IB Math EE - An Easy Guide To A 34/34

It’s time we address the elephant in the room.

 

IB Mathematics Extended Essay.

 

There, we said it.

 

If you’ve taken up IB Math EE, we’re here to tell you that it isn’t over, contrary to what you might have heard.

 

Researching, planning, and finally writing a good IB Math EE is no walk in the park, but rest assured that you’ll feel different once you’ve gone through this valuable piece of document.

 

Nail IB presents the only comprehensive guide you need to nail your IB Math EE.

 

Let’s keep it real.

 

IB Math EE is a rigorous, independent, academic research essay that calls for,

• a keen interest in Mathematics,
• strong mathematical aptitude & reasoning,
• a focused and disciplined approach, and most importantly,
• essential tips, techniques, and quality guidance.

 

When one opts for IB Math EE, one should ensure that they possess a strong passion for Mathematics along with a solid mathematical foundation. Not to mention, be willing to devote their time and effort to this self-directed piece of research.

 

Disclaimer - If you have second thoughts, you might want to reconsider and re-evaluate your choice because it’s no use aiming in the dark.

 

This, of course, is not enough!

 

The last missing piece of the IB Math EE puzzle is invaluable tips and techniques.

 

We figured, given the panic and stigma around Math Extended Essay, what students need, is not some more panic; instead, expert guidance to keep them pumped to write their EE papers with skill, precision, and utmost zeal. And so, true to our word, we’re here to help you out.

 

Say it out loud for me - I got this!

 

Before we dive any further, we are thrilled to share our premium IB Math resources with you. Check out the IB Math AI SL bundle and the IB Math AI HL bundle, including everything from comprehensive, up-to-date video lecture courses by Adam Nazha to curated IB Resource Libraries. All your IB DP Math queries, now answered!

 

While you’re at it, check out our IB Math AA SL repository, where Patrick Jones (yep, you got that right, our very own PatrickJMT - the best Mathematics instructor in the world) will guide you with a brilliant video lecture course he has created to help you nail your concepts and exams alike! Happy learning!

 

Coming back to our one-stop guide for all things IB Math EE, let us see what this article will be covering.

• Extended Essay & What is it❓
• IB Math EE Vs Math IA 🥊
• WTH Is An IB Math Extended Essay? 🌋
• A Brief About IB Math EE ? 🩲
• Sexy Pointers You Can't-Miss 🤤
• 4 Ways To Find The Right Math EE topic ⭕
• Formulate Your Research Question 🔎
• Planning Your Research and Essay 📖
• Structuring Your Essay 🏗️
• Writing Your Essay Writing Your Reflection 🪞
• IB Math EE Criteria 🧮
• IB Math EE Examples 🛹

 

 

First things first, let’s briefly discuss what an Extended Essay is.

 

As the IB defines it, the Extended Essay is a 4000-word in-depth study, part of the IB Diploma Programme core mandatory for all students.

 

A 500-word reflection component-inclusive of 3 reflections - is submitted with the academic writing.

 

This, of course, is done under the supervision of your IB advisor. The important thing to note is that you can choose to write an Extended Essay on any subject offered by the IB in your session, though it is highly recommended you settle on a subject you are studying as a part of your IB curriculum.

 

The purpose of an Extended Essay is to motivate students to conduct formal research on a subject area of interest, independently work on the chosen research question and gain guidance every step of the way from their respective chosen IB mentors.

 

The IB highlights the significance of the Extended Essay as:

• Hands-on learning for undergraduate research
• An opportunity for students to research an area of interest relating to one of the 6 DP subjects opted by the student.

 

The skills the Extended Essay aims at developing in students are:

• Coming up with a relevant Research Question
• Personally engaging with a topic of exploration
• A coherent communication of ideas
• Strong Argument building

 

For better understanding, go through this document on Extended Essays by the IB. It will make things clearer.

 

 

Students often confuse their Internal Assessments with Extended Essays, which is a grave mistake. Gaining clarity on both these components of the IB DP core is not only essential but necessary. Let us understand the significant difference between the two.

• While Internal Assessments require students to investigate and explore an idea, Extended Essays are more formal. Students need to perform both primary and secondary research on a research question they choose based on a diverse topic about the subject opted. Since EE is an independently researched essay, your mentor may not be able to give you all the answers you wanted, unlike the IA.
• Students have to write one Extended Essay on a subject of their choice for their IB Diploma Programme, but IAs need to be prepared for all the subjects.
• Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. The grade you get on your Extended Essay is combined with your Theory of Knowledge Essay/Exhibition score to assign you your overall score/points.

 

Word of caution: Do not choose the same investigation topic/research question for your Internal Assessment and the Extended Essay.

 

For a much better breakdown of the EE document, you must go through our article on the IB Extended Essay. It contains an IB EE checklist you cannot miss, a detailed overview of the structure and planning of the EE.

 

 

Now that we’ve got our basics right let’s get down to business. The scare around IB Math Extended Essay has the most confident students hesitate and doubt their choices. But we aren’t here to scare you. The myth about the horrors of the IB Math EE isn’t all false; in fact, it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slimming chance you can survive the battle that is Math Extended Essay.

 

If you’ve opted for Math Extended Essay, we’re assuming you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which is usually the case-your only hope at the end of the tunnel is your drive for the subject you’ve chosen. Being a rigorous subject for writing one’s Extended Essay, Mathematics can be especially demanding. So unless you want to play it risky, we suggest you reassess your liking for Mathematics. Once you know for sure, that’s when it begins. Lots of research. Since it is an independently written document, you want to be doing your homework well.

 

We will further break down the IB Math Extended Essay, from planning to execution, so that you can organize your thoughts and make appropriate decisions.

 

 

The Math Extended Essay is an in-depth research document covering any topic with a mathematical focus, i.e., not limited to the mathematics theory (shouldn’t be entirely descriptive). IB has divided Math Extended Essays into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics, examples include: geometry or fractal theory
• the application of mathematics in the proving of theorems, for example, number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• the effect of technology on mathematics
• in creating links between different branches of mathematics,
• or in bringing about a new branch of mathematics or causing a particular branch to flourish.

 

The point is, your Math EE topic should be an extension of your IB Maths syllabus or the practical application of the knowledge you’ve gained in class.

 

 

Before moving on to the planning and structure of the Math Extended Essay, here are some pointers you absolutely cannot afford to miss:

1. Attempting a Math EE requires a decent amount of hard work on your end. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. It’s futile to go for a complicated topic that you can’t comprehend and interpret.
2. The mathematical work you put in will have to meet a certain level of sophistication, so avoid going for a topic that gives rise to a trivial research question. Your research question shouldn’t be too generic or broad on similar lines. Ensure you can sufficiently narrow down your area of investigation.
3. Another thing to keep in mind is that the topic you finally choose should have a good foundation of research and room for a novel contribution.
4. Incorporate Primary and Secondary research wherever appropriate.
5. Proper Referencing should be done for the essay.
6. For Reflection, emphasize the Planning, Research, and Writing Process.

 

 

Spitball ideas - You begin here. Write down any interesting ideas you can come up with. This is your brainstorming session.

 

Do your Research - You could not, would not want to meddle with this step, let alone skip it. Research. Read reports, articles, documentations. Keep jotting important points down simultaneously. Throughout your search for the right math EE topic, research will and must go on.

 

Approach professors/professionals/experts - Contact concerned lecturers, professors, and industry professionals. They can provide you with invaluable insights. It would be best if you also discussed ideas with your mentor.

 

Point to Note - Your goal should be to find a topic you understand and contribute to. It is always recommended to refer to your Math syllabus; something in there inspires you to get the ball rolling!

 

 

Your essay will be structured as a document answering the Research Question you’re working on. It should be focused, clear and arguable. You will be building your essay around your Research Question; hence pay close attention to it.

All you will include in your essay needs to be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will be using to achieve a plausible outcome.

Honing your Research Question is a continuous process. If it appears relatively easy or complex, please rephrase it. Good Research Questions may start with: “How can we model…”, “To what extent…”, etc.

 

 

Collect Primary and Secondary data and incorporate it wherever appropriate.

 

Primary sources for Math research include 

• Data-gathering
• Visualization
• Abstraction
• Conjecturing
• Proof

 

A few sources to gather Secondary data include Google Scholar, textbooks, databases such as JSTOR, etc. For your essay, know your aims and devise a step-by-step plan to answer your research question, all the while maintaining a mathematical focus.

 

 

• Though you have the freedom to approach your essay whichever way you like, there should be a consistent logical structure to it.
• The work done in your essay should develop to answer your research question.
• Subheadings will provide your work with much-needed coherence and viability.
• As you’re working on a Math EE, the IB expects you to communicate mathematically, basically:
  • Describe your way of thinking
  • Write definitions and Conjectures
  • Use symbols, theorems, graphs, and diagrams
  • Justify your conclusions.
• Visual aids such as graphs and diagrams should be included in the body, while tables and computer programs should be mentioned in the footnotes or the appendix.
• Data must be analyzed appropriately using relevant techniques, arguments correctly reasoned, methodology properly applied to come to a result.
• Provide the necessary explanation and commentary for all your work.
• Throughout the writing, you may need to re-evaluate the method, approach, and structure to fit the word count adequately.

 

Once you’re finished writing, you will have to reassess everything from scratch- the equations, the theory, etc., to ensure the coherence of your essay.

 

 

• The three reflections should highlight how the process of writing your essay changed in due course of work and what you’ve learned from it.
• The Reflection should emphasize the planning, research, and writing process.
• You should discuss your choices, the re-evaluations you had to make, the limitations of your work, and how you managed to overcome them, if at all.
• The three reflections are written in the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

 

 

Extended Essays are assessed externally by IB-appointed examiners and are marked on a scale of 0 to 34. The score obtained by a student corresponds to a particular band. The bands are:

A - refers to work of an excellent standard (Level-6)

B - refers to work of a good standard (Level-6)

C - refers to work of a satisfactory standard (Level-12)

D - refers to work of a mediocre standard (Level-4)

E - refers to work of an elementary standard (Level-6)

 

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma. Like we said, your EE is not a component you can mess up.

 

The Extended Essay Rubric includes the following Assessment Criteria:

Criterion A -  Focus and Method (Covers the topic, research question, methodology)

Criterion B - Knowledge and Understanding (Covers context, subject-specific terminology, and concepts)

Criterion C - Critical Thinking (Covers research, analysis, discussion, and evaluation)

Criterion D - Presentation (Covers structure, layout)

Criterion E - Engagement (Covers reflection on planning and progress)

 

 

Now that we’ve discovered and learned about the process of writing a Math EE, here are a couple of ideas to give you an idea about how your Math EE questions should be framed:

 

Topic - Archimedes’ calculation of areas

Research Question - What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s methods of integration?

 

Topic - Approximation of irrational numbers by rational numbers

Research Question - How well can π, e, √2, and other irrationals be approximated by rational numbers?

 

Topic -  The geometry of navigation

Research Question - What was the role of mathematics and geometry in navigation when we relied on the stars? Does it still play a part now we have man-made satellites?

 

You should also check out this sample band A Math EE published by the IB. This will give you a fair insight into making a band A essay. Also, go through band B, C, D extended essays to understand the loopholes to avoid.

 

And that’s a wrap!

 

We hope this comprehensive IB Math EE guide answers your queries regarding the EE. We also suggest you go through this IB Extended Essay guide to clarify the Extended Essay component of your IB DP curriculum. You should also give Nail IB’s Extended Essay guide a try; check it out here!

 

At Nail IB, we’re committed to delivering A-quality guidance so that your IB DP journey is smooth and successful. You can explore our take a test series here and access premium guides here.

 

Happy learning!