The analysis section is the heart of your IB Math Internal Assessment (IA). It’s where you demonstrate your mathematical understanding, connect ideas, and interpret results. Yet many students lose marks here—not because they lack skill, but because their analysis lacks coherence.
Writing a coherent analysis means building a logical, connected, and well-explained flow of reasoning. Every equation, graph, and explanation should link back to your main aim. This guide shows you how to achieve that level of mathematical clarity using tools like the RevisionDojo IA/EE Guide and Analysis Framework.
Quick Start Checklist
Before starting your analysis, make sure you’ve prepared:
- A defined aim or research question that your analysis answers.
- All your mathematical data, methods, or models ready to use.
- A clear outline for how your results will be presented.
- Access to tools like the Analysis Framework to help organize reasoning.
- Awareness of what examiners look for in Criterion B: Mathematical Communication and Criterion C: Personal Engagement.
When these pieces are in place, your analysis will not only be accurate but also easy to follow and deeply engaging.
What “Coherence” Means in Mathematical Writing
In the IB context, coherence means your mathematical ideas make sense together. Your reasoning unfolds naturally from one concept to another, and every part connects to the central purpose.
A coherent analysis is characterized by:
- Logical progression: Each step follows clearly from the last.
- Clear justification: Every equation and assumption is explained.
- Consistency: Symbols, variables, and notation remain the same.
- Connection to purpose: Every paragraph ties back to your aim.
Mathematical coherence doesn’t come from writing more—it comes from making every part of your analysis necessary.
Structuring a Coherent Analysis Section
You can think of your analysis as a story. It starts with a question, develops through exploration, and ends with insight. Here’s a simple structure that helps maintain flow:
1. Restate the Mathematical Focus
Begin the analysis by briefly reminding the reader of your objective.
For example:
“In this section, I will analyze how the logistic model predicts population growth under limited resources.”
This helps your examiner immediately understand how the math fits into your investigation.
2. Present Mathematical Tools or Models
Explain the tools, equations, or techniques you’ll use before diving into calculations.
For example:
- “I used differential equations to model rate of change.”
- “I applied regression analysis to find the best-fit curve.”
State why these tools are appropriate. This builds logical continuity from your methodology to your analysis.
3. Work Through Calculations Systematically
Now, show your mathematics in a clear, step-by-step manner.
- Label equations (e.g., Equation 1, Equation 2).
- Define variables before using them.
- Include brief text transitions such as “To find the value of k…” or “Substituting x = 5 into the equation…”
Avoid overwhelming the reader with unexplained algebra—examiners must see the reasoning behind your steps.
4. Interpret Intermediate Results
Don’t wait until the end to explain what your numbers mean. After each key result, interpret it in context.
Example:
“The solution shows that the population reaches half its carrying capacity after approximately 12 years, which aligns with observed data.”
This kind of commentary strengthens your communication score and keeps your analysis coherent.
5. Compare and Evaluate Results
After completing your main calculations, evaluate their accuracy and relevance.
- Do the results support your hypothesis?
- Were there alternative methods that might have worked better?
- Are your approximations reasonable?
A short evaluation at this stage shows higher-level thinking, not just computation.
Using the RevisionDojo Analysis Framework
The Analysis Framework helps students organize their reasoning so each mathematical step contributes directly to the argument. It prompts you to:
- Link each equation to the IA aim.
- Write a sentence of explanation for every formula used.
- Check that results are interpreted clearly.
- Verify that notation is consistent and readable.
By following this structure, you ensure your analysis reads like a seamless explanation rather than a list of equations.
Many students find that using this framework saves them time in the revision phase, since it minimizes structural edits and improves clarity from the start.
Common Pitfalls in the IA Analysis Section
Even advanced math students can fall into these traps when writing their analysis:
- Jumping straight into results without context:
Always explain why you’re using a particular method before showing calculations. - Inconsistent notation:
If “r” means radius in one section and rate in another, coherence breaks down. - Missing transitions:
A single sentence bridging each step—such as “To verify this result…”—keeps the logic flowing. - Unexplained assumptions:
Every model uses assumptions (e.g., neglecting air resistance). State them clearly so your reasoning appears sound. - Lack of interpretation:
Without explaining results, examiners can’t assess understanding, only computation.
Each of these issues lowers your Communication and Reflection marks—so fix them before submission.
How to Show Logical Flow in Equations and Explanations
The secret to coherence lies in how you connect mathematical ideas. Try these techniques:
- Sequential numbering: Number important equations for easy reference.
- Linking sentences: Explain how each step leads to the next.
- Balanced layout: Alternate between text, formulas, and visuals.
- Referencing graphs: After every figure or graph, write one or two sentences explaining what it demonstrates.
- Consistency in terms: If you start with “function f(x),” use that throughout—don’t switch to “g(x)” later.
The goal is for an examiner to read your analysis once and fully understand your mathematical process.
Demonstrating Personal Engagement Through Analysis
The IB rewards students who show genuine curiosity in their analysis. That doesn’t mean adding emotion—it means demonstrating ownership of the mathematics.
You can do this by:
- Discussing why you chose a particular method or model.
- Mentioning any insights you discovered while analyzing data.
- Reflecting on alternative paths you considered but didn’t pursue.
- Explaining how your approach evolved as you worked through the problem.
Personal engagement makes your analysis feel authentic and thoughtful, not mechanical.
Reflection Within the Analysis Section
While reflection is often a separate section, some of the strongest IAs integrate it throughout the analysis.
This could look like:
- A short note after a result: “This approximation works well for small values of x, but diverges for larger values.”
- Or at a transition point: “Initially, I expected exponential growth, but after analyzing the data, a logistic model fit better.”
This ongoing reflection demonstrates deep understanding and self-awareness—both critical for high marks in Criterion D (Reflection).
Using the IA/EE Guide to Strengthen Your Analysis
The IA/EE Guide includes structured prompts that align directly with examiner expectations. For your analysis, it encourages you to:
- Provide step-by-step mathematical reasoning.
- Maintain clarity even in complex calculations.
- Connect every result back to your central aim.
- Balance formulas with plain-language explanations.
When you align your analysis with these principles, you show mastery—not just of math, but of communication and reasoning.
Frequently Asked Questions (FAQ)
1. How detailed should my mathematical explanations be?
Explain every major step enough that another IB student could follow your reasoning. You don’t need to teach basic algebra, but every non-trivial calculation should include justification.
2. Can I use technology in my analysis section?
Yes—tools like Desmos, GeoGebra, or spreadsheets are encouraged. Just ensure you explain what they show and how they relate to your argument. Don’t let technology replace explanation.
3. What if my results are “wrong”?
Unexpected results aren’t a problem if you interpret and evaluate them honestly. Examiners value reasoning more than perfect outcomes.
4. How long should the analysis section be?
It’s usually the largest section of your IA, taking about 50–60% of the total word count. The goal is thoroughness without repetition.
5. How can I check if my analysis is coherent?
After writing, try reading it aloud or explaining it to someone else. If your listener can follow your reasoning from start to finish without confusion, your structure is coherent.
Conclusion
A mathematically coherent analysis turns your IB Math IA into a powerful piece of reasoning. It proves you can think logically, communicate clearly, and connect ideas effectively.
By using RevisionDojo’s IA/EE Guide and Analysis Framework, you can develop an analysis that flows naturally, demonstrates deep understanding, and earns high marks across all criteria. Coherence isn’t about complexity—it’s about clarity, purpose, and precision.
RevisionDojo Call to Action:
Bring clarity and confidence to your IB Math IA. Use RevisionDojo’s IA/EE Guide and Analysis Framework to organize your reasoning, strengthen your logic, and write an analysis that truly stands out.
