in front of a judge. Each side needs to present evidence. 

One lawyer is saying YES (i.e. reason is reliable, with examples) and the other is pointing out the weaknesses in what lawyer 1 is saying (i.e. reason is often not reliable, also with examples).

Your lawyer will make the case that you can’t be guilty of robbing the bank (her thesis), by using several arguments (claims); she’ll show that 

  1. You weren’t there
  2. You’re are a moral person and
  3. You don’t have the technical knowledge to pull off a job like that.

However, if your lawyer was a ToK student they would also be explaining reasons why you might be guilty (the counterclaims).

  1. Someone said they saw you there,
  2. You admitted to lying to your mom about candy one time and
  3. You are pretty good at computers.

The lawyers would use evidence to support each of these claims and counterclaims.

Making sure your evidence actually supports your claim is one of the toughest aspects of the essay.

The step-by-step method

The method has 4 sections and 7 paragraphs overall and specific aspects need to go in each.

First, write your introduction, using 150-200 words

Paragraph 1

-Say 2 interesting things about the prescribed title. "Many people find Mathematics and Natural Science very convincing. However, many of these same people would say that they don't have a strong understanding of either of these two fields. Both of these fields rely on rigorous methodologies."

-Define one or two of the key terms in the title. Here I might define Mathematics and Natural Science. (I would also look up the term "convincing". I might not include that definition in my essay, but I would like to know whether there are any conflicting definitions. That might help me say interesting things later on in the essay--for example in the conclusion.) 

-Narrow in on one aspect which is particularly interesting. "This essay with focus on the link between replicability of results, as a source of reliability." 

-State your thesis. What is your short answer to the prescribed title, your thesis. (You might decide, by the end of your essay, that your initial thinking was wrong, but you should know the point your claims are going to be supporting). 

-Give us a roadmap, a sentence that gives us a preview. This shows us what you’re going to do in your body paragraphs (your "developments"). Tell us AOKs you're going to use and which WOK you will be focused on most. This will make it easy for the marker to know what to look for. An example: “Mathematics can be seen as more reliable because it uses reason. Natural science can be less reliable because it relies on observation. ”

Next write your first development. 2 paragraphs totalling 600 words

Paragraph 2

-Claim. A claim a topic sen­tence that outlines your argument about the prescribed title. For example you could claim that, “Mathematics can be relied on because it is a purely logical system.”

-Explain. Elaborate and clarify your claim. “Mathematics is axiomatic and independent of subjective experience.“

-Example. A real life example, to clar­ify and sup­port the claim from your own experience. Examples should be personal, specific, precise and real. Did something happen in your Science class? Did you have a conversation with your or hear a story from your grandfather? These are evidence from your own life rather than examples from Darwin or Lincoln. So you could talk about how, “In mathematics we learned that the inside angles of a triangle, in Euclidian space, sum up to 180 degrees.”

Paragraph 3

-Counter-claim. Argue against your claim above. “However, it is possible to come to different conclusions using different systems of mathematics.”

-Example. An example that supports your counter claim. “There are different It is not possible to demonstrate that the interior angles of a triangle equal 180 degrees in Euclidian space, this cannot be proven within other systems, such as spherical geometry or hyperbolic geometry.”

-Link to prescribed title. Quickly sum up the (complicated) insights of this section. “It is therefore clear that mathematics is reliable to an extent, but often it can only show something to be true within one fixed system or approach.”

Now, write another two body paragraphs, looking at your second AOK. Use the same approach you saw in paragraphs 2 and 3. 600 words

Paragraph 4

-Claim.

-Explain.

-Example.

Paragraph 5

-Counter-claim.

-Example.

-Link to prescribed title.

Finally, write your 'conclusion'. Two paragraphs, totalling 200-250 words

Paragraph 6

-Your conclusion. Explain what big, general insights have come out of this--your conclusion. 

Implications and significance. Also tell us why it's important that we know this. When and how does it matter that we understand this lesson?

Paragraph 7

-Perspectives and extensions. If you can, try to pull in a very different perspective, on your conclusion. Perhaps you can recognize a very different way of approaching the question, which could have resulted in quite different insights than those you included in your essay. Or you could also mention one or two unresolved questions that this essay has revealed. You could also think of this as explaining some "limitations" or a weaknesses of your essay, but it's also about showing that the conversation isn't over yet. There is more to the question than you've had the room to explore.  

 

Obviously there is a lot more depth that we can go into about what makes a really great TOK essay, but this structure will get you started.

Here are some more ToK Essay tips you might want to consider or you can join my online program if you like www.tokmastery.com

 

 

Cite this page as:
Woods, Tim. “How to Structure a Theory of Knowledge Essay” IBMastery. IBMastery, 1 Jan 2016. Web. TODAY’S DATE <https://www.ibmastery.com/blog/how-to-structure-a-theory-of-knowledge-essay>

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