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Most IB students know the Mathematics Extended Essay is one of the program’s most significant requirements. It will test your analytical, research, and writing skills.
However, if you’re majoring in Mathematics, you may wonder how to organize an Extended Essay on this subject. Is writing this paper challenging? Have no fear; I can attest from personal experience that completing the Mathematics Extended Essay, if one approaches it systematically, may provide satisfying results. Let’s dissect it methodically.
What Is Extended Essay in Mathematics?
The Mathematics Extended Essay is among the most distinctive and challenging papers in the IB Diploma Program. It lets you use your problem-solving skills, learn about mathematical ideas, and create your original work by going into great detail about a mathematical topic. From what I’ve seen, the most important thing for a good Math EE is to choose a research question that is both theoretically sound and specific enough for a full investigation.
This essay is distinct from other papers in the IB program because it necessitates practical application and abstract reasoning. The process can be challenging and thrilling if you can demonstrate how the mathematical principles you work with are connected to real-world situations or perhaps even extant research, following the general IB criteria.
A few main things about the Math Extended Essay make it different from other writings. I’ll go over some of the most important parts with you:
- You should base your research question on a specific area of Mathematics. Rather than a broad topic like “Applications of calculus,” a better question would be, “How can calculus be used to model the path of a spacecraft?”
- Your paper is not a summary of ideas that already exist. Instead, you should think about mathematics ideas, research, and show your results.
- Good essay structure is everything. Your paper should have clear parts for the introduction, methodology, analysis, and conclusion. Each of these helps to build a strong case.
You must understand the math techniques for a Math EE and show you know your chosen subject. You will have to work with formulas, theories, proofs, or models in math. The IB likes creativity, so try to use new methods, ideas, or points of view. It means making your mathematical models or using ideas that already exist in a new way.
Find expert advice on how to write a focused, well-structured Computer Science Extended Essay that meets IB standards.
How to Choose a Research Question for Your Math Extended Essay?
From what I know, many students find themselves caught in this area. For instance, asking, “What does math do in the real world?” is too broad. Instead, ask yourself, “How can the Fibonacci sequence be used to model how sunflowers grow?” That’s a much better and more detailed question.
You can understand what works by examining how a good Mathematics EE question makes you use math to solve a problem or prove a theory. I think you should choose a topic you are interested in and can see yourself working on for a long time. This approach will keep you going as you go through the process.
I’ve seen students have trouble coming up with good research questions because they pick topics that are either too general or don’t involve enough math. For example, questions like “What are the most famous mathematical theorems?” or “How is math used in physics?” may sound attractive. Still, they won’t allow you to look into mathematical ideas.
A good research question, on the other hand, could be: “How can game theory be used to predict what will happen in a certain economic model?” or “How does the distribution of prime numbers change when there are a lot of numbers?” These questions are specific, can be researched, and are full of math that lets you do original research.
More Topics to Read:
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- How to Write IB Extended Essay
How Do You Structure a Math Extended Essay?
At first, writing a Math EE might seem challenging, but if you follow the proper format, it will be much easier. As an experienced IB writer, I can tell you how important having a clear, reasonable structure is.
1. Introduction
You set the scene for your research in the EE introduction. In this part, you’ll discuss your research question and why you chose it. Be brief and precise to tell the reader what to expect. From what I’ve seen, an introduction that quickly explains why your research question is important and how it relates to math can make a big difference.
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- Be clear about your research question. Your question should be focused and based on math. Don’t choose topics that are too broad or general; make sure you can go into detail.
- Set the background. Summarize the central ideas or theories you will use in your research.
- Choose what you want to look into. Make the limits of your research clear. What are you going to look into? What are you going to leave out?
When you set the scope early on, your research stays on track and is easy to handle throughout the essay.
2. Theoretical Background
You’ll set the stage for your research in this part by describing the mathematical ideas and theories you’ll be using. IB standards say that this part is essential for setting up the theory context of your research. From my own experience, I know how important it is to keep this part focused and on topic — don’t give the reader too many details that aren’t necessary.
- Explain key formulas and concepts. Explain the main mathematics ideas that will help you with your research. Do everything possible, but don’t get too caught up in the details.
- Link theory to your research question. Ensure that the ideas you discuss have something to do with your research question.
In this part, you should demonstrate that you understand the theory and how it fits with your research question.
3. Methodology
In your methodology section, you describe the steps you will take to answer your research question. In this part, you’ll talk about the tools, methods, and ways you’ll use to solve problems or collect and study data. From what I’ve seen, this part is very important because it describes your math skills and shows that you can research independently.
- Describe your steps. Did you use geometry, calculus, or some other kind of math? Try to be as detailed as you can.
- Describe the apps and tools used. In your study, list any tools you used, such as GeoGebra, Python, or MATLAB. With these tools, it’s easier to do complicated math.
- Explain any assumptions you made. For example, you should explain those assumptions if you ignored some factors or used rough numbers during your study.
By being specific about your methodology, you demonstrate to the reader that your approach is good and that you have considered the best tools for the research.
4. Results and Analysis
IB rules say that the results should be shown clearly, with full explanations for each step of writing. In my opinion, this is one of the most critical parts of your Math EE because it shows how well you understand the math that went into your research.
- Make your results stand out. Show your results with tables, graphs, and other visual tools. After each picture, there should be a clear description of what it shows.
- Look at the results. Take some time to figure out what your results mean after showing them. What do they tell you about your research question? Do they back up your theory or call it into question?
This part is where all your hard work pays off. You should show the data and explain how it relates to your research question.
5. Discussion
During the discussion, you can think about what you’ve learned. Figure out what your results mean and what they mean for the bigger picture. From what I’ve seen, many students skip this part, but it’s essential to show that you can think critically and review your work.
- Talk about your results’ importance. How does your research add to what we know about Mathematics? Could your results be used in the real world?
- Recognize your limitations. Of course, every study has some flaws. Be honest about any problems you had with the data or methodology.
Your discussion shouldn’t just be about your results; it should also show that you can think critically about your work and how it affected people.
6. Conclusion
In the EE conclusion, you can summarize what you found and think about the whole process. This part should quickly go over the most important things you learned from your research and maybe even suggest places for more research. A reasonable conclusion ties everything together and ensures the reader understands what you found.
How Long Should a Math Extended Essay Be?
IB rules say a Math EE should have between 3,000 and 4,000 words. This word limit applies to the whole essay, from the introduction to the conclusion. It does not apply to the list or the notes, though. To make sure your essay is both complete and brief, you should stay within this range.
From my observation, a good goal is to write about 3,500 words. This scope enables you to show your results, describe your methodology, and offer enough analysis without giving the reader too much information. A good Extended Essay is much more important than lots of it. Focus on clarifying your point of view and using your word count to get your point across quickly.
If you’re struggling with writing, you might want to use a Buy Extended Essay service to ensure your work meets the high IB standards. We can help you with everything from choosing a topic to writing and editing the final draft.
Valerie Green
Valerie Green is a dedicated educator who spends her time helping high school and college students succeed. She writes articles and guides for various online education projects, providing students with the tools they need to excel in their studies. Friendly and approachable, she is committed to making a difference in the lives of students.
