## Table of content

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 document.

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

Let's keep it accurate.

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 a strong passion for Mathematics and a solid mathematical foundation. Not to mention being willing to devote their time and effort to this self-directed research.

**Disclaimer - **If you have second thoughts, you should reconsider and re-evaluate your choice because it's no use aiming in the dark.

There needs to be more!

Invaluable tips and techniques are the last missing piece of the IB Math EE puzzle.

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.

**Say it out loud for me - I got this!**

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Returning to our one-stop guide for all things IB Math EE, let us see what this article will cover.

❓__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__

## Extended Essay & What Is It❓

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 critical 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 topic 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 from their respective IB mentors every step of the way.

**The IB highlights the significance of the Extended Essay:**

- 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 for by the student.

**The skills the Extended Essay aims to develop 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 more transparent.

## IB Math EE vs Math IA 🥊

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 essential. 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 primary and secondary research on a research question they choose based on a diverse topic about the subject. Since EE is an independently researched essay, your mentor may only be able to give you some of the answers you wanted, unlike the IA.
- Students must write one Extended Essay on a subject of their choice for their IB Diploma Programme, but I must be prepared for all the topics.
- Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. Your grade 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 must attend to and a detailed overview of the structure and planning of the EE.

## WTH Is An IB Math Extended Essay? 🌋

Now that we’ve got our basics to, let’s get down to business. The fear around IB Math Extended Essay makes 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; it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slim chance you can survive the Math Extended Essay battle.

If you’ve opted for Math Extended Essay, we assume you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which, 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 incredibly 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.

## A Brief About IB Math EE 🩲

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 includes 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 unit to flourish.

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.

## Sexy Pointers You Can't-Miss 🤤

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

- Attempting a Math EE requires a decent amount of hard work. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. Going for a complicated subject, you can’t comprehend and interpret futile.
- 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.
- Another thing to remember is that the topic you finally choose should have a good research foundation and room for a novel contribution.
- Incorporate Primary and Secondary research wherever appropriate.
- Proper Referencing should be done for the essay.
- For Reflection, emphasize the Planning, Research, and Writing Processes.

## 4 Ways To Find The Right Math EE Topic ⭕

**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, and documentation. Keep jotting important points down simultaneously. The study will and must go on throughout your search for the right math EE topic.

**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 there inspires you to get the ball rolling!

## Formulate Your Research Question 🔎

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 build your essay around your Research Question; hence pay close attention to it.

All you will include in your essay must be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will use 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.

## Planning Your Research & Essay 📖

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 while maintaining a mathematical focus.

## Structuring Your Essay 🏗️

- Though you can approach your essay in whichever way you like, there should be a consistent logical structure.
- 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, correctly reasoned arguments, and adequate methodology to achieve 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.

## IB Math EE Reflection, What To Do? 🪞

- 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 overcame them, if at all.
- The three reflections are written at the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

## IB Math EE Criteria 🧮

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 the creation of a good standard (Level 6)

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

**D -** refers to the product of a mediocre standard (Level 4)

**E -** refers to the design of an elementary average (Level 6)

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma.* As 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, and 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)

## IB Math EE Examples 🛹

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 integration methods?

**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 manufactured satellites?

You should also check out this __sample band, A Math EE, published by the IB__. This will give you an honest insight into making a band-A essay. Also, go through ** band B, C, and 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 try Nail IB’s Extended Essay guide; 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-test __series here and access__ ____premium guides__ here.

Happy learning!