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?