1. What Exactly is the Math IA?
1.1 About the Math IA
The Math IA is an internal assessment that makes up 20% of your final grade. Also known as the mathematical exploration component, students are expected to create a 6-12 page research paper with a topic of their choice.
Although the IB Mathematics curriculum includes two subjects, Analysis & Approaches (AA) and Applications & Interpretations (AI), the IA itself is the same for both of them. For SL students, the content is based on what you have learned in class. On the other hand, HL students will be expected to write something that is not from the IB syllabus.
1.2 Distribution of Marks
The criteria for both Math AA and AI are the same. The distribution of marks is also the same for both SL and HL students. The criteria includes the following five components: Presentation, Mathematical Communication, Personal Engagement, Reflection, and Use of Mathematics.
| Presentation | Mathematical Communication | Personal Engagement | Reflection | Use of Mathematics |
| 4 marks | 4 marks | 3 marks | 3 marks | 6 marks |
As you can see, the IA puts a lot of focus on the Use of Mathematics as it makes up 6 marks of your entire IA (20 marks in total). So don’t forget the importance of this component!
1.3 The Process
Here is the process of crafting your IA:
- Deciding the topic
- Research
- Doing the calculations
- Analysing the results
- Constructing the IA
The Math IA is mainly researched based unlike the Science IA.
After deciding your topic, you will have to conduct some research on the formulas and concepts that you would like to use and see if they can be applied to real life situations. When you managed to fully understand the use of the formulas, use them to do your calculations. Your aim is to find a solution to your investigation through this process.
The next step of this is to analyse your process of calculations and gain feedback from your teachers. Finally, construct your IA using all the information mentioned above.
It is said that the process of deciding the topic is the hardest part of the Math IA. Your IA directly links to your final score for maths, so having a good understanding of how to structure your IA is very important. Don’t worry! In this article, you will find tons of advices for writing your IA!
2. How to Decide Your Math IA Topic
2.1 Show the Examiner How Math Can Be Applied to Our Everyday Lives
Many students have trouble deciding what to write for the IA. As a result, many would try to see if they can link their hobbies such as music and geography to mathematical concepts. However, it is actually better to choose a mathematical concept first and then think about how you can apply that to our everyday lives.
In simple words, your Math IA should be something that can show the examiner how mathematical concepts can be used in the real world. So, without doubt, the main spice is the use of mathematical formulas and concepts.
If you choose your topic through your hobbies first, then there is a possibility that your focus might go off the road. As a result, you might end up talking more about your hobby instead of math. However, if you choose your topic through the mathematical concepts first, you will most likely end up going into the right direction.
Therefore, it is recommended that you make a list of mathematical formulas and concepts first. Then, think about which ones are suitable for applying to real life.
2.2 How Difficult Should the Math be?
The next question that many of you might ask is, “how difficult should the math be?”. The truth is, it doesn’t have to be more difficult than the curriculum itself. For SL students, choose something that is the same level as the curriculum. The same goes for HL students.
SL students shouldn’t be too worried as you can choose anything from the syllabus. However, for HL students, many of you might be quite frustrated as you can’t choose something that is from the curriculum. It is also difficult to judge how hard a mathematical concept is. For those of you who are struggling, here are some links that can give you some inspiration!
- 50 IB Math IA Topic Ideas
https://www.lanternaeducation.com/ib-blog/50-ib-maths-ia-topic-ideas/
- 20 Math Internal Assessment Topic Ideas for IB Standard Level
https://writersperhour.com/blog/20-math-internal-assessment-topic-ideas-for-ib-standard-level
- IB HL Math IA Topics
https://coggle.it/diagram/WQCrik-6SAABUsF1/t/ib-hl-math-ia-topics
3. How Should You Write Your Math IA?
As mentioned above, the IA is based on five components. So how can you score high on these components?
3.1 Understanding the Components
<Presentation>
The way you present the data and the formulas will be evaluated. Your research content and results should also be effectively communicated throughout the IA.
Things that you should consider
- Make your IA easy to read
- Use the same font for all the mathematical formulas
- Colour your graphs and tables
- Number your graphs and figures (refer back to the numbers when talking about them)
- Don’t go over the page limit
- Show your IA to a third person (your family or friends) to see if it is easy to read
<Mathematical Communication>
Your use of mathematical symbols and equations will be evaluated. You should also define the mathematical terms when necessary.
Things that you should consider
- Use mathematical equations for your explanations
(or use tools such as screenshots of your graphing calculator, data, or graphs)
- Define terms that you haven’t learned in class
<Personal Engagement>
The personal engagement component is where you should show your personal interest in the topic as well as originality.
Things that you should consider
- Talk about your personal experience and explain why you chose to research on the topic
- Talk about the challenges that you have faced and how you have solved them
- Show how your IA has led to your personal growth
- Use first person pronouns when explaining your thoughts and personal experiences
- Explain your feelings when faced with challenges
(ex. I thought of _______, therefore I tried to __________)
<Reflection>
This component evaluates whether students have effectively reflected on their research.
Things that you should consider
- Explain anomalies and give future solutions for the problems
- If you have conducted your research in a wrong manner and managed to fix it in the end, explain how you have corrected your mistakes.
<Use of Mathematics>
This component is used to see whether the math you have used matches the level of your course.
Things that you should consider
- The most important thing is to show whether you have fully understood the topic rather than how difficult your topic is
- Choose a simple topic, but dive deep into the topic and analyse it thoroughly
3.2 The Structure
There isn’t a specific answer to how you should structure your Math IA. There are IAs that score high without having labels for the Introduction and the Conclusion.
However, as you have seen in the “Presentation” section, the effectiveness of your presentation is one of the important points that you should consider while writing your IA. Therefore, it is recommended that you divide your IA into different sections. Again, there isn’t a rule for this so as long as it is easy to read, it should be fine!
Here is one of the ways that you can structure your IA:
- Introduction
- Background Information
- Calculation
- Conclusion
- Citation
So how should you write each section? Read the section below to find out more!
3.3 How Should You Write Each Section?
<Introduction>
Your introduction should talk about what the IA is about, why you chose that particular topic, and the purpose of your IA. Remember to write the following in your introduction!
- Research question
Describe what you are investigating in a brief manner.
- Rationale
Write about why you chose the topic and how you are going to conduct your research. Remember to include your personal experiences when explaining because this will help you score better in the Personal Engagement component!
- Aim
Be explicit about what you are trying to find out through this research.
<Background Information>
In this section, you should talk about what kind of knowledge (mathematical concepts, formulas, ways of researching) is needed in order to conduct an investigation on your research question.
The most important thing is to make your IA understandable to someone who has 0 knowledge about the mathematical concepts. Therefore, explain the mathematical concepts, ways of researching & collecting data, and all the steps involved clearly.
<Calculation>
This is the practical part of your IA where you have to give an answer to your research question. It is the place where you should use the mathematical concepts explained in you background information to further explore the topic.
The ways of your investigation depends on your topic. However, you are most likely going to collect data and do calculations based on it. The Mathematical Communication component is based on this section so use the mathematical formulas to explain your processes rather than using words.
Because there will be a lot of information in this section, the key is to make sure that everything is presented neatly and concisely. If you have collected a set of data, use visuals representations such as graphs to present it. That way, you can also gain points int he Presentation component too.
In order to make everything easy to understand, you should also include every single mathematical formula regardless of how simple it is.
<Conclusion>
For the conclusion, you should reflect on your entire IA instead of simply stating what happened. Here are some things that you should keep in mind when writing the IA.
- Evaluation of results
By now, you have probably answered the research question through your calculations. Using this answer, refer back to your rationale. Reflect about why you chose that topic, whether you have managed to find out what you wanted to know, and whether the answer was the same as your hypothesis.
- Limitation and challenges faced
Write about the strengths and weaknesses of your research. Again, the most important thing is your reflection. Reflect on the strengths and weaknesses. Then, explain why it went well or why it didn’t go well. Also mention your solution to certain problems that you faced during your research.
- Improvements and further exploration
State improvements that you will make in the future if you were to conduct this research again. Also talk about how you research can lead to other possible research topics. Writing about how your IA leads to the future can help you conclude it perfectly.
<Citations>
Include all citations with the correct style and format.
4. What You Should Remember
After looking at how you should write your IA, you probably have a good grasp of how everything goes now. Lastly, this article will introduce some important points that you should never forget while writing your IA!
4.1 What’s the Point of Your Research?
The main point of your research is the fact that it is a piece of research conducted by students, rather than it being a full explanation about the logic behind a mathematical concept. The examiner wants to know how the student has thought about the research process and how he/ she has analysed the results.
There is a page limit so always remember to include your own thoughts into your IA rather than a whole bunch of explanations.
4.2 Know the Importance of Your Teacher’s Feedback
Your math teacher is going to be your IA examiner so the IB limits the amount of time your teacher help you in order to protect your originality.
As a result, your feedback time is limited to only once or twice. Use this time wisely and give your best shot. Your draft should be a completed IA so that your teacher can give you advice on how to bring it to a higher level.
4.3 Handy Softwares That You Can Use
There are several softwares that can help draw graphs and figures. It is important to have clear graphical representations or tables in your IA so here are some handy softwares that you can use!
- GeoGebra
This can be used for geometry, algebra, statistics and calculus application.
- Microsoft Excel
This software can help you with collecting data and making graphs from your data.
- Microsoft Word
You can insert mathematical formulas using this software.