The Mathematical Exploration.

What is the Exploration?

A 12–20 page written investigation on a topic chosen by the student. The aim is not to discover new mathematics but to engage personally with mathematics that genuinely interests the student — using techniques from the syllabus (or sometimes beyond it) to investigate a question.

How it is marked

Five IB criteria, marked out of 20 in total.

• A

  Presentation

  /4

  Coherent, well-structured, concise. The reader can follow the argument without re-reading.

  Mark-band descriptors›

  • 0Not reached.
  • 1–2Some structure but unclear, with irrelevant detours or sections that don't connect.
  • 3–4Coherent, well-organised, concise. A reader can follow it without getting lost.
• B

  Mathematical communication

  /4

  Correct and consistent notation, terminology, graphs and diagrams.

  Mark-band descriptors›

  • 0Not reached.
  • 1–2Notation and terminology used somewhat, with errors or inconsistencies (e.g. mixing $=$ and $\approx$, missing units).
  • 3–4Notation, terminology, and graph/table labelling consistently appropriate.
• C

  Personal engagement

  /3

  Genuine interest and ownership of the topic — independent thinking, original approach, real curiosity.

  Mark-band descriptors›

  • 0Not reached.
  • 1Limited evidence the student chose or shaped the topic — feels generic.
  • 2Some genuine evidence — own choice of context, example, or extension.
  • 3Substantial — original framing, hand-collected data, or a real voice running through the work.
• D

  Reflection

  /3

  Critical thought about what was done, what worked, what didn't, and what would come next.

  Mark-band descriptors›

  • 0Not reached.
  • 1Limited — brief comments at the end.
  • 2Meaningful — student reflects on what worked, what didn't, and the limitations of their model.
  • 3Substantial — critical reflection threaded throughout: choices justified, alternatives considered.
• E

  Use of mathematics

  /6

  Mathematics that is correct, sufficiently sophisticated for the course level, and meaningfully integrated into the investigation.

  Mark-band descriptors›

  • 0Not reached.
  • 1–2Mathematics is below the level of the course, or course-level but with significant errors.
  • 3–4Course-level mathematics used correctly, appropriate to the topic.
  • 5–6Course-level mathematics used with sophistication, precision, and a clear sense the student understands what they're doing — not just executing.

These descriptors are paraphrased from the IB Mathematics Internal Assessment criteria. The authoritative wording lives in the subject guide; see the IB AI-in-assessment page for the IB's current stance on AI.

Our timeline at CdN

We run the Exploration deadline a year ahead of the typical IB schedule — first draft early in May of Year 12, final version in the last week of the summer term. It is the first major piece of independent writing in the Diploma, and getting it out of the way early means fewer competing deadlines in Year 13. The trade-off is that the final version lands close to the Year 12 exams; we plan the spring term carefully so students do not hit both at once.

1. 1
   Year 12 · Spring

   Topic brainstorming and a first draft proposal in class.
2. 2
   Year 12 · April

   Students develop their draft alongside the spring teaching term.
3. 3
   Year 12 · early May

   First full-draft deadline — the version students submit for teacher feedback.
4. 4
   Year 12 · May–June

   One round of teacher feedback (the official one allowed by the IB), followed by final edits.
5. 5
   Year 12 · last week of summer term

   Final version submitted to the department; forwarded to the IB at the official submission window.

Resources we provide

Once a student has settled on a topic, their teacher puts together a starter set of resources tailored to that topic — recommended readings, accessible papers if appropriate, useful tools (Desmos, GeoGebra, Wolfram Alpha), and links to past student examples where they help. The reading list is meant as a starting point, not a syllabus: use what genuinely helps your investigation; ignore the rest.

• A short topic-specific starter reading list, curated by the teacher.
• Tool recommendations — Desmos for plotting and modelling, GeoGebra for dynamic geometry, Wolfram Alpha for symbolic checks, a spreadsheet or Python notebook when data is involved.
• Anonymised past-student examples (or extracts) when they illuminate what a strong line of inquiry looks like for a similar topic.
• Pointers to the standard IB-published exemplars, plus a note on how each one earned its marks.