The Internal Assessment (IA) in IB Math is a unique and significant component of the International Baccalaureate (IB) Mathematics curriculum. It offers students the opportunity to explore mathematical concepts in a personalized and in-depth manner, showcasing their understanding, creativity, and analytical skills. However, this component is often one of the most feared portions of the curriculum by IB Math students. But why is that? We'll go through every aspect of an Internal Assessment to better understand what it is all about?

What is the Math IA (according to the IB)?

A Math IA is an opportunity for students to show their knowledge and skills in Mathematics without the constraints imposed by exams, for example. In a Math IA, students can explore a topic of their own choice, in their own way, and by adhering to some guidelines, produce a body of work and arrive at a meaningful conclusion showing the Math they have learned in the course.

The IB's expectations for a Math IA

Being a rigorous course, when producing their IAs, students must now only show a complete understanding on the topics being used to carry out the exploration, but also do it in a organized manner, using the appropriate notation and arriving at a meaningful conclusion.

In a broad view, the IB looks for several key elements in a successful Math IA:

• Mathematical Understanding: Students should demonstrate a thorough understanding of the mathematical concepts they are exploring. This involves accurate calculations, logical reasoning, and a clear connection to the topic.
• Personal Engagement: The IA should reflect the student’s personal interest and engagement with the topic. This can be shown through the choice of topic, the approach taken, and the reflection on the process and results.
• Communication: Clarity and coherence are crucial. The IA should be well-structured, with a clear introduction, method, results, and conclusion. The mathematical language should be precise, and any graphs, tables, or diagrams should be appropriately used and well-labeled.
• Reflection: Students should critically reflect on their work, discussing the implications of their findings, potential limitations, and areas for further exploration.

Also, collaboration and teamwork are key elements of the IA writing process, and that extends not only to a student's peers but also to the student's teacher. It is expected that the student seeks and offers help when:

• Generating ideas
• Selecting the topic for the exploration
• Sharing research sources with his peers
• Acquiring necessary knowledge, skills and understanding
• Seeking feedback for the writing process

It is important to mention that while you should talk through your ideas with others, it is not appropriate to work together on a single exploration (the work should be produced by the student only).

The purpose of a Math IA (according to the IB)

In addition to testing the objectives of the course, the exploration allows students to:

• Enjoy Mathematics and develop an appreciation of its elegance and power.
• Develop your personal insight into the nature of math
• Appreciate how developments in technology and mathematics have influenced each other.
• Apply and transfer skills to alternate situations, other areas of knowledge, and future developments.
• Appreciate the moral, social, and ethical implications of Mathematics.
• Appreciate the international dimension of Mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives.
• Appreciate the contribution of Mathematics to other disciplines.
• Show, with confidence, how you have developed mathematical

The student must think of the audience for his IA to be his/her peers.

How do students view the IA?

In this section, we are going to take a look at how students view a Math IA, their perception and what thy should expect from their school and school teacher.

Why the Math IA is Feared

1. Independence and Originality: Unlike other assessments, the Math IA requires a high degree of independence and originality. Students must choose their topic, conduct research, and present their findings in a coherent and mathematically rigorous manner. This can be daunting, especially for those who are not used to such open-ended tasks.
2. Breadth of Knowledge: The Math IA can cover any area of mathematics that is part of the syllabus, and sometimes beyond. The vastness of potential topics can be overwhelming, making it challenging to narrow down a manageable and interesting subject. This is by far one of the biggest challenges faced by the students: with great power comes great responsibility.
3. High Expectations: The IB sets high expectations for the IA. Students are required to demonstrate a deep understanding of the mathematical concepts involved, along with clear communication and critical thinking skills.

Let's discuss the IB's expectations regarding the Mathematics’ internal assessment (IA) more broadly.

What the student may expect when writing an IA

You can choose form a wide variety of activities including modelling, investigations and applications of mathematics. Your teacher will give appropriate guidance at all stages of the exploration.

Also, a student should expect that the teacher will guide students through activities that help student schoose a topic for their exploration.

Time allocation

In class time

You may expect some class time to discuss what an IA is, going through some assessment criteria with your teacher and brainstorming a few ideas. Also, some time to meet your teacher individually to discuss your specific idea, ask questions you may have about the work, meet your teacher to discuss your choice of topic and your progress.

Your own time

Research a suitable topic (click here to assess if your topic is a good one), collect and organise your data and decide which mathematical processes apply, write your exploration, present a draft to your peers for some peer review and feedback (THIS SHOULD ACTUALLY BE CLASS TIME), submit a draft to your teacher and make the appropriate changes, and submit the final exploration

A possible schedule

Place a possible schedule here

The process of starting and submitting the final work should take no longer than 3 months (nobody benefits from that process going beyond that)

Understanding the Rubric

The IA is assessed using a rubric that focuses on five key criteria. The maximum total number of marks which can be awarded is 20, and they are distributed as follows:

1. Presentation (Criterion A) [out of 4]: This criterion looks at the overall structure and clarity of the IA. Is the work logically organized? Are the mathematical concepts and methods clearly explained?
2. Mathematical Communication (Criterion B) [out of 4]: This includes the appropriate use of mathematical notation, symbols, and terminology. Is the mathematics presented clearly and accurately?
3. Personal Engagement (Criterion C) [out of 3]: This assesses the student’s personal interest and enthusiasm for the topic. Does the IA reflect the student's genuine engagement and curiosity?
4. Reflection (Criterion D) [out of 3]: This criterion looks at the depth of the student's reflection on the mathematical process and outcomes. Are the implications and limitations of the findings discussed?
5. Use of Mathematics [out of 6]: This assesses the appropriateness and accuracy of the mathematics used. Are the mathematical methods and concepts correctly applied and justified? This is the only portion of the IA that changes whether you're an HL or SL student: list the changes here

Find the rubric and its criteria for all four courses here (this is an official IB document)and a smaller pdf version of it in these links: SL criteria and HL criteria (create one for myself using LaTeX and branding it with the IB Math Study brand).

Going through each criterion in more detail.

Criterion A: Presentation

The first criterion examines your IA's overall cohesion and arrangement. A full 4 points are awarded for the clarity of your explanations and structure, even though students usually concentrate on the complexity of math that their exploration displays. Make sure your IA is clearly structured to ensure you score in the top range of this criterion. It would be best if you divided your essay into:

• Introduction: outlines the purpose of the investigation. What goals do you have for this mathematical inquiry, and why are you researching it? Describe in broad strokes how you propose to approach your explanation. Be sure to include proof of your personal involvement and a statement outlining your own interest in the subject.
• Primary Body Paragraphs: the majority of your grade. This is your mathematical investigation to address the query you raised at the beginning. Diagrams, tables, and graphs ought to be a part of this section rather than an appendix. Large data sets or any extra numbers that might not be absolutely relevant to your research issue should only be included in appendices.
• Conclude by summarizing your research. Refer to your introduction and clarify whether the evidence and calculations you examined validated your initial theory.

What is a coherent exploration?

A coherent exploration is logically developed, easy to follow and meets its aim. This refers to the overall structure or framework, including introduction, body, conclusion and how well the different parts link to each other. A coherent exploration:

• Is easy to follow and logical
• Should "read well" and clearly express ideas
• Includes graphs, tables and diagrams when needed - not attached as appendices

What is a well-organized exploration?

A well-organized exploration includes an introduction, describes the aim of the exploration and has a conclusion. Relevant graphs, tables and diagrams should accompany the work in the appropriate place and not be attached as appendices to the document. Appendices should be used to include information on large data sets, additional graphs, diagrams and tables. A well-organised exploration includes:

• A rational (why this topic was chosen)
• An introduction (discuss the context of the exploration)
• A clearly defined aim
• A body that includes any exploration, investigation or proof
• A meaningful conclusion that summarizes your findings

What about conciseness?

A concise exploration does not show irrelevant or unnecessary repetitive calculations, graphs or descriptions. A concise exploration:

• Focuses on and achieves the aim
• Explains all stages in the exploration clearly and concisely
• Avoids irrelevancies
• Does not show unnecessary repetitive calculations, graphs or descriptions.
• Incorporates clear and sufficient explanations for the written mathematics so that your peers can easily follow your argument

Final thoughts

If in reading your work the reader needs to pause to clarify where a result came from or how it was achieved, this generally indicates flawed communication.

Criterion B: Mathematical Communication

The second criterion mostly examines the mathematical terminology you have employed during your investigation. What is meant by "language of mathematics"? Symbols, terminology and notation.

Your key points for this second criterion come from ensuring that these three elements are correct and consistent across your IA. Instead of using terms like "plug in" or "put in," more mathematically complex terms like "substitute" should be used.

Only software-generated notation from calculators and computers is accepted. If not, you should utilize the proper mathematical notation in their work.

You should define all of your important words and variables when you first introduce them, just like you should with any other IA.

Your IA should not begin with a glossary of terms. As an alternative, provide a brief explanation of a topic when you bring it up to show that you comprehend the arithmetic being presented.

To express the information as clearly as feasible, use a variety of mathematical representations. It is only a bonus if you can present the same data in several formats (formulae, diagrams, tables, charts, graphs, models, or other). This shows the examiner that you comprehend the information and can present it in a variety of ways, which will make it easier for the reader to understand.

Simple errors like leaving out or mislabeled axes labels on your diagrams or failing to provide a thorough explanation of your diagram are frequent causes of students losing points. Keep your diagram moving forward! If you use a specific visual format to portray the facts, describe to the reader what you hope the figure will illustrate.

This criterion assesses to what extent you:

• Use appropriate mathematical language including notation, symbols and terminology. Calculator/computer notation is only acceptable if it is computer generated.
• Define key terms and variables
• Use multiple forms of mathematical representation, such as formulae, diagrams, tables, charts, graphs and models
• Used deductive method and set out proofs logically where appropriate.

What are examples of a level 1?

• Graphs not labelled
• Use of computer notation instead of mathematical notation
• No other forms of mathematical communication

What are examples of a level 4?

• Minor errors do not impar clear communication
• One form of mathematical communication is only used if it is appropriate to the topic being explored.

Some tips:

• Select the best form of presentation (do not represent the same data using two different diagrams unnecessarily)
• Select appropriate, relevant tools and representations such as: GDC, screenshots, graphs, tables, formulae, diagrams, models
• All tables and figures should have titles and labels, Table 1 / Figure 1 etc
• Don't insert screenshots of equations or formulae, use an equation editor
• If a mathematical process or diagram is included, then it must be referred to and commented on. If there is no comment then it is irrelevant to the exploration
• Use technology to enhance communication (for example it can be used to reduce or automate repetitive calculations)
• Express results to an appropriate degree of accuracy with reasons o If the answer is not exact then don't use $=$ instead use $\approx$ and state the degree of accuracy (for example, 3 significant figures)
• Label scales and axis clearly in graphs
• Set out proofs clearly and logically
• Avoid terms like "plug in" or "put in", instead use a more mathematical term such as "substitute"
• Define all your key terms when you first introduce them, do not have a list of definitions and the beginning of your IA
• Ensure that different names are given to different functions, $y_1$, $y_2$ and so on
• Computer notation/calculator notation should not be used (use an equation editor):

Criterion C: Personal engagement

This criterion mostly examines the ways in which you "own" the mathematics. This is also what will differentiate a well written investigation from a Wikipedia-type article. Making sure your IA stands out from the others is one thing to strive for, as the Math itself can always be elaborated and adjusted as needed (you'll have time to go through your calculations multiple times).

The IB makes it very clear that "reproduction of readily available mathematics or textbook-style explorations without the candidate's own perspective are unlikely to achieve the higher levels." This indicates that you aren't in the appropriate place if you can find the exact same question or area of investigation investigated elsewhere!

Many students misunderstand this requirement, believing that it requires them to have a personal investment in the subject matter they are selecting. You'll see sentences like "I've always been passionate about basketball, therefore I will analyse player's performance across the decades” which is just silly. Not to say that you cannot write an IA in a topic you're interested in, however the personal engagement will not come from that. Be awr taht examiners are aware of this absurdity.

Rather, you should ensure that your investigation is autonomous and distinct in order to receive high marks for the personal engagement criterion. It should demonstrate some creativity in the sense that you convey mathematical concepts in a unique manner and examine the subject from several angles. It involves speculating about topics you might find interesting and then figuring out how to frame your problem, formula, or inquiry to include those topics!

To receive the highest possible score for personal participation, your involvement needs to be genuine and further the investigation. Not only would the topic of this IA be one that you are somewhat personally interested in, but it also adds a level of intricacy that not many other students may have written about. Also, putting your own spin to it goes a long way. The main goal is of intimate engagement.

Things to strive for:

• Thinking independently or creatively
• Presenting mathematical ideas in your own way
• Exploring the topic from different perspectives
• Making and testing predictions

What is a significant personal engagement?

You demonstrate authentic personal engagement in the exploration on a few occasions. It is evident that these drive the exploration forward and help the reader better understand your intentions.

What is an outstanding personal engagement?

You demonstrate authentic personal engagement in the exploration on numerous occasions and they are of high quality. It is evident that these drive the exploration forward in a creative way. It leaves the impression that you have developed, through your approach, a complete understanding of the context of the exploration topic and the reader understands your intentions.

Some tips

• Choose a topic that you are genuinely interested in! Ask "what if...?" and explore
• Enjoyment or interest is not enough to represent personal engagement. Personal engagement should be what drives your paper forward
• Avoid superficial statements such as "I find myself thinking about the Fibonacci sequence on a daily basis as I see flowers in my garden" or "I've always been passionate about the Pythagorean theorem”. Nobody but Pythagoras can say that (and he is dead).
• Explicitly state your personal interest
• Your engagement must be evident in the work, rather than only being observed by the teacher. Textbook style explorations or reproduction of readily available mathematics without your own perspective are unlikely to achieve the higher levels.
• Thinking creatively and work independently:
• Ask questions, make conjectures then investigate and explore mathematical ideas
• Use your own language, examples, solutions, proofs and explanations to show ownership of the work
• Don't be afraid to express your passion and interest in the topic
• If the exploration allows, show initiative and go beyond your original aim/question
• If you do not fully understand the work it will be difficult to take ownerships and expend beyond the theory presented.

Criterion D: Reflection

The fourth reflection criterion isn't related to any one section of the investigation, though the conclusion is probably where it will be discussed the most. To ensure that you receive "reflection" marks, stay away from summarizing your outcomes. We must do more for the IB than merely demonstrate our accomplishments. We have done more than just take a few arithmetic tests, as seen by the ways we have evaluated our study, looked at what we may have learned along the way, and connected our results to our original goals. Since learning is the focus of the IB, demonstrate to the marker your progress during the IA.

There are many opportunities to demonstrate reflective abilities when you discuss your research and present the math you have utilized. You can check the veracity of the data in a certain secondary source or assess your methods. Is there anything you are unable to explain? Accept this instead than ignoring it! Analyzing your areas of improvement is a sign of competence. But simply bringing an issue to people's attention is insufficient. Make sure you describe how you have adjusted your exploration to account for it or handled it in light of it.

The criterion D might be conceptualized as your essay's overall evaluation score. However, this does not mean that you should criticize every aspect; rather, highlight those areas in which you believe you did particularly well! Using a balance of positive and negative points is a proven method to show the markers how self-aware you are!

But thinking only along these lines can put you in a narrative trap. Make sure you demonstrate "critical" reflection by thinking about potential research directions or the ramifications of your findings. It's a fantastic idea to tie up your exploration with a paragraph on one of these!

Critical reflection: This type of reflection is crucial, deciding or deeply insightful. This includes addressing the mathematical results and their impact on your understanding on the topic. Some ways of showing critical reflection are: considering what's next, discussing implications of results, discussing strengths and weaknesses of approaches and considering different perspectives. Substantial evidence: Present throughout the exploration. If it appears only at the end of the exploration, it must be of high quality and demonstrate how it developed the exploration to achieve a level 2.

Some tips

• Start in the introduction: Why did you choose this approach? Why was it better than the others you considered?
• Look at your method/approach, is there something you cannot account for? Don't ignore it, examining it, how could you gain an understanding or improve? How can you account for this issue that you have found?
• You can demonstrate reflection by:
• Consider the accuracy and reasonableness of results
• Consideration and evaluation of the strengths and weaknesses of your approach
• Consider possible assumptions/limitation for models or approaches used
• Consider other perspectives
• Make links to different subjects or areas of maths.
• Use a questioning style to aid your reflection: "what is the significance of what I have learned? "how could my ideas be extended?" "what if...?"
• Regularly review your findings and interpret results in context.
• Regularly reflect on your work. Ask and write down questions
• It is okay for your reflections to change over the course of your exploration, it is okay for your finding to not be what you expect.
• Reflections should lead to looking backwards (opposed to personal engagement which is looking forwards)

Criterion E: Use of Mathematics (SL)

This is the only criterion that differs from the SL and the HL courses.

The majority of your total IA score is based on this criterion. Your proficiency in mathematics will determine six of your twenty possible points. "Use of Mathematics" basically assesses how well you understand mathematics and how applicable it is to the investigation. We have repeatedly witnessed pupils become distracted from their investigation when they gather information or research a different issue that piques their attention. Even if your arithmetic is "right," you run the danger of losing a ton of points if you take the time and effort to answer a question that isn't related to the one you asked.

The level of the algebra you produce should be comparable to the material covered in your syllabus. This does not imply that you have to limit your research to the subjects listed on your syllabus, but it should still be done with the same level of rigor!

Furthermore, you are not showing that you understand anything just because you pose a question, perform the necessary computations, and provide the readers with the solution. Make sure you provide justifications for your decisions at every stage of your IA, outlining your reasoning behind the method you choose to solve the problem!

This criterion assesses to what extent you use mathematics that is relevant to your exploration.

What is relevant Mathematics?

The IB defines "relevant" as including only arithmetic that is specifically meant to address the topic you posed in your introduction. It supports the development of the exploration towards the aim. Overly complicated mathematics, where simple mathematics would suffice is not relevant.

Relevant: supports the development of the exploration towards the aim. Overly complicated mathematics, where simple mathematics would suffice is not relevant.

What is commensurate with the level of the course?

The mathematics used should either be part of the syllabus or at a similar level. It should not be completely based on mathematics listed in prior learning.

What is to demonstrate?

This is a command term meaning "to make clear by reasoning or evidence, illustrating with examples or practical application".

Obtaining the correct answer is not sufficient to demonstrate understanding. For knowledge and understanding to be thorough, it needs to be demonstrated throughout the exploration. Lines of reasoning must be shown to justify steps in the mathematical development of the exploration (a process).

Mathematics is regarded to be correct even if there are occasional minor errors as long as they do not detract from the flow of the mathematics or lead to an unreasonable outcome.

You are encouraged to use technology to obtain results, however understanding must be demonstrated throughout the process.

What is precise?

Mathematics is error-free and uses an appropriate level of accuracy at all times

What is sophisticated?

Mathematics should be commensurate with the HL syllabus, or if it is from the SL syllabus it should be used in a complex way that is beyond what could be reasonably expected of an SL student. Could be understanding and using challenging mathematical concepts, looking at a problem from different perspectives or seeing underlying structure to link different areas of mathematics.

What is rigour?

Clarity of logic and language when making mathematical arguments and calculations. Each relevant development must be justified or proven. You are encouraged to use technology to obtain results, however understanding must be demonstrated in order to achieve higher than level 1.

General tips

• It is better to have a few small elements of mathematics or even a single sub-topic done well, than a lot of things done not so well
• Using more complex mathematics than in the course does not produce higher marks, especially as it is much harder to demonstrate understanding
• If your choice of mathematics is not in the course ensure you explain it clearly, assuming the reader does not already know the topic
• If you are using technology to find a regression model, or similar, this is commensurate, however, you need to show understanding by justifying your choice and showing understanding of the process
• Apply problem-solving techniques. Use a mathematical straegy
• Show your mathematical process clearly: use supporting analysis, calculation or examples as you formulate a model.
• Only include things relevant to the task
• Always think in the context of the task
• Do not include long proofs that are copied or that you don't completely understand
• Furthermore, avoid making your investigation too complicated! You may even face penalties if you can demonstrate a concept using a basic mathematical tool rather than receiving further rewards. It will backfire.

Criterion E: Use of Mathematics (HL)

Previous boundaries for the IA

These were used in 2021.

It is important to remember that these are scaled XXXblablabla (reference the article I am writing on how to calculate the actual IB grade)

Finding Ideas for your Math IA

Choosing a topic for your Math IA can be one of the most challenging aspects. There is nothing worse for an examiner than reading an IA with a research topic that has been seen multiple times.

Here are some suggestions to get you started and making sure you have an interesting research question:

• Everyday Life Applications: Consider how mathematics applies to everyday scenarios. For example, you could explore the mathematics behind music, sports, cooking, or architecture.
• Interdisciplinary Topics: Look at the intersection of mathematics with other subjects such as physics, economics, biology, or computer science.
• Historical Context: Investigate a famous mathematical problem or theorem and its historical significance.
• Data Analysis: Use statistical methods to analyze real-world data. This could involve studying trends in sports performance, climate data, or social media usage.
• Personal Interests: Think about your hobbies or passions and how mathematics might relate to them. This could be anything from gaming strategies to the mathematics of fashion design.
• Youtube channels: In order to get inspired, one could use YouTube channels’ videos such as the following. They all have a deep alignment with what is expected by the IB as to what an IA requires: investigative analysis ad problem-solving skills of unique problems.
• Numberphile
• Numberphile2
• Mathologer
• Stand-up maths
• Mind your decisions
• Think twice
• Tipping point Math
• Websites: To get inspired, one could use websites such as Clastify to go through examples of IAs submitted by other students. On that website you can filter IA's by subject (AA/AI/HL/SL) and final grade. Also, through a subscription, you can view the IB moderator's commentsXXXis it really the moderator's comments?

One quick comment about YouTube videos: there has been a growing trend of students transcribing YouTube videos (with a few changes here and there) to create their "unique” Math exploration. Not only this can be traced by their teachers or IB Examiners, but also with the use of AI tools like Turnitin are getting better at detecting that type of plagiarism.

Here is what the IB says about academic integrity.

Using research papers

Research papers (found on Google Scholar for example) might be used as inspiration. However, XXX

Here is what the IB says about academic integrity.

A more hands-on approach in searching for an IB AI topic

Given many fields rely on Mathematics for analysis and investigation, when looking for an intersection of mathematics with other subjects, you could run multiple searches in Google or ChatGPT. Also, make sure you search for topics and subjects that you genuinely like. Make sure you either search for papers that have this investigative approach, or that allow you to use it to run an investigation you have in mind. Also, you might search for topics that might have been derived from the YouTube videos you watched from the channels above.

Google searches: Quote some examples here. When searching, search for pdfs given they are elaborated with more care

• (one example of search)

ChatGPT: Quote some examples here

Make it into a real-world problem, something that interests you.

After deciding on the topic you'll write about, create your research question. Make it unique and interesting.

Are there any research questions that I should avoid?

Absolutely. Here is a list of Math Internal Assessments (IAs) from the IB curriculum that have been widely used by students and may lack novelty:

• Avoid any topics that have been done ad nauseam. Examples are along the lines of "Exploring the golden ratio in Nature and Art”, "Modeling population growth using exponential functions”, "The Mathematics of music and sound waves”, "The Mathematics behind fractals”, "Exploring the Fibonacci sequence in Nature”, "Statistical analysis of sports performance”, "Mathematics Behind Projectile Motion”, "Mathematics of epidemics”, "Cryptography and RSA encryption”, "Optimizing traffic flow using mathematical models” or "Non-Euclidean Geometry”, to mention a few. Students should avoid these altogether or add a novel twist to these commonly used ideas to ensure originality and a deeper exploration of the subject matter (which may be harder than it sounds).
• Simple correlation analysis. We've seen over and over research questions along the lines of "The correlation between X and Y” (X and Y being anything like shoe size and height, or GDP and life expectancy). On the former, the student will more often than not come up with data from his own "personal research” (which is sometimes just fake data).
• As mentioned previously, Anything along the lines of “Mathematics of Gambling and Probability” (exploring the probabilities behind common gambling games such as poker, roulette, and lotteries.). A complete analysis of the probabilities involved in poker, along with the numerous factors that might affect a hand, makes it unfeasible.
• Anything that you can find on a guide or blog post titled along the lines of "The 20 IA ideas you can do”

Examples of good IA's

Here are some great examples of IAs. By this point, you should be able to assess why they are such great IAs. You don't need to read all 20, stick to those from your Math course.

All of the examples below scored either a 6 or a 7. Most of them were created by our team, therefore they can be shared but not sold (read this disclaimer)

Examples + what makes them so good (include that analysis in our document)

The practical terms of writing an IA

Lalala.

Break it down into separate sections

Lalalaa

Rationale

This is where you'll make your IA shine, after all, first impressions are extremely important If you start by saying silly things like "I've always been passionate about the Pythagorean theorem” and try to fool your examiner, he'll shut down and give you no love. By the way, read the section XXX to get to know more about personal engagement.

Explain why your research question is a good one, sell the idea! Use half of a page, maybe a page, to go through this section. If it is a real-world problem, that is even better (more interesting). The aim (goal) should be crystal clear. Mention what is the goal, and what type of analysis you'll carry out (the Math topics you'll tackle)

Introduction

It should involve more Math, very concise. Summarize your procedure. Use no more than 10 to 12 lines.

Body

This is the bulk of the exploration, the part where you'll explore all the Mathematics behind your exploration. Here, you should carry the reader by the hand, being extremely meticulous and explaining the whole process with rich detail. You'll even define the variables you're using for later reference (which makes the reading much easier).

Split your work whenever appropriate (be careful to not overdo it).

Use equations, write Math properly.

Know that here you'll show personal engagement

Citations across the whole document (whenever appropriate). Citing does not mean you are plagiarizing: when used appropriately, it shows you researched the topic extensively. Ethical guidelines should be adhered to throughout the planning and conducting of the exploration.

Tip: hand write the Math before typing it

Analysis and evaluation (across the whole document)

Conclusion

Do know that any analysis and evaluation should be done throughout the paper, not just in the final page. However, this is the section where you'll summarize every finding, looking back at the research question.

The standards (font size, spacing, and such)

Global

• You may write in first person
• The references are not assessed, however if they are not included, your IA may be flagged in terms of academic honesty
• The mathematics used should be in accordance with the level of the course. That does not mean you cannot go beyond the curriculum, but if that is the case, do it slightly and not in the whole text. If you stick to that, going beyond the curriculum will not penalize you.

Cover page

• The title of the exploration
• Number of pages
• Candidate number
• Session (form example, May 2024)

The actual work

• You can write your IA using Microsoft Word or Google Docs. Some students will get ancy and use LaTeX (if you don't know what LaTeX is, don't even bother)
• Always use the appropriate Math notation (more on that XXXmention here where I explain that)
• Use double spacing
• Use the Times New Roman font 12
• Number your pages
• You should write from 12 to 20 pages of content (it does not include the cover page, the appendix, and the bibliography)
• All tables and images must be labeledXXX
• Citations across the whole document (whenever appropriate)

Be precise and coherent. Do not extend your text to fit the required number of pages: anyone can tell someone that is just stalling. If you cannot fill at least 20 pages with your IA, your research question is probably too simple or you're not writing your paper properly. On a similar note, if you need more than 20 pages to carry it out, your research question is probably too hard or you are just not writing your paper properly.

Mention the number of pages, font, double spacing, how to do a bibliography, how to label images and tables, you name it.

On academic honesty

All work submitted is to be authentic, based on your individual and original ideas with the ideas and work of others fully acknowledged. These sources must be referenced using a standard style, in a consistent manner. All sources must be credited, including those that have been paraphrased or summarised. The reader should be able to easily distinguish between your words and those of others, by the use of quotation marks (or other methods such as indentation) followed by the appropriate citation which denotes an entry in the bibliography. You should use in-text referencing and a bibliography. The Cranbrook Guide to APA Referencing can be found on the Cranbrook Senior Library canvas page.

Final (and essential) tips, FAQ and conclusion

Let's go through a few final tips and hints when writing your IA.

Final tips

• If your IA looks like a Wikipedia article, that means that you've successfully explored some concept in Mathematics, however you failed in making it personal. For example: "The Newton-Raphson root-finding method” is the title of an IA in which a student learns the concept and applies it to a few selected examples, without any context whatsoever. However, XXXstate an example using this same research question which would make it good
• This is pretty obvious but let me just go ahead and say it: plagiarism takes many forms and shapes XXX mention a few expectations from the IBXXX. Also, something that we're seen out there is transcribed YouTube videos XXXexplain this betterXXX and yes, they can be flagged by plagiarism and may cost your diploma. Find here all the IB guidelines for academic integrity (an official IB document).
• You do not need to go beyond the difficulty level of the course. From the IB course guide: "Students are expected to produce work that is commensurate with the level of the course, which means it should not be completely based on mathematics listed in the prior learning. The mathematics explored should either be part of the syllabus or at a similar level.”

FAQ from IB Math students

Conclusion

By understanding the expectations and rubric of the IA, and by choosing a topic that genuinely interests you, the Math IA can become a rewarding and less daunting experience. Embrace the opportunity to delve deep into a mathematical concept and showcase your skills in a unique and personalized way.

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Students repeatedly sought guidance on the internal assessment (IA), a 12–20 page mathematical exploration. One post asked “What do we need to do in a Math AA IA? Is there an official guide?”reddit.com. Others asked how to choose a concept or whether certain topics were overused.

Answer:

1. Purpose of the IA. The IA is an individual written investigation that allows you to explore a topic of personal interest using mathematics from your syllabus. It accounts for 20 % of your final grade. The IA is not supposed to be a research paper on advanced mathematics; rather, you should demonstrate that you can apply mathematical techniques correctly, communicate clearly and reflect on the process.
2. Selecting a topic. Choose a context that genuinely interests you—something from hobbies, sports, music, economics or natural phenomena. The key is to incorporate mathematics appropriate to your level. For AA HL, you might model the trajectory of a basketball using projectile motion and calculus, analyse fractal dimensions in art, or explore optimisation problems. For AA SL, modelling population growth with exponential functions or analysing patterns in music frequencies using trigonometry can be suitable. Avoid topics that require mathematics beyond your syllabus or that have been overdone (e.g., simple area‑under‑the‑curve calculations without deeper insight).
3. Ensure sufficient mathematics. The IA in which a student was predicted 0/20 because they “included little mathematics”reddit.com illustrates the importance of substantive math. Your exploration should include algebraic manipulations, calculus or statistical analysis rather than only descriptive writing. Use diagrams, equations and graphs and show each step of your reasoning. Cite formulas appropriately and clarify assumptions.
4. Structure and criteria. The IA is assessed on five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection and Mathematics. Write a clear introduction explaining your aim and why the topic interests you; define variables and state any assumptions. In the body, carry out mathematical methods logically and explain their relevance. Reflection means discussing the implications of your results, evaluating accuracy and acknowledging limitations. Personal engagement may be shown through original data collection, creative modelling or linking the mathematics to your personal experiences. Conclude by summarising findings and suggesting extensions.
5. Official guidance. There is no single “official IA template,” but the Mathematics AA subject guide (available from your teacher) contains detailed assessment criteria. Many schools also provide checklists. Use these to self‑evaluate your draft. Ask your teacher for feedback at multiple stages but remember the final work must be your own.

A worrying post described a student who received a predicted score of 0/20 because their IA contained minimal mathematicsreddit.com. They debated whether to scrap the topic or incorporate more math.

Answer:

1. Diagnose the problem. A zero prediction usually indicates that the exploration lacks required mathematical content, fails to show personal engagement or does not meet formatting criteria. Ask your teacher for detailed feedback: Which criteria are currently unsatisfactory? Which sections lack mathematical depth or clear communication?
2. Revise rather than start over—unless the topic is unsuitable. If your topic is conceptually sound but your analysis is superficial, you can often salvage the IA by adding more rigorous mathematics. For example, if you modelled the area of a fractal shape but merely described pictures, you might extend the work by deriving recurrence relations, calculating fractal dimension or testing convergence. If the topic inherently limits mathematical exploration (e.g., ranking your friends’ music tastes with simple averages), it may be better to choose a new topic.
3. Incorporate appropriate syllabus content. To raise your score, ensure that you include calculus, algebraic manipulation or statistical inference appropriate to your level. For AA HL, complex numbers, calculus of parametric curves or matrix methods can add depth. For AA SL, transformations of functions, binomial expansions or regression analysis can demonstrate sufficient mathematics. Always explain the steps and interpret results.
4. Improve structure and reflection. Even if the mathematics is correct, poor organisation and lack of reflection can drag down scores. Use headings, label diagrams clearly and ensure that each equation is explained. Reflect critically on your model’s assumptions and limitations. Discuss how changing parameters affects the outcome and what further work could be done.
5. Manage your time. Starting over might be necessary if you cannot add meaningful mathematics quickly. However, avoid last‑minute changes that compromise quality. Use your teacher’s interim feedback to guide revisions and allocate time to rewriting, formatting and checking citations.