Mathematics Internal Assessment (IA) is a crucial component of the IB Diploma Programme. It is a student-led exploration that enables the learner to delve deeper into a mathematical concept or problem of their interest. The Math IA is a 6-12 page report that showcases the student’s ability to conduct independent research, analyze data, apply mathematical concepts, and present their findings in a clear and coherent manner. Writing a Math IA can be daunting, but with proper planning and execution, it can be a rewarding experience that helps you understand the beauty and power of mathematics. In this guide, we will discuss how to organize your Mathematics IA.

## IA Cover Page

Title page should include:
The IB Number (In the format “ABC123”)
Session (i.e. May 2021)

## IA Important Rubric Requirements

Page Count: 12-20 Pages in length with double spacing. The page length per subsection is not set, but one can imagine it should correspond to the marking rubric.

E.g., use of mathematics carries a weighting of upto 6/20 while reflection carries a weighting of upto 3/20. Hence, you should expect to spend more pages on calculations than your reflection.

Personal Engagement: A unique part of this IA is the personal engagement.

Bibliography: A detailed bibliography is required so you must keep all sources which you utilise throughout your IA process.

## IA Layout

Section 1: Introduction
Introduction â€“ Why, what, then how.
Why? Your IA introduction should include a rationale for why you have chosen your topic for your Mathematical Exploration (the name of this IA). You should find some personal way to engage with your chosen topic to satisfy this requirement. Choose a topic youâ€™re genuinely interested in, state said interest explicitly and use your own personal examples where possible.

What? Picking a topic â€“ specifically an aim â€“ should be considered carefully and in conjunction with your tutor/teacher to ensure there is sufficient depth to your topic (as this depends on whether youâ€™re taking SL or HL Math). Make your aim explicitly â€“ this is important.
Note the difference between receiving a 6/6 for the use of mathematics rubric for HL/SL according to the IB:

SL â€“ â€śRelevant mathematics commensurate with the level of the course is used. The mathematics explored is correct. Thorough knowledge and understanding are demonstrated.â€ť
HL â€“ â€śRelevant mathematics commensurate with the level of the course is used. The mathematics explored is precise and demonstrates sophistication and rigour. Thorough knowledge and understanding are demonstrated.â€ť

In both cases you should use mathematics of a similar level to what you are studying in your respective studies. However, in HL, the mathematics that is explored must be precise and shows sophistication and rigour.

Some examples of previous IA topics are listed below (these are basic topics and not finalised research questions) and in the appendix. However, remember that there ought to be some personal engagement within the topic-choosing process:
â€śWhy planes travel a curved route and not a seemingly direct routeâ€ť
â€śDoes the stock marketâ€™s returns warrant its variance?â€ť
â€śProjectile motionâ€ť
â€śLâ€™HĂ´ptalâ€™s rule and evaluating limitsâ€ť
â€śImage rotations using rotational matricesâ€ť

How? You must outline how your exploration topic relates to your specific curriculum, how youâ€™ve completed the exploration, and provide any necessary background information â€“ your classmates should be able to understand your IA if they were to read it.

Section 2 (Body): Theory & Calculation

Theory
Provide only the relevant theory needed to reach a conclusion/understanding of your aim. If there is a particular method (in mathematics, there are often numerous ways to reach the same answer) that youâ€™ve used you should explain the method and why youâ€™ve used this method.

Calculation
For this section you must include all formulae and assumptions (i.e., the actual numbers) used to make your calculations and the mathematical steps that you took to reach your aim. Note assumptionsâ€™ pertinence if someone wants to repeat your exploration. After going through your mathematical work you must explain how they relate to your exploration topic. Depending on the type of exploration in which you are partaking you should use appropriate graphs, tables, x-y-z planes, or other methods of presenting your results. See below.

As can be seen from the figures above, figures are labelled appropriately. Calculations come with brief explanations and connect the earlier theory with the specific scenario in your exploration.

Section 3: Reflection, Conclusion, and Bibliography of Mathematical Exploration
Conclusion
Your conclusion is a continuation of section 1 and 2. You are answering your aim from your introduction (section 1) with the theory and calculations in from section 2. This should be done in a clear, concise, and coherent manner. Not only should you explain the results and implications of your calculations, but you ought to relate this to the aim raised in your introduction. You may also include much of the reflection in your conclusion if you prefer a more integrated approach. Note the IB says the following regarding where the reflection should be placed: â€śSubstantial evidence means that the critical reflection is present throughout the exploration. If it appears at the end of the exploration it must be of high quality and demonstrate how it developed the exploration in order to achieve a level 3.â€ť This implies a preference for integration but it does not mean you are excluding yourself from a level 3/3 grade for the reflection rubric.

Reflection
Your reflection should occur throughout your IA; however, you may also include a separate section depending on the layout of your IA. Hereâ€™s what you should do:
Consider limitations and extensions of your conclusion.
Similarly consider strengths and weaknesses.
Relate the mathematics within the exploration to your personal knowledge (or personal engagement).
Raise future research questions.
The IB states your reflection must be â€ścrucial, deciding or deeply insightful. It will often develop the exploration by addressing the mathematical results and their impact on the studentâ€™s understanding of the topic.â€ť

Bibliography
You should include a thorough bibliography to support your introduction, background, theory, and perhaps calculations. Types of relevant sources include online databases, your school textbook, or specific theories found both online and physically.

Appendix