tok math essay example

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The validity of mathematics as an area of knowledge has been founded on its ability to rely on basic assumptions and universally accepted definitions.

Mathematicians often use aspects such as deductive reasoning and a system of axioms to prove mathematical truths or theorems.

Based on this factor, students can easily answer any knowledge questions that arise with a degree of certainty that is unmatched in other fields.

This makes it a perfect area of knowledge to explore various knowledge issues.

One of the main reasons why mathematics embodies assumptions that are universally valid is the fact it based on reason. Additionally, as it relies on its own language of symbols, it is able to reduce any contextual or cultural influences when it comes to knowledge production.

Despite the strict confines associated with its methodology, mathematics has also been regarded as an enormously creative subject. This is highlighted by the extent to which it asks its practitioners to rely on ways of knowing such as their imagination.

In addition, while pure mathematics does not rely on the application of sense perception during the process of inquiry, the application of the resultant knowledge relies on techniques used in other areas of knowledge.

This explains why most of the knowledge questions that arise in fields such as the arts and the natural sciences are underpinned by mathematical theories. 

For instance, the arts possess a close link with mathematics due to the fact that formal requirements for symmetry or harmony rely on mathematical structures.

Examples and Explanations

• Claim - Mathematicians recognize that there is a shared genuine conviction adopted by the individual researchers which allow them to examine the alternating sides of a disagreement Example – The assertion by Edward Nelson in 2011 that the Peano Arithmetic was essentially inconsistent.
• Counterclaim - Giving equal treatment to the contrasting sides in mathematics does not necessarily result in the production of knowledge or new insights. Example – Continuous disagreement over the axiom of foundation

Different guidelines on how to structure a tok essay have shown that some areas of knowledge easily resolve disagreements when compared to others.

Mathematics is one of the fields whereby experts rely on methodologies that are geared towards the development of a consensus.

As highlighted in the theory of knowledge , IB Diploma Program, mistakes often occur in mathematics. However, the experts involved often use ways of knowing such as intuition and reason to spot these mistakes and dispel any disagreements that arise from them.

It can, therefore, be surmised that consensus in mathematics is not achieved through coercion. Mathematicians recognize that there is a shared genuine conviction adopted by the individual researchers which allow them to examine the alternating sides of a disagreement. This is mainly because there exists a social standard of what experts regard as proof.

A tok real-life example that illustrates this claim is the assertion by Edward Nelson in 2011 that the Peano Arithmetic was essentially inconsistent.

The professor of mathematics from Princeton University argued that he had found proof that showed this inconsistency. The mathematical community quickly dispelled the disagreements that begun to rise within the field by finding a loophole in Nelson’s argument.

This example shows that the internalization of mathematical knowledge contrasts with other areas of knowledge because different opinions often lead to a consensus.

Alternatively, one can argue that giving equal treatment to the contrasting sides in mathematics does not necessarily result in the production of knowledge or new insights.

One of the main reasons that mathematicians appeal to mutually inconsistent propositions during the analysis of knowledge claims is to ensure that they can establish a sound position.

However, based on aspects such as analogical reasoning, different points of view can be perceived as accurate due to factors like confirmation bias. An instance that exemplifies this argument in the continuous disagreement over the axiom of foundation.

This specific theory has been cited as one of the fundamental backbones to the understanding of the set-theoretic universe.

Despite this fact, there are advocates and detractors that conflict on the validity of the Foundation. However, due to the fact that there is a consensus that this foundation has no significant impact on other parts of this field, this disagreement has not been dispelled.

“Reliable knowledge can lack certainty.” Explore this claim with reference to two areas of knowledge.

The maverick tradition within this area of knowledge has continuously rejected the claim that the universal truth of mathematical knowledge exists.

Mathematicians who support this idea have argued that no mathematical knowledge can be considered valid for all knowers.

As a result, while the concept of certainty in mathematics is acknowledged, it is limited to human knowledge. This essentially means that the trajectory of knowledge production within this area of knowledge follows a path that is gradually refined and developed. During this process, the certainty present is increased.

This assertion justifies the claim that reliable knowledge within mathematics can possess some form of uncertainty. This is evident from the mathematical proofs that have been appropriated by this knowledge community such as the infinite number of primes and the irrationality of root 2.

This knowledge has been considered reliable despite lacking certainty in the past millennium.

To counter this claim, one can also argue that the main defining characteristic of this area of knowledge is its ability to generate formulas that are known with certainty.

Some of the accepted mathematical truths are considered irrefutable due to their level of certainty. In reference to this tok prescribed title , mathematics is unique in that it embodies assumptions and principles that are universally accepted. This can be vindicated by the experts’ reliance on reason.

Therefore, any knowledge that is determined to be reliable has to possess a high level of certainty.

For example, geometry has been readily accepted in all parts of the world due to the certainly of the language and symbols involved.

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Guide to the TOK Essay

What’s covered:.

• What is Theory of Knowledge (TOK)?
• What is the Theory of Knowledge Essay?

How is the Theory of Knowledge Essay Scored?

How to structure your theory of knowledge essay.

The International Baccalaureate Diploma Programme (IB/IBDP) is a rigorous and rewarding internationally based educational program that offers courses in numerous studies, from humanities to chemistry. Students take part in a two-year curriculum that includes external examinations, internal assessments, research papers and community service hours. Essentially, students will have to do a bit of everything, especially with IB’s core, which is CAS, TOK, and the extended essay (EE). Understanding how TOK, IB’s flagship class, is assessed with its essay is important to success in the course overall. 

What is Theory Of Knowledge (TOK)?

Theory of Knowledge is IB’s way of introducing a more intuitive way of thinking into classrooms. TOK is at its surface as simple as it sounds: you essentially learn the “what” and “why” of how we learn and understand knowledge. In order to assess students of their skills in TOK, IB uses an essay and a presentation. The essay makes up 67% of your total TOK score, making it the most important task to focus on for getting a high score. 

What is the Theory Of Knowledge Essay?

The TOK essay is a 1600 word essay written about topics usually given to students from their teachers from a list of numerous options. It is an essay that promotes arguments and counterarguments for the topic at hand. Understanding your ways of knowing (WOKs) and areas of knowledge (AOKs) is extremely crucial before you even start choosing a topic to write on, as your essay will revolve around and structure itself based on these two concepts. Being able to demonstrate higher-level thinking and using examples to solidify the points you make in your essay is also important. Additionally, you’ll need to reference every source of information that you use, since that is something examiners look for as well.

As said earlier, 67% of your grade is from the essay, and your overall TOK score receives a letter grade using a calculated score out of thirty. Your essay score and presentation score are each out of ten. The grades for your TOK presentation and essay are determined by sending material to the board of IB, from which they designate a grader/examiner to read your essay and grade based on a rubric that determines the level of knowledge you exhibit in your writing.

The following formula should better explain how to find your TOK grade. 

(presentation score) + (essay score * 2) = overall score out of 30

The grade boundaries out of 30 that determine your letter grade can vary each year so checking in with your school for the most recent ones is the best course of action, but an example set would be like this:

Once you have a letter grade for IB, your extended essay, which is another part of the core, is also included into a larger grading schema to calculate your core score, which is three additional points required to complete and earn the diploma. The following table details this grade further:

Doing well in the core is important to passing IB and getting three points out of the total 45 attainable points. 

There’s a trick that most IB students use in writing the TOK essay, and it boils down to understanding four key components of learning:

• Content : Understanding knowledge issues
• Clarity : Structuring your essay in a legible and clear/easy to read manner
• Creativity : Using your personal ways of thinking and applications of knowledge specific to your understanding of the knowledge issue
• Critical Thinking : Using a counter argument for every argument you have to analyze your own claims constantly 

Dividing your actual essay into three main chunks helps, starting with an introduction. Your introduction should be where you state your knowledge question, the central point of your essay, and you should make use of jargon specific to the concept. As the basis of your essay, the introduction should be where you form claims and counterclaims that either support or challenge the knowledge question through heavy analysis and evaluation. 

The body of the essay follows the introduction, and it is where most of the conceptual analysis of your knowledge question takes place. Every argument and its counterargument should have a dedicated paragraph of its own, and make sure to not jump back and forth too much throughout the essay. to avoid creating messy transitions for the reader and potentially harming your score. Understanding the essay from the reader’s point of view is important, as it will help you better understand how to structure the body of your essay.

A conclusion in the TOK essay is mainly for finding closure among the numerous arguments that have been taking place thus far in the essay. Make sure to summarize but not repeat previous information entirely to refresh the reader. A conclusion should essentially loop back to the beginning of the essay, the knowledge question. The knowledge question’s answer should be the conclusion and the stopping point of the essay, and by now the answer you provide should be backed by paragraphs of supporting claims and counterclaims. If done right, concluding the essay can be how you earn most of your points. 

Start Early

Starting early is an obvious and effective advantage to students. Aside from TOK, let alone the presentation, IB has substantial work that requires focus and allocated time dedicated to it, such as external examinations and the extended essay. These tasks are equally as important as the TOK essay, so starting your outlining, drafting or even just planning early will set you up for success.

Send Your Drafts to Your Teacher

Your TOK teacher is a great resource for drafting essays and making edits to perfect your final product. Making use of time outside of the classroom to catch your teacher for a quick review of your essay could be a bigger advantage than you realize. Making use of an outside perspective is essential to forming a great essay. 

While your final IB grade isn’t as important as you’d think regarding college admissions, understanding how to pass TOK and using the lifelong practices you’ll learn in the class is even more important. TOK creates students who think outside conventional methods, making them excellent candidates in the eyes of college admissions offices. Taking TOK and showing proof of understanding it as well as capability of academic rigor is what colleges are looking for. For more information on how your chances of college admissions might look, use CollegeVine’s admissions calculator !

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Sat / act prep online guides and tips, the complete ib extended essay guide: examples, topics, and ideas.

International Baccalaureate (IB)

IB students around the globe fear writing the Extended Essay, but it doesn't have to be a source of stress! In this article, I'll get you excited about writing your Extended Essay and provide you with the resources you need to get an A on it.

If you're reading this article, I'm going to assume you're an IB student getting ready to write your Extended Essay. If you're looking at this as a potential future IB student, I recommend reading our introductory IB articles first, including our guide to what the IB program is and our full coverage of the IB curriculum .

IB Extended Essay: Why Should You Trust My Advice?

I myself am a recipient of an IB Diploma, and I happened to receive an A on my IB Extended Essay. Don't believe me? The proof is in the IBO pudding:

If you're confused by what this report means, EE is short for Extended Essay , and English A1 is the subject that my Extended Essay topic coordinated with. In layman's terms, my IB Diploma was graded in May 2010, I wrote my Extended Essay in the English A1 category, and I received an A grade on it.

What Is the Extended Essay in the IB Diploma Programme?

The IB Extended Essay, or EE , is a mini-thesis you write under the supervision of an IB advisor (an IB teacher at your school), which counts toward your IB Diploma (learn more about the major IB Diploma requirements in our guide) . I will explain exactly how the EE affects your Diploma later in this article.

For the Extended Essay, you will choose a research question as a topic, conduct the research independently, then write an essay on your findings . The essay itself is a long one—although there's a cap of 4,000 words, most successful essays get very close to this limit.

Keep in mind that the IB requires this essay to be a "formal piece of academic writing," meaning you'll have to do outside research and cite additional sources.

The IB Extended Essay must include the following:

• A title page
• Contents page
• Introduction
• Body of the essay
• References and bibliography

Additionally, your research topic must fall into one of the six approved DP categories , or IB subject groups, which are as follows:

• Group 1: Studies in Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts

Once you figure out your category and have identified a potential research topic, it's time to pick your advisor, who is normally an IB teacher at your school (though you can also find one online ). This person will help direct your research, and they'll conduct the reflection sessions you'll have to do as part of your Extended Essay.

As of 2018, the IB requires a "reflection process" as part of your EE supervision process. To fulfill this requirement, you have to meet at least three times with your supervisor in what the IB calls "reflection sessions." These meetings are not only mandatory but are also part of the formal assessment of the EE and your research methods.

According to the IB, the purpose of these meetings is to "provide an opportunity for students to reflect on their engagement with the research process." Basically, these meetings give your supervisor the opportunity to offer feedback, push you to think differently, and encourage you to evaluate your research process.

The final reflection session is called the viva voce, and it's a short 10- to 15-minute interview between you and your advisor. This happens at the very end of the EE process, and it's designed to help your advisor write their report, which factors into your EE grade.

Here are the topics covered in your viva voce :

• A check on plagiarism and malpractice
• Your reflection on your project's successes and difficulties
• Your reflection on what you've learned during the EE process

Your completed Extended Essay, along with your supervisor's report, will then be sent to the IB to be graded. We'll cover the assessment criteria in just a moment.

We'll help you learn how to have those "lightbulb" moments...even on test day!  

What Should You Write About in Your IB Extended Essay?

You can technically write about anything, so long as it falls within one of the approved categories listed above.

It's best to choose a topic that matches one of the IB courses , (such as Theatre, Film, Spanish, French, Math, Biology, etc.), which shouldn't be difficult because there are so many class subjects.

Here is a range of sample topics with the attached extended essay:

• Biology: The Effect of Age and Gender on the Photoreceptor Cells in the Human Retina
• Chemistry: How Does Reflux Time Affect the Yield and Purity of Ethyl Aminobenzoate (Benzocaine), and How Effective is Recrystallisation as a Purification Technique for This Compound?
• English: An Exploration of Jane Austen's Use of the Outdoors in Emma
• Geography: The Effect of Location on the Educational Attainment of Indigenous Secondary Students in Queensland, Australia
• Math: Alhazen's Billiard Problem
• Visual Arts: Can Luc Tuymans Be Classified as a Political Painter?

You can see from how varied the topics are that you have a lot of freedom when it comes to picking a topic . So how do you pick when the options are limitless?

How to Write a Stellar IB Extended Essay: 6 Essential Tips

Below are six key tips to keep in mind as you work on your Extended Essay for the IB DP. Follow these and you're sure to get an A!

#1: Write About Something You Enjoy

You can't expect to write a compelling essay if you're not a fan of the topic on which you're writing. For example, I just love British theatre and ended up writing my Extended Essay on a revolution in post-WWII British theatre. (Yes, I'm definitely a #TheatreNerd.)

I really encourage anyone who pursues an IB Diploma to take the Extended Essay seriously. I was fortunate enough to receive a full-tuition merit scholarship to USC's School of Dramatic Arts program. In my interview for the scholarship, I spoke passionately about my Extended Essay; thus, I genuinely think my Extended Essay helped me get my scholarship.

But how do you find a topic you're passionate about? Start by thinking about which classes you enjoy the most and why . Do you like math classes because you like to solve problems? Or do you enjoy English because you like to analyze literary texts?

Keep in mind that there's no right or wrong answer when it comes to choosing your Extended Essay topic. You're not more likely to get high marks because you're writing about science, just like you're not doomed to failure because you've chosen to tackle the social sciences. The quality of what you produce—not the field you choose to research within—will determine your grade.

Once you've figured out your category, you should brainstorm more specific topics by putting pen to paper . What was your favorite chapter you learned in that class? Was it astrophysics or mechanics? What did you like about that specific chapter? Is there something you want to learn more about? I recommend spending a few hours on this type of brainstorming.

One last note: if you're truly stumped on what to research, pick a topic that will help you in your future major or career . That way you can use your Extended Essay as a talking point in your college essays (and it will prepare you for your studies to come too!).

#2: Select a Topic That Is Neither Too Broad nor Too Narrow

There's a fine line between broad and narrow. You need to write about something specific, but not so specific that you can't write 4,000 words on it.

You can't write about WWII because that would be a book's worth of material. You also don't want to write about what type of soup prisoners of war received behind enemy lines, because you probably won’t be able to come up with 4,000 words of material about it. However, you could possibly write about how the conditions in German POW camps—and the rations provided—were directly affected by the Nazis' successes and failures on the front, including the use of captured factories and prison labor in Eastern Europe to increase production. WWII military history might be a little overdone, but you get my point.

If you're really stuck trying to pinpoint a not-too-broad-or-too-narrow topic, I suggest trying to brainstorm a topic that uses a comparison. Once you begin looking through the list of sample essays below, you'll notice that many use comparisons to formulate their main arguments.

I also used a comparison in my EE, contrasting Harold Pinter's Party Time with John Osborne's Look Back in Anger in order to show a transition in British theatre. Topics with comparisons of two to three plays, books, and so on tend to be the sweet spot. You can analyze each item and then compare them with one another after doing some in-depth analysis of each individually. The ways these items compare and contrast will end up forming the thesis of your essay!

When choosing a comparative topic, the key is that the comparison should be significant. I compared two plays to illustrate the transition in British theatre, but you could compare the ways different regional dialects affect people's job prospects or how different temperatures may or may not affect the mating patterns of lightning bugs. The point here is that comparisons not only help you limit your topic, but they also help you build your argument.

Comparisons are not the only way to get a grade-A EE, though. If after brainstorming, you pick a non-comparison-based topic and are still unsure whether your topic is too broad or narrow, spend about 30 minutes doing some basic research and see how much material is out there.

If there are more than 1,000 books, articles, or documentaries out there on that exact topic, it may be too broad. But if there are only two books that have any connection to your topic, it may be too narrow. If you're still unsure, ask your advisor—it's what they're there for! Speaking of advisors...

Don't get stuck with a narrow topic!

#3: Choose an Advisor Who Is Familiar With Your Topic

If you're not certain of who you would like to be your advisor, create a list of your top three choices. Next, write down the pros and cons of each possibility (I know this sounds tedious, but it really helps!).

For example, Mr. Green is my favorite teacher and we get along really well, but he teaches English. For my EE, I want to conduct an experiment that compares the efficiency of American electric cars with foreign electric cars.

I had Ms. White a year ago. She teaches physics and enjoyed having me in her class. Unlike Mr. Green, Ms. White could help me design my experiment.

Based on my topic and what I need from my advisor, Ms. White would be a better fit for me than would Mr. Green (even though I like him a lot).

The moral of my story is this: do not just ask your favorite teacher to be your advisor . They might be a hindrance to you if they teach another subject. For example, I would not recommend asking your biology teacher to guide you in writing an English literature-based EE.

There can, of course, be exceptions to this rule. If you have a teacher who's passionate and knowledgeable about your topic (as my English teacher was about my theatre topic), you could ask that instructor. Consider all your options before you do this. There was no theatre teacher at my high school, so I couldn't find a theatre-specific advisor, but I chose the next best thing.

Before you approach a teacher to serve as your advisor, check with your high school to see what requirements they have for this process. Some IB high schools require your IB Extended Essay advisor to sign an Agreement Form , for instance.

Make sure that you ask your IB coordinator whether there is any required paperwork to fill out. If your school needs a specific form signed, bring it with you when you ask your teacher to be your EE advisor.

#4: Pick an Advisor Who Will Push You to Be Your Best

Some teachers might just take on students because they have to and aren't very passionate about reading drafts, only giving you minimal feedback. Choose a teacher who will take the time to read several drafts of your essay and give you extensive notes. I would not have gotten my A without being pushed to make my Extended Essay draft better.

Ask a teacher that you have experience with through class or an extracurricular activity. Do not ask a teacher that you have absolutely no connection to. If a teacher already knows you, that means they already know your strengths and weaknesses, so they know what to look for, where you need to improve, and how to encourage your best work.

Also, don't forget that your supervisor's assessment is part of your overall EE score . If you're meeting with someone who pushes you to do better—and you actually take their advice—they'll have more impressive things to say about you than a supervisor who doesn't know you well and isn't heavily involved in your research process.

Be aware that the IB only allows advisors to make suggestions and give constructive criticism. Your teacher cannot actually help you write your EE. The IB recommends that the supervisor spends approximately two to three hours in total with the candidate discussing the EE.

#5: Make Sure Your Essay Has a Clear Structure and Flow

The IB likes structure. Your EE needs a clear introduction (which should be one to two double-spaced pages), research question/focus (i.e., what you're investigating), a body, and a conclusion (about one double-spaced page). An essay with unclear organization will be graded poorly.

The body of your EE should make up the bulk of the essay. It should be about eight to 18 pages long (again, depending on your topic). Your body can be split into multiple parts. For example, if you were doing a comparison, you might have one third of your body as Novel A Analysis, another third as Novel B Analysis, and the final third as your comparison of Novels A and B.

If you're conducting an experiment or analyzing data, such as in this EE , your EE body should have a clear structure that aligns with the scientific method ; you should state the research question, discuss your method, present the data, analyze the data, explain any uncertainties, and draw a conclusion and/or evaluate the success of the experiment.

#6: Start Writing Sooner Rather Than Later!

You will not be able to crank out a 4,000-word essay in just a week and get an A on it. You'll be reading many, many articles (and, depending on your topic, possibly books and plays as well!). As such, it's imperative that you start your research as soon as possible.

Each school has a slightly different deadline for the Extended Essay. Some schools want them as soon as November of your senior year; others will take them as late as February. Your school will tell you what your deadline is. If they haven't mentioned it by February of your junior year, ask your IB coordinator about it.

Some high schools will provide you with a timeline of when you need to come up with a topic, when you need to meet with your advisor, and when certain drafts are due. Not all schools do this. Ask your IB coordinator if you are unsure whether you are on a specific timeline.

Below is my recommended EE timeline. While it's earlier than most schools, it'll save you a ton of heartache (trust me, I remember how hard this process was!):

• January/February of Junior Year: Come up with your final research topic (or at least your top three options).
• February of Junior Year: Approach a teacher about being your EE advisor. If they decline, keep asking others until you find one. See my notes above on how to pick an EE advisor.
• April/May of Junior Year: Submit an outline of your EE and a bibliography of potential research sources (I recommend at least seven to 10) to your EE advisor. Meet with your EE advisor to discuss your outline.
• Summer Between Junior and Senior Year: Complete your first full draft over the summer between your junior and senior year. I know, I know—no one wants to work during the summer, but trust me—this will save you so much stress come fall when you are busy with college applications and other internal assessments for your IB classes. You will want to have this first full draft done because you will want to complete a couple of draft cycles as you likely won't be able to get everything you want to say into 4,000 articulate words on the first attempt. Try to get this first draft into the best possible shape so you don't have to work on too many revisions during the school year on top of your homework, college applications, and extracurriculars.
• August/September of Senior Year: Turn in your first draft of your EE to your advisor and receive feedback. Work on incorporating their feedback into your essay. If they have a lot of suggestions for improvement, ask if they will read one more draft before the final draft.
• September/October of Senior Year: Submit the second draft of your EE to your advisor (if necessary) and look at their feedback. Work on creating the best possible final draft.
• November-February of Senior Year: Schedule your viva voce. Submit two copies of your final draft to your school to be sent off to the IB. You likely will not get your grade until after you graduate.

Remember that in the middle of these milestones, you'll need to schedule two other reflection sessions with your advisor . (Your teachers will actually take notes on these sessions on a form like this one , which then gets submitted to the IB.)

I recommend doing them when you get feedback on your drafts, but these meetings will ultimately be up to your supervisor. Just don't forget to do them!

The early bird DOES get the worm!

How Is the IB Extended Essay Graded?

Extended Essays are graded by examiners appointed by the IB on a scale of 0 to 34 . You'll be graded on five criteria, each with its own set of points. You can learn more about how EE scoring works by reading the IB guide to extended essays .

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

How well you do on each of these criteria will determine the final letter grade you get for your EE. You must earn at least a D to be eligible to receive your IB Diploma.

Although each criterion has a point value, the IB explicitly states that graders are not converting point totals into grades; instead, they're using qualitative grade descriptors to determine the final grade of your Extended Essay . Grade descriptors are on pages 102-103 of this document .

Here's a rough estimate of how these different point values translate to letter grades based on previous scoring methods for the EE. This is just an estimate —you should read and understand the grade descriptors so you know exactly what the scorers are looking for.

Here is the breakdown of EE scores (from the May 2021 bulletin):

How Does the Extended Essay Grade Affect Your IB Diploma?

The Extended Essay grade is combined with your TOK (Theory of Knowledge) grade to determine how many points you get toward your IB Diploma.

To learn about Theory of Knowledge or how many points you need to receive an IB Diploma, read our complete guide to the IB program and our guide to the IB Diploma requirements .

This diagram shows how the two scores are combined to determine how many points you receive for your IB diploma (3 being the most, 0 being the least). In order to get your IB Diploma, you have to earn 24 points across both categories (the TOK and EE). The highest score anyone can earn is 45 points.

Let's say you get an A on your EE and a B on TOK. You will get 3 points toward your Diploma. As of 2014, a student who scores an E on either the extended essay or TOK essay will not be eligible to receive an IB Diploma .

Prior to the class of 2010, a Diploma candidate could receive a failing grade in either the Extended Essay or Theory of Knowledge and still be awarded a Diploma, but this is no longer true.

Figuring out how you're assessed can be a little tricky. Luckily, the IB breaks everything down here in this document . (The assessment information begins on page 219.)

40+ Sample Extended Essays for the IB Diploma Programme

In case you want a little more guidance on how to get an A on your EE, here are over 40 excellent (grade A) sample extended essays for your reading pleasure. Essays are grouped by IB subject.

• Business Management 1
• Chemistry 1
• Chemistry 2
• Chemistry 3
• Chemistry 4
• Chemistry 5
• Chemistry 6
• Chemistry 7
• Computer Science 1
• Economics 1
• Design Technology 1
• Design Technology 2
• Environmental Systems and Societies 1
• Geography 1
• Geography 2
• Geography 3
• Geography 4
• Geography 5
• Geography 6
• Literature and Performance 1
• Mathematics 1
• Mathematics 2
• Mathematics 3
• Mathematics 4
• Mathematics 5
• Philosophy 1
• Philosophy 2
• Philosophy 3
• Philosophy 4
• Philosophy 5
• Psychology 1
• Psychology 2
• Psychology 3
• Psychology 4
• Psychology 5
• Social and Cultural Anthropology 1
• Social and Cultural Anthropology 2
• Social and Cultural Anthropology 3
• Sports, Exercise and Health Science 1
• Sports, Exercise and Health Science 2
• Visual Arts 1
• Visual Arts 2
• Visual Arts 3
• Visual Arts 4
• Visual Arts 5
• World Religion 1
• World Religion 2
• World Religion 3

What's Next?

Trying to figure out what extracurriculars you should do? Learn more about participating in the Science Olympiad , starting a club , doing volunteer work , and joining Student Government .

Studying for the SAT? Check out our expert study guide to the SAT . Taking the SAT in a month or so? Learn how to cram effectively for this important test .

Not sure where you want to go to college? Read our guide to finding your target school . Also, determine your target SAT score or target ACT score .

As an SAT/ACT tutor, Dora has guided many students to test prep success. She loves watching students succeed and is committed to helping you get there. Dora received a full-tuition merit based scholarship to University of Southern California. She graduated magna cum laude and scored in the 99th percentile on the ACT. She is also passionate about acting, writing, and photography.

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IB Maths Resources from Intermathematics

IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides

Is maths invented or discovered?  One of the most interesting questions to investigate with regards to maths ToK is the relationship between maths and reality. Why does maths describe reality? Are the mathematical equations of Newton and Einstein inventions to describe reality, or did they exist prior to their discovery? If equations exist independent of discovery, then where do they exist and in what form? The following discussion on maths and reality is not intended to be a model ToK essay – but simply a resource to help a discussion on this topic. At the end of the piece I have included a number of other interesting ToK maths questions for potential discussion.

Mathematics and Reality

We live in a mathematical universe. Mathematics describes the reality we see, the reality that we can’t, and the reality that we suppose. Mathematical models describe everything from the orbital path of Jupiter’s moons, to the flight of a football through the air, from the spiral pattern of a shell to the evolution of honey bee hives, from the chaotic nature of weather, to the expansion of the universe.

But why should maths describe reality? Why should there be an equation linking energy and mass, or one predicting the decay of a radioactive atom or one even linking three sides of a triangle? We take the amazing predictive powers of mathematics for granted, and yet these questions lead onto one the most fundamental questions of all – is mathematics a human invention, created to understand the universe, or do we simply discover the equations of mathematics, which are themselves woven into the fabric of reality?

The Second Law of Motion which links force, mass and acceleration, drawn up by Sir Isaac Newton in 1687, works just as well on the surface of Mars as it does on Earth. Einstein’s equations explaining the warping of space time by gravity apply in galaxies light years away from our own. Heisenberg’s uncertainty principle, which limits the information we can know simultaneously about a subatomic particle applied as well in the post Big Bang universe of 13.7 billion years ago as it does today. When such mathematical laws are discovered they do not simply describe reality from a human perspective, but a more fundamental, objective reality independent of human observation completely.

Anthropic reasoning

Anthropic reasoning could account for two of the greatest mysteries of modern science – why the universe seems so fine-tuned for life and the “unreasonable effectiveness of mathematics” in describing reality.

The predictive power of mathematics might itself be necessary for the development of any advanced civilisation. If we lived in a universe in which mathematics did not describe reality – i.e. one in which we could not use the predictive mathematical models either explicitly or implicitly then where would mankind currently be?

At the core of mathematical models are an ability to predict the consequences of actions in the natural world. A hunter gatherer on the African savannah is implicitly using a parabolic flight model when throwing a spear, if mathematical models do not describe reality, then such interactions are inherently unpredictable – and the evolutionary premium on higher cognition which has driven human progress would have been significantly diminished. Our civilisation, our progress, our technology is all founded on the mathematical models that allow us to understand and shape the world around us.

Anthropic reasoning requires that the act of conscious questioning itself is taken into account. In other words, it is certain that we would live in a universe both fine-tuned for mathematics and fine-tuned for life because if our universe was not, we would not be an advanced civilisation able to consider the question in the first place.

This reasoning does however require that we simply accept what appear to be the vanishingly small probabilities that such a universe would be created by chance. For example, Martin Rees, in his book, “Just Six Numbers” looks at six mathematical constants which were they to alter even slightly would create a universe which could not support life.

Whilst tossing a coin and getting 20 heads in a row is unbelievably unlikely, if you repeatedly do this millions of times, then such an occurrence becomes practically assured. Therefore using this mathematical logic, any vanishingly small probabilities can be resolved. The universe is the way that we observe it, precisely because it is a universe taken from the set of all universes in which we can observe it.

Mathematics as reality

An even more intriguing possibility is that maths doesn’t merely describe reality – but that maths itself is the reality. When we view a website, what we are actually viewing is the manifestation of the website source code – which provides all the rules that govern how that page looks and acts. The source code does not simply describe the page, but it is what generates the page in the first place – it is the underlying reality that underpins what we observe. Using this same reasoning could explain why our continued search for a Theory of Everything continually discovers new mathematical formulae to explain the universe – because what we are discovering is part of the universal source code, written in mathematics.

MIT physicist Max Tegemark, describes this view as “radical Platonism.” Plato contended that there exists a perfect circle – in the world of ideas – which every circle drawn on Earth is a mere imitation of. Radical Platonism takes this idea further with the argument that all mathematical structures really exist – in physical space. Therefore there is a mathematical structure isomorphic to our own universe – and that is the universe we live in.

Whilst this may seems rather far fetched, it is worth noting that in quantum mechanics it is difficult to distinguish between mathematical equations and reality. It is already clear that mathematical equations -wave functions – describe reality at the subatomic level. At this level the spatial existence of particles is described not in terms of classical co-ordinates, but in terms of a probability density function. What is still not clear after decades of debate is whether this wave function merely describes reality (e.g. the Copenhagen interpretation), or if this wave function itself is what really exists (e.g. the Many Worlds interpretation). The latter interpretation would necessitate that at its fundamental level mathematical equations are indeed reality.

It is clear that there is a remarkable relationship between mathematics and reality, indeed this relationship is one of the most fundamental mystery in science. We live in a mathematical universe. Whether that is because of nothing more than a statistical fluke, or because of the necessary condition that advanced civilisations require mathematical models or because the universe itself is a mathematical structure is still a long way from being resolved. But simply asking the question, “Why these equations and not others?” takes us on a fantastic journey to the very bounds of human imagination.

Other Maths ToK questions for discussion

Mathematics and the world (1) We can use mathematics successfully to model real-world processes. Is this because we create mathematics to mirror the world or because the world is intrinsically mathematical? (2) Why is it that some mathematicians and students of mathematics feel that mathematics is in some sense “already there” to be discovered? (3) In the light of the questions above, is mathematics invented or discovered? (4) Mathematicians marvel at some of the deep connections between disparate parts of their subject. Is this evidence for a simple underlying mathematical reality? (5) Some educational systems make a distinction between pure mathematics and applied mathematics. Does this reflect a fundamental difference in approach to mathematical knowledge?

Mathematics and knowledge claims (1) What do mathematicians mean by mathematical proof, and how does it differ from good reasons in other areas of knowledge? (2) Are all mathematical statements either true or false? (3) Can a mathematical statement be true before it has been proven? (4) It has been argued that we come to know the number 3 through examples such as three oranges or three cups. Does this support the independent existence of the number 3 and, by extension, numbers in general? If so, what of numbers such as 0, -1, i (the square root of -1) and a trillion? If not, in what sense do numbers exist? (5) In the light of the question above, why might it be said that mathematics makes true claims about non-existent objects? (6) In what sense might chaos (non-linear dynamical systems) theory suggest a limit to the applicability of mathematics to the real world?

Mathematics and the knower (1) Can mathematics be characterized as a universal language? (2) Why is it that mathematics is considered to be of different value in different cultures? (3) How would you account for the following features that seem to belong particularly to mathematics: some people learn it very easily and outperform their peers by years; some people find it almost impossible to learn, however hard they try; most outstanding mathematicians supposedly achieve their best work before they reach the age of 30? (4) Are there aspects of mathematics that one can choose whether or not to believe? (5) How do we choose the axioms underlying mathematics? Is this an act of faith? (6) Do the terms “beauty” or “elegance” have a role in mathematical thought? (7) Is there a correlation between mathematical ability and intelligence? (8) How have technological innovations, such as developments in computing, affected the nature and practice of mathematics?

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Exploring Mathematics As An Area of Knowledge in TOK Essays

Mathematics is an incredibly important area of knowledge, and a key part of the Theory of Knowledge course. Through the study of mathematics, we can explore the world around us and gain a better understanding of the universe and our place in it. Mathematics provides us with the tools to make sense of the world and to build models of reality.

In this guide, we will be examining the role of mathematics as an area of knowledge, and discuss how it can be used when writing a TOK essay. We will look at the history of mathematics, some arguments and observations related to the field, how it is related to the four areas of knowledge, its relevance to the nature of knowledge and ethical considerations when talking about mathematics.

Ultimately, by the end of this guide, you should have a better understanding of why mathematics is such an important subject to consider and how it can be applied in a TOK essay. Let’s get started!

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The History of Mathematics

Mathematics has been around since the very beginning of human civilization, being used by our ancestors to measure, calculate, and understand the world around them. At first, maths was used as a tool for practical tasks such as tracking the course of the sun and stars and measuring the land. Ancient Babylonians were the first to use algebraic equations, while the Egyptian and Greeks were the pioneers of geometry.

As time went on, mathematics evolved with the help of countless inventors, engineers, and thinkers. In the 17th century, calculus began to take shape and became the foundation for modern physics. By the 19th century, mathematics had become an integral part of everyday life, from engineering projects to currency conversion. Today, mathematics is essential for computers, research, and progress in all areas of science.

Mathematics is applicable to nearly every aspect of life – it helps us understand the universe, build machines and tools that make life easier, and predict future outcomes. It is so important that it has become a language of sorts, offering us a unique way of understanding the world and making sense of things that would otherwise remain unknown. We use maths to measure, calculate, and explore the unknown, to better comprehend our place in the universe.

Arguments and Observations about Mathematics

The field of mathematics is one that has been studied for centuries and is heavily intertwined with many aspects of life. When it comes to researching and reflecting on mathematics in the context of TOK essays , there are many different arguments and observations that can be made. It’s important to keep an open mind when considering mathematics from these different perspectives as different people may have different views.

One way of looking at mathematics is as a tool. In this case, mathematics can be used to help make decisions and create solutions to problems. Many of the advances made in science and engineering wouldn’t be possible without its use. It can also be seen as a way of organizing chaos and making sense of the world.

Others view mathematics as more than a tool– as an art form, or even a language. Mathematicians often talk of beauty they find in equations and results, while computer scientists use mathematical concepts to write algorithms and create programs. By solving problems and exploring new ideas, humans can better understand the world around them and make more informed decisions.

Finally, mathematics can be seen as having a moral dimension. For example, if a person knows the likelihood of an event occurring, they may be more likely to act on that information than if they had no knowledge of the situation. Each person must decide what their ethical code is when it comes to using and interpreting mathematical data.

By considering mathematics from different angles and highlighting how it can be useful in many different contexts and situations, discussions about mathematics can become more interesting and informative. From basic arithmetic to complex formulas, mathematics can be used in many different ways.

Areas of Knowledge

If you’re writing a TOK essay, then it’s important to understand how mathematics fits into the four Areas of Knowledge. These areas are: Sense Perception, Language, Reasoning, and Emotion.

Let’s start by looking at Sense Perception. As we know, mathematics is all about numerical relationships, understanding how numbers interact and how they can be used to solve problems. In this way, math is based on our senses, as it requires us to observe and measure the things around us. This means that mathematics falls under the Area of Knowledge of Sense Perception because it uses our senses to find patterns, draw connections, and make predictions.

The second Area of Knowledge is Language. Mathematics relies on language to communicate its ideas and results. Without language, mathematics would have no meaning or significance. This means that mathematics connects to the Area of Knowledge of Language as it utilizes symbols and words to discuss and explain mathematical concepts.

Next, let’s look at Reasoning. Mathematics is about using logic and thought processes to come to conclusions and prove assumptions. This means that mathematics falls under the Area of Knowledge of Reasoning due to the fact that it requires a person to be able to reason and think critically in order to arrive at a solution.

Finally, there is the Area of Knowledge of Emotion. Mathematics can often evoke emotions, both positive and negative. It can bring feelings of awe, excitement, and even fear. This means that mathematics can be related to the Area of Knowledge of Emotion since it has the power to influence the way we think and feel.

In conclusion, mathematics has undeniable relevance to all of the four Areas of Knowledge. By understanding and exploring the links between mathematics and each area, a writer can gain a greater appreciation for the subject and potentially uncover new ideas when writing a TOK essay.

Mathematics and the Nature of Knowledge

Mathematics plays a key role in helping us to define and categorize our world around us. It allows us to understand fundamental truths that would be impossible to comprehend without it. The use of mathematics provides a basis for understanding the same truths consistently and accurately, which is important to ensure that our knowledge claims are reliable.

The power of mathematics lies in its ability to be used as a universal language. It can be used to explain the physical and abstract realms in the same way. This makes it easier to utilize in different contexts, providing a consistent approach to problem-solving no matter what the problem is.

As well as providing a means of understanding, mathematics also helps us to measure, quantify and analyse the world around us. For instance, physicists use math to understand the motions of planets or the behavior of particles, which gives us an insight into the physical world. Economists also rely on mathematics to analyze and forecast economic trends.

Moreover, mathematics also has applications in the social sciences. It can be used to measure social indicators such as poverty levels or crime rates, allowing us to make informed decisions about these areas. We can also draw upon mathematical models to assess risk in situations and make decisions accordingly.

Ultimately, mathematics is at the core of all areas of knowledge, providing us with the tools we need to understand, measure and analyse our world. It is also a powerful tool when it comes to writing a TOK essay, as mathematical proofs and arguments are often used to support claims made in regards to knowledge.

Mathematical Proofs

The concept of mathematical proofs is an important one when it comes to discussing mathematics as part of a TOK essay. A proof is essentially a way of verifying that a certain statement is true, based on various sets of evidence or assumptions. It is used in mathematics to ensure that any conclusions are backed up by facts and logical deductions.

Proofs play an important role in the field of knowledge and can be used to support conclusions or fill in gaps in existing knowledge. Mathematical proofs are used to validate theories and hypotheses, as well as provide insight into the structure and order of the natural world around us.

Mathematical proofs can take on many different forms—some more complex than others. Generally speaking, a proof involves showing that a given statement is true based on previously accepted facts and that the result will always be the same regardless of how it is approached. Common techniques used in proofs include deduction, comparison, and proof by contradiction.

Proofs are an essential tool for gaining a better understanding of mathematics and its application in the world around us. They allow us to make sure that our knowledge claims are properly supported and that we can gain a greater understanding of the nature of truth and certainty. By utilizing proof techniques, we can further develop our understanding of mathematics and use it to create new knowledge.

Ethical Considerations

Mathematics is an area of knowledge that can have strong ethical implications. When writing a TOK essay , it is important to consider these implications and think about the moral dimensions of mathematics.

Mathematics can be used to support certain arguments or provide evidence for certain conclusions. It is important to remember, however, that mathematics is not always definitive. In some cases, there may be multiple interpretations depending on ones perspective and values.

For example, theories in economics or social sciences may be based on or backed up by mathematical models. The values and assumptions underlying these models may differ, leading to different interpretations of the evidence.

At the same time, mathematics can be used to support ideas and arguments that are unethical. Therefore, it is important to consider who the argument is benefiting, who it is having a negative impact on, and what moral judgments should be applied when forming an opinion.

When writing a TOK essay, ethical considerations should be taken into account. For example, ask yourself questions like “Could this mathematical method be used to support a moral claim?”, or “Are there any ethical implications of this mathematical proof?”

By taking ethical considerations into account when writing a TOK essay , you will be able to create a more thorough and considered argument, which will demonstrate your understanding of the subject.

Mathematics is a unique way of exploring the world around us, and plays an important role in developing our understanding of the nature of knowledge. Through this guide, we have explored how mathematics helps us define and categorize the world around us by providing a basis for understanding the nature of truth and certainty. We have also discussed the four areas of knowledge and examined some arguments or observations that could be made in regards to mathematics as a field of knowledge.

When it comes to writing an essay on these topics, ethical implications should be taken into consideration, along with mathematical proofs that can be used to support any knowledge claims. All of these elements should be thoughtfully considered in order to complete an effective TOK essay that addresses the relevance and importance of mathematics in the greater context of knowledge.

• Last Edit 11 May 2023

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Nick Radlinsky is a devoted educator, marketing specialist, and management expert with more than 15 years of experience in the education sector. After obtaining his business degree in 2016, Nick embarked on a quest to achieve his PhD, driven by his commitment to enhancing education for students worldwide. His vast experience, starting in 2008, has established him as a reputable authority in the field.

Nick's article, featured in Routledge's " Entrepreneurship in Central and Eastern Europe: Development through Internationalization ," highlights his sharp insights and unwavering dedication to advancing the educational landscape. Inspired by his personal motto, "Make education better," Nick's mission is to streamline students' lives and foster efficient learning. His inventive ideas and leadership have contributed to the transformation of numerous educational experiences, distinguishing him as a true innovator in his field.

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How To Write A ToK Essay - Updated 2023

Ace your ToK Essay with our expert tips & tricks! Get the latest and greatest techniques on "How To Write A ToK Essay" and impress the IB examiners.📝💡

Table of content

• Introduction

Purpose Of ToK

Assessment of tok, the game plan, execution of the gameplan, planning for tok essay, structure of tok essay, conclusions, bibliography.

Introduce your topic accurately and state your thesis statement for the essay carefully.  A thesis statement is like a teaser to your entire essay wherein you define your key terms and introduce your interpretation of the question. Make sure that you do not reword the prescribed title in your thesis. Instead, it needs to, as the word says, INTRODUCE your readers to what your essay is about. A strong introduction allows the reader to deduce what knowledge question(s) you are trying to answer.

So, in a nutshell

• Write interesting things about the given TOK essay title .
• Define key terms
• Narrow in on the particularly interesting aspect
• State your thesis statement . This will be your short answer to your given title if you don't know how to write a killer thesis statement check out this blog from SparkNotes .
• State your Roadmap. This will help the readers in understanding the direction of your essay.

How to write a TOK Essay? 

To answer that, you must familiarise yourself with what a TOK Essay is about.

Before you start reading this article,  Amanda  has some excellent TOK tips for you!

Theory of Knowledge is one of the most meta subjects that IB offers. Despite its complexity, TOK helps in providing a base for holistic learning and allows students to have a multidisciplinary experience. 

To understand TOK is to understand the essence of IB, a task that most people consider unattainable.

But not for you! 

Thank your lucky stars who made you land on Nail IB. How exactly will Nail IB help you? 

Well, nailing International Baccalaureate is something we will discuss later. 

Let's focus on cracking your TOK essay, shall we?

TOK demonstrates how students  can apply their knowledge  with  greater awareness  and  credibility .

Big words, huh? 

Now that we know that we cannot just slide through the Theory of Knowledge, let's understand how we can conquer this battle all guns blazing.

ToK essay’s primary objective is to answer the  why  behind our studies. 

It makes one aware of the real-life implications of their subjects. The students gain greater awareness of their personal and ideological assumptions and appreciate the diversity of different perspectives. It helps the students find their unique perception, a prerequisite for excelling in the IB TOK essays.

Before we dive into our gameplan, let’s overview the rules of the game.

There are two assessment tasks in the TOK: an essay and a presentation . While a presentation encourages students to explore a real-life situation through the lens of TOK, an essay is written on the basis of the various questions provided by the International Baccalaureate Organisation.

• The presentation is to assess a student’s ability to apply TOK thinking to a real-life situation whereas IB TOK essay is more conceptual.
• The essay is externally assessed by IB and must be on any one of the prescribed TOK essay titles issued by the IB for each examination session.
• Word limit of a TOK essay is 1600 words ( excludes extended notes, footnotes, bibliography).

Now that we have unleashed the game, let’s move ahead towards the gameplan of acing both, your presentation and your essay.

One of the fundamental tasks of TOK is to examine different areas of knowledge and find out their similarities and differences.

The TOK essay requires the students to investigate two Areas of Knowledge (AOK)  and two Ways of Knowing   (WOK) . AOKs and WOKs are investigated via questions such as:

• How do we know what we know? (WOK)
• What counts as evidence for X? (AOK)
• How do we judge which is the best model of Y? (WOK)
• What does theory Z mean in the real world? (AOK + WOK)

The aforementioned are  Knowledge Questions  which help combine the Areas of Knowledge and the Ways of Knowing that they are using. This eliminates the superficial way of learning and makes an individual sensitive to the nature of the information.   Our acquisition of Knowledge can be broadly divided into Shared Knowledge and Personal Knowledge.

Shared knowledge: What WE know It is the product of more than one individual. Although individuals contribute to it, shared knowledge does not solely depend upon the contributions of a particular individual—there are possibilities for others to check and amend individual contributions and add to the body of knowledge that already exists.

Personal knowledge: What I know It is essentially dependent on the experiences of a particular individual. Also known as procedural knowledge, it is gained through experience, practice and personal involvement and is intimately bound up with the particular local circumstances of the individual such as biography, interests, values, and so on.

The best hack to ace TOK essay is to develop a habit of making connections between the construction of knowledge, its acquisition and its relevance in the real world. 

After that one needs to develop an interest in understanding the difference between diversity and cultural perspectives and personal assumptions.

One also needs to critically reflect on their own beliefs and assumptions, leading to more thoughtful, responsible and purposeful lives.

Yes, this is what you signed up for. It may sound a little intimidating but once you get the hang of it you will be able to see the matrix and understand this beautiful world a little better.

Understand that to provide the best version of your writing, it will take you more than one or two drafts. First and foremost, you need to pick your essay topic diligently. Try to choose an essay topic that best interests you. The topic should also allow you to explore the Areas of Knowledge towards which you are naturally inclined. Here are a few sample questions:

a) 'Ways of knowing are a check on our instinctive judgments.' To what extend do you agree with this statement?

b) With reference to two areas of knowledge discuss the way in which shared knowledge can shape their personal knowledge.

c) How can we know if knowledge is produced more through 'Passive Observation' or 'Active-Experiment' within the Human and Natural-sciences under a Mathematical-Perspective?

d) "The whole point of knowledge is to produce both meaning and purpose in our personal lives". Assess the validity of this statement.

Great things take time. It took me more than a couple of weeks to finalize this TOK essay guide. It is completely okay if the first few drafts may not look pleasing or award-winning to you. You will require sharpening your perspective towards the topic each time you polish your draft. Your writing journey from a dull draft to a masterpiece will be a whole process that you will have to be patient with. Have faith in yourself and proceed stepwise.

You need to consider the opinions of others who have devoted hours of research and a lifetime of dedicated studying the topic that surrounds your writing. Unravelling the realms of your mind palace is so Sherlock but let’s not deny the fact that at times, Watson is the one whose expertise helps Sherlock through pretty difficult times. I mean even Batman needs a Robin. In support of my awesome sauce examples, the point I am trying to make is that  finding support for our claims and counterclaims through research is a good thing .

Use real-life examples to support your claims and counterclaims. These examples need to be documented researched examples like studies, experiments, articles, presentations by well-known people, etc. Examples that stem from your diploma subjects are highly encouraged, but those will need to be supported by research as well.   

It is suggested that you choose a title, stick to it, tackle it and not be afraid. Do not change your mind unless there is a good reason. Also, try choosing Areas of knowledge that you truly enjoy. You know slaying a known devil is much easier than an unknown one. Allot a TIMELINE to your essay. Start with creating an outline of your essay. This will help you to track your progress and accomplish your goals

You can use tools like  Trello  to organize your ideas and plan your TOK essay.

Areas of Knowledge (AOKs): TOK distinguishes between eight areas of knowledge. They are mathematics, the natural sciences, the human sciences, the arts, history, ethics, religious knowledge systems, and indigenous knowledge systems. It is suggested that students study and explore six of these eight.

Ways of knowing (WOKs): TOK identifies eight specific WOKs- language, sense perception, emotion, reason, imagination, faith, intuition, and memory. It is suggested that studying four of these eight in-depth would be appropriate. WOKs underlie the methodology of the areas of knowledge and provide a basis for personal knowledge.

Moving ahead, let us discuss the structure of your TOK essay.

Your essay will consist of 4 broad segregations

Before breaking down further on the pillars, keep the following in mind

• Please note what the TOK essay title is asking you. (Read it a couple of times. We highly recommend that you brainstorm ideas with your TOK coordinator)
• Make sure you understand the command term and the question it is asking.
• What kind of knowledge is being elicited?
• When choosing your areas of knowledge (AoK) and ways of knowing (WoK) make sure that you are able to draw contrasts and comparisons, that is, you are able to find evidence that supports as well as challenges your claims.
• Identify key terms in your TOK essay title. Make sure you define them. Your essay will gravitate around them. Key terms/words in your titles are your essay anchors. Your response should be built around them.
• Your writing skills come in handy while you work on your IB TOK essay. Like any other essay make sure you have proper thesis statements and topic sentences to guide the evaluator through your work.
• Respect the TOK essay title. Rephrasing the topic is not encouraged . Your main job is to address the title.

The body can be mainly divided into 3 segments.

Body (1st Segment)

• AoK Claim:  Here you investigate your first Area of Knowledge and draw parallels between your AoK and the question. This is done by stating your claim. Claims can be general in nature and need not reference a particular area of knowledge. They help you shape your essay and investigate the question further. 
• Evidence: Example of a real-life situation, describe thoroughly and accurately, which supports your stated claim. (AoK)
• Counter-Claim: State your counter-claim: like claims, those can be general and need not reference a particular area of knowledge. Counterclaim helps you show the other side the coin and gives your essay a holistic nature. 
• Evidence: A referenced real-life situation/example. Describe thoroughly and accurately, show how this supports your counterclaim (AoK ).
• Don’t forget to weave in your WoKs:  You need to take into account the source of your knowledge. Here you can also investigate if your nature of acquiring the knowledge has, in any way, affected it. It is good practice to question if your knowledge would be different had it been acquired through a different source/method
• Mini-conclusion: Here you analyze your examples in reference to your claims and counterclaims. You must connect to your thesis statement and the prescribed title. How does your proposed argument, in this particular part of the body, connect to the prescribed title and the knowledge questions you are trying to answer?

Body (2): Follow the above process for your second AOK.

• Use this part of your essay to compare and contrast your varying AoKs. You need to connect them to your thesis and your prescribed title clearly showing how your arguments respond to the PT.

Your conclusion section will make your essay come together. It is the glue that will make your essay stick together. Herein, you need to

• Reiterate your thesis (initial response).
• Use your mini conclusions to write a final conclusion.
• Tell the reader what the significance is for knowing what we know in this particular PT.
• Discuss implications as well.
• Offer another perspective, how will the perspective of a different person affect the claims/counterclaims you make in the essay?
• Don’t forget to make the end strong.

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Deciphering the Ancient Mayan Timekeeping System

This essay is about the Mayan calendar emphasizing its advanced integration of astronomy and mathematics. It explains the Tzolk’in and Haab’ systems detailing their roles in religious ceremonies agricultural practices and timekeeping. The essay also explores the calendar’s deep spiritual and cultural significance highlighting its connection to Mayan mythology and its lasting impact on Mesoamerican societies. The Mayan calendar’s complexity and precision reflect the civilization’s intellectual achievements and enduring legacy.

How it works

Mayan civilization known for his movements in astronomy and mathematics developed the refined calendar system that prolongs oczarowywa? scientists and historians today. But old timekeeping method what is characterized by his tangled hieroglyphs and cyclic calculations offers the valuable penetrating in Mayan culture and their deep understanding of the merciful phenomena.

Central to Mayan of calendar are two main systems: Tzolk’in and Haab’. Tzolk’in often imposed till saint or divine calendar consists of 260 days divided by 13 cycles of 20 days each.

Every day is presented by combination of number with 1 to 13 and one of 20 expressive day of the names. This cycle recurs creating a standard that was critical for religious ceremonies agricultural practices and the personal successes.

In a difference from that the calendar of Haab’ follows 365 sunny days divided by 18 months of 20 days each plus additional period of 5 “nameless” days known how Wayeb’. This calendar was substantial for the agricultural planning marking seasons and coordinating civil activity within the limits of Mayan of society. Synchronization of calendars of Tzolk’in and Haab’ attained insertions through the complicated system allowed to Representatives of people of maya to envisage merciful events with wonderful exactness.

After his practical applications Mayan calendar the retained deep spiritual and cultural value. Then was confused bound to mythology where Gods and blue bodies played critical roles to interpretation of time and creation of universe. For example Popol Vuh saint book of Quiché of maya pours the space order set by Gods pawned on motions of stars and planets that were removed in the calculations of calendar.

Scientists prolong to study the patient inheritance of calendar of Representative of people maya aiming to extricate his difficulties and to understand his more wide values for old societies of Mesoamerican. Calendar not only served as instruments for timekeeping but and how the symbol of cultural identity and intellectual achievement. His influence stretched on the collapse of classic Mayan of civilization there is what confirmed his acceptance and adaptation by later native cultures in Central America.

Upon completion Mayan calendar stands how the testament of ingenuity and to astronomic mastery of old maya. His double systems of Tzolk’in and Haab’ bound to his spiritual value and cultural resonance distinguish refinement of Mayan of civilization in understanding and interpretation of passing of time. As we are dug deeper in his messes we open not only a measuring method but and deep testament to the human search for knowledge and understanding space.

Cite this page

Deciphering the Ancient Mayan Timekeeping System. (2024, Jul 06). Retrieved from https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/

"Deciphering the Ancient Mayan Timekeeping System." PapersOwl.com , 6 Jul 2024, https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/

PapersOwl.com. (2024). Deciphering the Ancient Mayan Timekeeping System . [Online]. Available at: https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/ [Accessed: 8 Jul. 2024]

"Deciphering the Ancient Mayan Timekeeping System." PapersOwl.com, Jul 06, 2024. Accessed July 8, 2024. https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/

"Deciphering the Ancient Mayan Timekeeping System," PapersOwl.com , 06-Jul-2024. [Online]. Available: https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/. [Accessed: 8-Jul-2024]

PapersOwl.com. (2024). Deciphering the Ancient Mayan Timekeeping System . [Online]. Available at: https://papersowl.com/examples/deciphering-the-ancient-mayan-timekeeping-system/ [Accessed: 8-Jul-2024]

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