This is a complete guide to the Mathematics AA and AI Internal Assessment. Follow these steps to ensure your IA meets a high standard.

## Table of Contents

With very little practical information available online and teachers barely helping us with IAs, the process is such a struggle now. On top of that, the Maths IA has become a VERY significant part of your final grade in the last year (especially non-exam route).

So I put together a complete guide to the Math IA mixed in with a bunch of personal advice to make this entire project a lot easier. These are the steps you need to ensure your IA meets a high standard.

I'm going to presume you know the basics but, if not, **go properly read the IA section in the Mathematics AA or AI guides**. You are being assessed on 5 criteria for the Internal Assessment. If you can truly understand how the whole assignments graded, you won't do useless things like including irrelevant maths or creating a fictional story about your love for linear regression (please don't...)

## 1. Big Takeaway: Methodology First, Topic Second

Find the mathematical method that will lead you to a final number or equation and THEN think about the topic you want to apply that method to.

Contrary to what everyone says, the way you start the IA is very important. Most of us just use a topic like football shots or a piano composition and make some maths up about it. But this only forces irrelevant math into your IA and weakens your entire exploration.

Remember the reason the IB wants you to do an IA is so that you can "develop a wider appreciation for mathematical concepts and processes". So let's do exactly that.

Instead of thinking about the topic first, find and deeply understand a mathematical technique or method that is an extension of the concepts in the maths course. Learn about this topic and its common applications in the world. Then, brainstorm the ways you can apply this method to investigate a different topic/application that you're interested in.

For me, I knew wanted to explore ordinary differential equations and after learning advanced ways to use them I decided to focus on modelling tumor growth in the brain. Another friend of mine used integration and La Grange multipliers to find the most efficient way to lose calories on a treadmill.

Both of us scored 7s and as you can see we started off by researching calculus-based techniques and took time to understand all of the math behind them before thinking about the topic that we'd want to investigate using mathematical method/s.

Other successful mathematical concepts include the volume of revolution (calculus) based IAs because you can learn to plot multiple curves for difficult objects with a large potential for further application. Moreover, statistical methods such as correlation + regression or testing for normality (eg. in certain fashion or food products) can also score highly if you go in-depth with the techniques and analysis.

**How do I find and choose my mathematical method?**

Start with Khan Academy's Mathematics page and read through the chapters and topics for calculus and statistics (those are the main ones). On top of all the IB-related topics, there is a nice compilation of different techniques and applications beyond the scope of the course that you can use for your IA too.

Research the chosen mathematical method further and actually try to fully understand and appreciate how it is used. Use books, PDFs, and find obscure YouTube videos to help with exploring the topic. Ensure that you only pick a topic once you are 100% sure you can understand and apply it.

Shortlist 2-3 topics and go through how your researched mathematical technique will be applied and how you will actually explore it. Flesh each topic out as much as possible and scope what your IA will look like before deciding on one. I, personally, shortlisted both modelling the growth of the GBM tumor and modelling the spread of different infectious diseases (different topics using similar mathematical methods and concepts).

## 2. Plan? Purpose? Personal Engagement?

### Make the RIGHT Start: Thoroughly Scope and Plan

Before starting, it is crucial that detailed notes are made on a) the mathematical approach specific to your topic b) the analysis of the maths and c) your overarching aim.

The trend the IB examiner reports mention is that students present difficult math concepts and equations without knowing how to properly apply them or without even having a clear purpose for their investigation. You can easily avoid this by properly scoping out the investigation before you start typing.

Research and plan the important details of the method you're using and the analysis you want to conduct. Ensure that you connect every part of the whole exploration to the purpose.

Just starting after finding a topic isn't wise for this IA. I made this mistake and had to restart after writing 3 full pages on one topic without realising that my entire mathematical approach would be better suited to the topic I previously ruled out. It is so important to design the right framework for the idea, you shouldn't just wing it because a lot of people do and get stuck in the middle.

### The First Section is Easy Tick-boxing

There is no template and no perfect structure for your IA. But I'd suggest dividing the first section up into an Introduction, Rationale, and Aim/Plan of Action for clarity. Always make it a habit to clearly "show" the examiner the ways in which you are fulfilling the criteria. Make it easy for them to give you marks.

These are a few important questions to ask yourself as you write the first section up:

Is the aim of the exploration clear and explicit for anyone reading?

Are the key terms, main variables, and constraints defined (where required)?

Have you given a step-by-step plan of action and explanation of how you will explore your question/aim? (incl. description of data collection)

### Don't Over-Engineer Your Personal Engagement

Avoid cheesy background stories. Please. Students believe that the 3 marks for PE are only awarded if they talk about the overwhelming curiosity they've had about Pascal's triangle their whole life. Do not add blatant lies like these, examiners see right through them and it undermines your investigation.

The PE criterion C is most misunderstood. Instead of creating an unnatural backstory, show the examiner authentic personal engagement. Show them that you have "driven the exploration forward in a creative way". Make sure the topic has **some** personal importance to you but add layers of complexity to your investigation to exhibit organic engagement. Every bit of extra effort you put to further your investigation is evidence of your personal involvement.

In my IA, there was no experimental data for certain variables in my tumor growth model so I learned how to use the Matlab software to optimise and find estimations of the unknown parameters myself. Learning a new skill and finding a creative solution for the missing variables was a very strong example of my personal engagement. Keep in mind this is just what I did and there are much simpler ways to achieve the PE marks too.

Did you do preliminary experiments to ensure your exploration makes sense? After you accomplished the purpose, did you further your aim by testing the equation against other variables too? How did you manipulate the final results to further analyse them? Adding new and unique levels of complexity is the key.

## 3. Use of Mathematics

It is better to do a few things well than a lot of things not so well.

"If the mathematics used is a) relevant to the topic being explored, b) commensurate with the level of the course and c) understood by the student, then it can achieve a high level in criterion E."

### How Much Math is Enough Math?

The mathematics used needs to be relevant to a topic in the course obviously and we shouldn't be using any maths that we don't understand. Usually, students use "overly abstract and sophisticated concepts beyond their course" without truly understanding the math. Examiner reports reveal that a lot of IAs force these complicated methods in the hopes of gaining extra marks but end up losing marks because they couldn't clearly link every part of the exploration to their investigation. This is the official feedback given by the IB:

"Students should be discouraged from using difficult mathematics beyond the HL syllabus if this cannot lead to some creativity or personalised problem."

A cascade of formulas taken from some online journal without citation isn't the way you score in criteria E. Using mathematics beyond the HL syllabus will often lack thorough understanding and will make it "difficult for students to demonstrate Personal Engagement or Reflection too". You need to ensure that you deeply understand the mathematical methods being used in your IA. Everything included should be thoroughly justified and should be helping you build towards your aim.

### Demonstrating Understanding VS Getting a Correct Answer

These are two very different things. Obtaining the correct answer isn't even enough to demonstrate "some understanding" and won't even guarantee getting a 2/6 in Criteria E. Clearly, demonstrating understanding is a big deal.

It's one of the reasons I've constantly emphasised the fact that you need to gain a deep understanding of the mathematical methods and concepts before even starting. Instead of just adding calculations onto your IA, explain every step and justify everything you do to solve the problem.

"Illustrating with examples or practical applications" within your explanations is the strongest way to demonstrate your knowledge of the mathematics. Be explicit, excruciatingly clear, and don't shorten this part of your IA.

## Reflection: More Than Just A Conclusion

The biggest mistake people make with their "reflection" is believing this criterion can be fulfilled with a few paragraphs summarising their exploration at the end of their IA. The IB examiner's report for the IA confirms this: Many students just discuss "the scope and limitations of the work done and include no meaningful or critical reflection."

The IB wants to see your growth throughout the IA. They assess how the student reviews, analyses, and evaluates their exploration at different stages. Reflective elements should be present throughout.

For example, in the introduction itself, you can briefly reflect on the method you've chosen. Why is this the best way to address the aim of your investigation? During data collection, you can question the credibility and room for errors in the data and results. Discuss ways in which you can address or account for that. Continuously examine the strength of your investigation and include reflective elements throughout.

For the higher achievement levels make sure you do these:

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**mplications of the results:**linking your results to the aim of the exploration and the real impact these conclusions can make.**Consider further explorations:**there are always better methods or more advanced maths that can be used to solve the problem you are addressing. Evaluate and compare them against your own approach in 1 or 2 paragraphs.**Compare strengths and weaknesses**of the mathematical methods and data analyses you conducted.**Bonus: Brainstorm the topic from a different perspective**(use technology such as software for model development).

Throughout IB we're literally trained to critically evaluate and reflect on all of our work and progress. It's an inherent advantage we have compared to most other students. Let's use it well.

Hey. Your tips are very useful. I am interested in doing tumour growth modelling as well but I am having difficulty finding data of tumour growth in people. Could you share where you accessed your data for your modelling?