Maths IA criteria · 3 marks
Criterion D: Reflection
Reflection is the difference between a report and an exploration. Criterion D rewards reflection that is meaningful and, at the top, critical — and it must run through the work, not appear only in a final “limitations” paragraph. It is worth 3 marks.
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What Criterion D assesses
How you review, analyse and evaluate the exploration: what your results mean, how good your methods and models are, what the implications and limitations are — and whether that reflection shapes what you do next.
This is our summary, not the IB's wording. The descriptors themselves, with a checklist and a self-grade sheet, are on the IA criteria page. For a rough band for your own draft, answer the guided questions in the free IA self-check.
What the mark bands look like in practice
| Band | What the examiner typically sees |
|---|---|
| Low (1) | Limited or superficial reflection, often only at the end: “my results were accurate”, “I could have collected more data”. |
| Middle (2) | Meaningful reflection: results are interpreted in context and limitations are linked to the aim, though mostly at the end or not acted on. |
| Top (3) | Critical reflection throughout: deeply insightful comments that question the method and results, compare approaches, explore implications — and lead to the next step in the exploration. |
Our summary in plain English, not IB wording — see the official IB guide via your teacher.
Checklist for Criterion D
- After each major result: what does it mean in context, and is it reasonable?
- “What next?” — reflection that leads to the next step (“the residuals show a pattern, so I tried…”).
- Comparisons between methods or models, with reasons for choosing one.
- Strengths and weaknesses of your model, linked to specific evidence (residuals, predictions).
- Limitations that matter to your aim — and how much they change your conclusion.
- Implications: what your answer means for the real decision or question.
- What you learned, mathematically, and how the exploration could be extended.
- A conclusion that refers back to the reflections you made along the way.
Examiner tips
Critical means deciding.
Critical reflection is crucial and decisive: it changes something. “The linear model underestimates the last five values, so it cannot be used for prediction beyond 40 minutes; I therefore…” is critical. “The model was quite accurate” is not.
Reflect as you go.
The strongest IAs have short reflective paragraphs after every result. If all your reflection is in the conclusion, it needs to be of very high quality and clearly show how it shaped the work.
Limitations should be specific.
“More data would improve accuracy” applies to every IA ever written. Name the limitation that most affects your answer and estimate its effect.
Weak vs strong: an example
Loses marks
“My model was quite accurate. A limitation is that there might have been human error.”
Earns marks
“The exponential model fits the first 20 minutes well (residuals below 0.5 °C), but every residual after 25 minutes is negative, so the model cools too slowly as the tea approaches room temperature. Evaporation stops mattering at low temperatures, which suggests the constant k is not constant. I therefore fitted separate models before and after 25 minutes.”
Common Criterion D mistakes
- A generic limitations list at the end (“human error”, “small sample”).
- Describing results (“the graph increases”) instead of interpreting them.
- Never saying whether the aim was achieved.
- Reflection that does not lead to any change or next step.
What the IB subject reports say about Criterion D
- The weakest criterion in the reports: most reflection is a short summary at the end rather than critical thinking along the way.
- Reflect at the end of each section, and let what you find decide the next step.
- Evaluate the method, not just the result: sampling and sample size, the assumptions of a test, how a model behaves outside the data, and goodness of fit beyond quoting R².
- Generic lists of limitations and extensions (including ones produced by AI) earn nothing; nor do conclusions based on personal opinion rather than your results.
Our own summary of the moderators' comments in the IB's Mathematics subject reports (AA and AI, SL and HL, May 2024 to November 2025), which the IB releases to schools. Not the IB's wording, and not an IB publication.
Frequently asked questions
Where should reflection go in a Maths IA?
Throughout. Add a short reflection after each significant result — what it means, whether it is reasonable, what you will do next — and then bring these together in the conclusion.
What is the difference between meaningful and critical reflection?
Meaningful reflection interprets results and links limitations to the aim. Critical reflection goes further: it questions and evaluates, compares approaches, and changes what you do next.
Is a limitations section enough for Criterion D?
Usually not. A list of limitations at the end tends to be judged limited or meaningful at best. Reflection that runs through the work and drives decisions is what reaches the top band.
Reflecting on a model
In a modelling exploration, much of Criterion D is how you judge your models: residual plots, the sum of squared residuals, testing on points you did not use, extrapolation and the limits of the domain. See choosing and comparing models (residual plots, testing on unused points), the reflection mistakes that cost marks and the IA modelling workflow.
Reflecting on a statistics exploration
In a statistics exploration, Criterion D is about your sample, bias, the test's conditions and causation. Each IA statistics guide has a limitations list for its technique — for example the χ² test, the t-test and sampling and ethics.
Related: all five criteria with a self-grade sheet · annotated exemplars marked on every criterion · have Pete review your draft one-to-one · IA structure and format
Types of IA where theory meets reality, giving plenty to reflect on: simulation & monte carlo methods · kinematics & physics-style modelling · fractals & chaos.
Free: the Criterion D checks, and the other four, in one PDF
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