How to write a Math Extended Essay [2022 Ultimate Guide]

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Math EE examples

Mathematics Extended Essays generally try to verify a particular result, or they try to find new developments, which is very rare. An example of a title could be How Fundamentals of Number Theory Facilitate Public-Key Cryptography through the RSA Cryptosystem.

How to write a Math Extended Essay [2022 Ultimate Guideline]

Introduction

Ask a thoughtful question. Learning how to frame a scientific question properly is difficult, particularly so early in your academic career as high school.

Discuss your difficulties with your professors and fellow students and receive their opinions.

Now, consider the following advice:

a) Within the field of interest, what are you most curious about? Do you have any queries or believe you need additional information on the topic you are keen to know more about? Is there a subject that interests you that you may use to guide your future career while you plan for university programs? Before selecting a topic ensure that you have assessed whether it has enough data to avoid falling short of the required 4000 words.

b) Once you have settled on a particular topic you are interested in learning more about, conduct a fast search to check if the historical literature has already offered a sufficient response. Conduct a short and quick assessment of history textbooks and research the secondary literature on Google Scholar to find out what’s already been known about this problem.

Ascertain whether the studied sources provide a precise, reliable, and valid answer to the question. Do you think, for example, that the secondary sources and the textbook sufficiently handled the issue? Are there any areas of knowledge that need more research? Are there any biases or misrepresentations in the primary and secondary sources that would have lowered the credibility of the response, given that your research question might shed some light on?
Create a question that could guide your further research and analysis of this topic ask yourself if you identify a need for extra investigation due to knowledge gaps in the literature or questionable sources for the solutions provided.

The opening paragraph of a successful extended essay should discuss how skillfully the question was crafted and why it is important. Show the examiner what is already known about the subject in the body of published studies and what fresh understanding and information your question will add to the canon of historical writing.

Remember to provide due credit to any primary or secondary materials (textbooks, Google Scholar articles, etc.) you utilized to investigate the state of knowledge on the subject.

Methodology

Create a strategy to answer your question. After the question has been adequately answered in an extended essay, the author’s approach to responding to the question must be discussed.

You must outline your process so that the examiners may perform a similar search and get the same results to assess your findings’ validity.

This is an important stage in the methodology to ensure the reliability of your findings.

Here are some guidelines to assist you in creating the methodology:

Ask about the trustworthy sources that deal with the topic of your inquiry. You might consult a university librarian, a local public library, or even one of your teachers for help with this stage.

Create a list of the scholars with the best reputations and the works they published on the subject you are interested in. Identify each scholar and then explain why their name or the name of their text is an important source for your investigation.

Use Google Scholar to look through every paper written by a scholar that tries to address the question. You will have to cite your search phrases in your extended essay, so maintain a record of them.

After that, download a text that is relevant to your question.

List the resources you have found and indicate beside each one why it is important to your inquiry.

To come up with the answer to your question, decide if you need to consult any primary sources, such as a government document, journalistic accounts of the events, official interviews held in front of a public audience, and first-person accounts of the actions by historians or regular people, etc.

Search for these resources online, at your neighborhood library, or in a library at a university. Create a list of the materials you’ve found and explain why each one is important to your investigation next to each one.

Briefly describe how you searched for your resources inside the body of your lengthy essay.

Don’t forget to describe how you found the trustworthy secondary sources, the Google Scholar search phrases you used to find additional secondary sources, and the procedures you followed to find primary sources.

Historiography analysis

A thorough analysis of your sources should follow the description of your method. Assess any prejudice, distortion, etc., by analyzing the historiography of both secondary and primary sources.

Summarize the findings of the historiography analysis in the extended essay’s body, citing significant secondary and primary sources especially to show their reliability as sources.

It is a smart idea to incorporate an in-depth analysis of the crucial sources (either primary or secondary) that you will rely on most to address your point.

Arguments

Continue your historiography study by providing a thorough response to the question you presented in part 1.

a. Critically respond to the query you made in part 1 with several supporting points.

To begin, thoroughly read your primary and secondary sources. After reading each source, summarize the most important details it contains for you, answering your question on a separate piece of paper.

Using this technique, you may begin to lay out what the other source has to say regarding the subject you have posed. Using this method will also make it simple to properly reference primary and secondary sources when developing your history extended essay ideas.

b When you evaluate each source, consider the importance and worth of the data it provides based on your assessment of its lack of bias and distortion in the historiography research you conducted in section 3.

c. After that, utilize the information you have acquired from the sources, look for long-term trends uniformly true across all the bases, and indicate a suitable answer to your question.

Once you have determined the pattern of good responses to your question, develop the main arguments that will help offset the explanation in point 1.

For each argument point, cite the relevant primary or secondary sources you used to support your position.

How to write the body of a mathematics extended essay

The essay’s body should be organized as a rational argument. This can take many forms depending on the essay’s topic. Still, as the idea is developed, it should be apparent to the reader what pertinent evidence has been found, where/how it has been found, and how it supports the argument.

Subheadings within the main body of the essay will aid the reader in understanding the argument in some disciplines, such as the sciences (and will also help the student to keep on track).

Students must structure their Philosophy extended essays according to the accepted standards of the subject.

Once the essay’s main body is complete, it is possible to finalize the introduction (which tells the reader what to expect) and the conclusion (which says what has been achieved, including notes of any limitations and questions that have not been resolved).

The examiner won’t read notes and appendices therefore ensure that all of the important sources are in the body of your extended essay.

Each argument point should be written in a paragraph and included in the body of your lengthy essay.

Condense your main points of contention in a thesis statement. The thesis statement needs to be expressed as follows: “I argue that XYZ is the right response to the query based on Arguments 1, 2, 3, and so on.”

Based on how many arguments you have created. The body of your extended essay should contain both the thesis statement and an introduction to the question you addressed in point 1.

In an extended essay, the thesis statement serves as the reader’s road map while they read the article. It outlines how you will persuade the reader that the proposed solution is accurate by giving a methodical and trustworthy description of how you concluded (the methodology) and what credible evidence you have found to support the truthfulness of the response (historiography analysis) (the argument points).

Conclusion

In the conclusion, you should restate your thesis statement, which was stated following your part 1 introduction to the question.

If there were any shortcomings in your approach, knowledge, or understanding of the topic that kept you from providing a complete response in the extended essay, explain them in your conclusion and explain why.

This will make it easier for other researchers to revise and build on your response. Additionally, it will help the examiner understand how honest your answer is.

Additionally, it demonstrates to the examiner that you are a competent, experienced researcher dedicated to the scientific goal of acquiring precise knowledge and conscious of their shortcomings in communicating that knowledge.

In your conclusion, make recommendations for further study on your question. What else about your inquiry and response do we need to know? What else should future research be focused on?

Also, explain how the knowledge presented in your extended essay may be applied to improve society.

What immediate steps can you take to promote enterprises, organizations, governments, industries, research, technology, etc., using the knowledge you have gained?

This will show that you are a socially responsible student interested in using science to enhance society.

Presentation and formatting

When you’re finished with your extended essay, ensure it is well-presented and easy to read.
On the cover page, include the title, author’s name, and word count. Think about including a concise visual representation of your subject.
Add a page number to each page.
Describe the document’s contents.
Write an abstract of approximately 250 words that includes your thesis statement, your question, why it is important and relevant, a description of your methodology, a synopsis of your historical research, a report of your points of disagreement, and a summary of your findings. Add the abstract after the table of contents.
Give the segments of the extended essay—including the abstract, introduction, mythology section, historiography section, arguments section, and conclusion, references, and appendix— clear titles to make them easier to read.

At the conclusion of the essay, identify all of your sources. Ensure your sources are properly credited and formatted in a standardized way in the text’s body.

Ensure that your reference list is properly formatted and follows a standard format. A source, a caption, a number, and a title should all be included with tables, images, and graphs.

Tables, pictures, and graphs should all be cited inside the body of the long essay.
The caption should accurately explain the picture and highlight for the reader the key details they should infer after looking at it.

If necessary, add an appendix after the references.

IB mathematics extended essay criteria

Criterion A: Research Question

The research question should be expressed as a proposition, question, or statement. It should be concentrated on a subject that relates to psychology, is behavioral, and can be covered consistently throughout the entire essay.

Criterion B: Introduction

Put the research question in the context of what is already known and understood about the subject in this part. Personal experiences or opinions of the student shouldn’t be included in this area.

It is important to consider any prior psychological studies relevant to the study question. The studies presented here may provide general support, but it is doubtful they will provide a fully adequate response to the research question.

It is the student’s responsibility to note the accomplishments, shortcomings, and omissions of earlier work and to demonstrate how their essay might contribute to the solution of some of the issues that have been noted.

Criterion C: Investigation

There are many resources available for queries that are likely to be posed in extended essays about psychology. These include textbooks, scholarly publications, motion pictures, broadcast media, print media, and online sources.

Film, television, radio, newspapers, and internet-based sources should all be used cautiously as the information they convey could not be reliable or accurate.

Students shouldn’t always take the conclusions drawn from these resources at face value; the essay should evaluate the concepts and conclusions from these sources.

The content of movies, TV shows, radio shows, newspapers, and websites should be viewed with healthy and informed skepticism until authoritative judgment permits their research results or hypotheses to become accepted.

Whereas the student’s own experiences may be utilized to support the claim made in the essay, the delivery or interpretation of such information should only serve to provide examples. It should make up a very small portion of the overall evidence.

Criterion D: Knowledge and Understanding of the topic

The results of empirical research and the theories that underpin it should be included in extended essays in psychology. Such content may discuss non-human animals or humans and the behaviors that go along with them.

Students should use cultural, moral, sexual identity, and methodological considerations when appropriate; they should demonstrate how these elements may influence how the research problem is interpreted.

Criterion E: Reasoned Argument

The argument’s main point should be the research question, as it is explored throughout the essay. How the argument is put together frequently brings into conflict various beliefs and research findings. The learner should delineate and evaluate these various points of view and gather the crucial details that underpin the presented argument. The student’s job is to convince the examiner of the truth and justify their opinion. The most effective way to do this is to use a logical approach and build up successive prominent points.

Criterion F: Application of Analytical and Evaluative Skills Appropriate To the geography extended essay

Applying the student’s constructed analytical and evaluative elements requires extremely demanding intellectual energy. Because these will contribute to the core of the argument, the analysis and evaluation need to be handled in great detail. The student also can exercise reflexivity, the process of thinking back on one’s experiences and viewpoints that have influenced the investigation’s procedures and how points have been interpreted.

Criterion G: Use of Language Appropriate To the Subject

Students must show in their writings how psychology employs its vocabulary in a specific way. The vocabulary used by psychologists and how it is employed well within the profession should be familiar to students who have never studied psychology as a particular topic. So, ensure you use the correct terminologies and avoid being vague and general.

Criterion H: Conclusion

The argument is summarized in conclusion. The conclusion of a logical chain was constructed using several psychological research findings and theories to support the argument.

Criterion I: Formal Presentation

This factor relates to how well the essay adheres to academic standards about the format of research papers. It is considered improper to present essays without a bibliography or citations for quoted material (level 0). Essays that fail to include the essential components page, table of contents, and page numbers—are graded at the minimum level 2 (satisfactory) and the maximum level 3 (poor) (maximum level 1).

Criterion J: Abstract

The simplicity that the abstract summarizes the research and the geography extended essay counts, not the strength of the research question, the strength of the supporting evidence, or the strength of the findings.

Criterion K: Holistic Judgment

This criterion rewards qualities like intellectual initiative, intuition, range, and depth of knowledge. Examples of how to show these skills include:

Selecting a pertinent research issue that challenges the student’s thinking but is also doable in the allotted time
Use of a reflexive method that incorporates the perspectives
The learner’s imagination makes a special contribution to understanding the subject.
Location and wise use of resources.
Analysis and evaluation of psychological information to provide prominent points for the argument.

Math Extended Essay IB Sample

These are examples of math EE essays done by a student who received glowing remarks from the examiner and that got an A

Math Extended Essay Sample 1

https://xmltwo.ibo.org/publications/DP/Group0/d_0_eeyyy_gui_1602_1/samples/assessment/EE_mathe_exampleD_en.pdf

Title of Math Extended Essay: The Mathematics of Musical Consonance

Research question: Why are some Musical Intervals More Consonant than Others?


Criterion	Mark awarded	Commentary
A: Focus and method [Maximum possible mark: 6]	5	An appropriate topic and research question; well researched and clearly of interest to the candidate, but perhaps a little over-ambitious.
B: Knowledge and understanding [Maximum possible mark: 6]	4	The student’s understanding is not clearly demonstrated in much of the mathematics used, for example, in the trigonometry (pages 8–9) and particularly in the Fourier Series material (pages 10–17).
C: Critical thinking [Maximum possible mark: 12]	9	Candidates should clearly show all steps in a mathematical argument. Writing “this differentiates to” without showing the steps is poor. Overall, it is a well-argued essay, although quite a lot of the mathematics used is unconvincing.
D: Presentation [Maximum possible mark: 4]	2	Some layout considerations are missing or applied incorrectly, but weaknesses in the structure and/or layout have not significantly impacted the reading, understanding, or evaluation of the essay. For example, there is no word count on the title page and no bibliography mentioned in the contents. The essay lacks page numbers in some areas and section headings.
E: Engagement [Maximum possible mark: 6]	5	The student’s reflections are thoughtful and interesting. Perhaps the student could have shown more capacity to consider actions and ideas in response to challenges by realizing that the mathematics used was a little over ambitious and refined their research question accordingly.
Total marks awarded	25/34

Math Extended Essay Sample 2

https://xmltwo.ibo.org/publications/DP/Group0/d_0_eeyyy_gui_1602_1/samples/assessment/EE_mathe_exampleB_en.pdf

Title of Math Extended Essay: Line Stitching and Area: How to find the area underneath a polygon when two adjacent sides of a square are divided into n equal parts and the corresponding points on two sides are connected.

Research question: How to measure the area underneath the line segments obtained through connecting points of n(n ε Z+) equal sections accordingly from two adjacent sides of a unit square?


Title of essay:	The Mathematics of Musical Consonance
Research question:	Why are some Musical Intervals More Consonant than Others?
Assessment details
Criterion	Mark awarded	Commentary
A: Focus and method [Maximum possible mark: 6]	5	An appropriate topic and research question; well researched and clearly of interest to the candidate, but perhaps a little over ambitious.
B: Knowledge and understanding [Maximum possible mark: 6]	4	The student’s understanding is not clearly demonstrated in much of the mathematics used, for example, in the trigonometry (pages 8–9) and particularly in the Fourier Series material (pages 10–17).
C: Critical thinking [Maximum possible mark: 12]	9	Candidates should clearly show all steps in a mathematical argument. Writing “this differentiates to” without showing the steps is poor. Overall, it is a well-argued essay, although quite a lot of the mathematics used is unconvincing.
D: Presentation [Maximum possible mark: 4]	2	Some layout considerations are missing or applied incorrectly, but weaknesses in the structure and/or layout have not significantly impacted the reading, understanding, or evaluation of the essay. For example, there is no word count on the title page and no bibliography mentioned in the contents. The essay lacks page numbers in some areas and section headings.
E: Engagement [Maximum possible mark: 6]	5	The student’s reflections are thoughtful and interesting. Perhaps the student could have shown more capacity to consider actions and ideas in response to challenges by realizing that the mathematics used was a little over ambitious and refined their research question accordingly.
Total marks awarded	25/34