Open the full How to Mark the IB Maths IA guide Use this practical marking reference while assessing and standardizing student explorations.

Marking the IB Mathematics exploration can be deceptively difficult.

The assessment criteria are clear enough when read in isolation. The challenge comes when you have a real student exploration in front of you. One section may be extremely strong while another is inconsistent. A student may use sophisticated mathematics without demonstrating much understanding. Another student may use comparatively simple mathematics but explain, justify and reflect on it exceptionally well.

The goal is therefore not to count features or search for isolated phrases that “earn” marks. It is to make a defensible, criterion-referenced judgment based on the evidence across the exploration.

For the current Mathematics: Analysis and Approaches and Mathematics: Applications and Interpretation courses, the exploration is marked out of 20 using five criteria:

Criterion A: Presentation, 4 marks
Criterion B: Mathematical Communication, 4 marks
Criterion C: Personal Engagement, 3 marks
Criterion D: Reflection, 3 marks
Criterion E: Use of Mathematics, 6 marks

IB describes the mathematical exploration as a short report centred on mathematics, with an emphasis on mathematical communication, commentary, mathematical writing and thoughtful reflection.

This article gives an overview of how teachers can approach the marking process consistently and, just as importantly, explain their judgments clearly during moderation.

1. Start by reading the exploration as a whole

One of the easiest mistakes is to begin marking Criterion A before you have finished page 1.

Instead, read the complete exploration once before assigning marks.

During that first read, establish:

What is the student's aim?
What mathematics are they using?
What decisions does the student make?
Does the investigation develop logically?
What conclusions are reached?
Does the student evaluate or refine the mathematics along the way?

This first reading helps you understand the mathematical story of the exploration.

On the second reading, you can begin tagging evidence for Criteria A to E.

This distinction matters because the same passage can sometimes provide evidence for several criteria, but for different reasons.

For example, a student might identify that a regression model behaves unrealistically outside the observed domain.

That could provide evidence for:

Criterion D, because the student is critically evaluating the model.

It could also lead to evidence for:

Criterion C, if the student independently decides to test a different model.

And it could contribute to:

Criterion E, if the mathematical reasoning behind that decision demonstrates understanding.

The evidence overlaps, but the criteria remain separate.

2. Use a best-fit approach, not a checklist

A common marking trap is turning the descriptors into a checklist.

For example:

Student mentioned a limitation: Criterion D achieved.

Or:

Student used calculus: Criterion E must be high.

Neither conclusion necessarily follows.

The question is not simply whether a feature exists. You need to judge its quality, frequency, relevance and effect on the exploration.

When a student's work appears to sit between two achievement levels, ask:

Which descriptor describes the overall evidence more accurately?

A useful borderline-marking test is:

The lower level is clearly achieved because ________. The higher level would require stronger evidence of ________. On balance, this exploration is better described as ________.

This forces you to identify the actual difference between the levels rather than awarding a mark based on an overall impression.

Criterion A: Presentation

Criterion A assesses whether the exploration functions as a coherent mathematical report.

The current guide describes a top-level exploration as coherent, well organized and concise. Coherence involves logical development and whether the exploration meets its aim. Organization includes a clear structure, an aim and conclusion, and appropriate placement of graphs, tables and diagrams.

What should teachers look for?

Look for:

a clearly stated aim
logical development
sections that contribute to the investigation
graphs and tables positioned close to the relevant discussion
a conclusion that addresses the aim
minimal unnecessary repetition
relevant rather than decorative content

Presentation is not primarily about aesthetics.

A beautifully designed exploration is not automatically well presented, and a visually plain exploration can still score highly.

One of the most important distinctions is between 3 and 4.

A strong exploration may be coherent and well organized but still lose the highest level because it is unnecessarily repetitive.

For example, students sometimes show the same type of calculation eight times after the method has already been established.

That may weaken concision.

A useful annotation could be:

A: repeated calculation adds no new mathematical insight; concision affected.

Criterion B: Mathematical Communication

Criterion B looks at how successfully the student communicates mathematics.

Look for:

appropriate mathematical notation
variables defined where necessary
appropriate terminology
readable equations
labelled graphs
appropriate scales and units
sensible accuracy
consistency across the exploration

A useful distinction here is between communication being mostly consistent and being consistent throughout.

An isolated notation error should not automatically prevent a student from receiving the highest level. The broader question is whether the communication remains clear and appropriate across the exploration.

For example:

B: variables defined clearly before use.

is far more useful as a teacher annotation than:

Good notation.

It tells a moderator exactly what evidence you have identified.

Criterion C: Personal Engagement

Personal Engagement is probably one of the most misunderstood criteria.

It does not measure:

how hard the student worked
how many hours they spent
whether they love football
whether they collected their own data
whether the teacher knows they were enthusiastic

The evidence has to be visible in the submitted exploration.

IB guidance emphasizes that personal engagement must be demonstrated in the student's work. A teacher saying that a student was highly engaged is not enough. Higher levels involve authentic decisions that help drive the exploration forward.

Useful evidence might include a student:

testing their own prediction
modifying a method
exploring an unexpected result
comparing methods for a mathematical reason
changing the domain after examining a model
devising an original classification or measure
pursuing an alternative direction after identifying a problem

Consider this distinction.

Weak evidence

I chose basketball because basketball is my favourite sport.

That establishes personal interest.

It does not necessarily demonstrate meaningful mathematical ownership.

Stronger evidence

The residuals became increasingly negative beyond 6 metres, so I restricted the domain and fitted a second model to determine whether the relationship changed.

Now the student's own observation is changing the mathematical investigation.

That is much more relevant to Criterion C.

Criterion D: Reflection

Reflection is another area where teachers often need to distinguish between different levels of quality.

IB distinguishes between:

limited reflection
meaningful reflection
substantial critical reflection

Simply reporting a result is not strong reflection. Higher-level reflection involves evaluating what the mathematics means, questioning the approach or using reflection to develop the investigation further.

Consider the progression below.

Description

The model has an R² value of 0.94.

This tells the reader what happened.

Meaningful reflection

Although the model produces R² = 0.94, it systematically overestimates the final three observations, reducing its usefulness for the stated aim.

Now the student is considering what the result means.

Critical reflection

Although the first model produces the larger R², its behaviour near the end of the domain is inconsistent with the observed trend. I therefore compared the residuals with those produced by a logistic model. The logistic model was ultimately more suitable because...

Now reflection is actively developing the exploration.

This is an important distinction.

A paragraph headed Limitations at the end of the document does not automatically produce a strong Criterion D mark.

For the top level, teachers should look for substantial critical reflection that is integrated into the development of the exploration, or exceptionally strong reflection that clearly demonstrates how the investigation developed.

Criterion E: Use of Mathematics

Criterion E is worth six marks and often produces some of the most difficult marking decisions.

The most important principle is:

More complicated mathematics is not automatically better mathematics.

The mathematics should be appropriate to the aim.

If a student uses an unnecessarily complicated technique where a simpler method would solve the problem more effectively, complexity alone should not be rewarded.

Teachers should consider three broad questions:

Is the mathematics relevant and appropriate?
Is it mathematically correct?
Does the exploration demonstrate that the student understands it?

The third question is particularly important when technology is involved.

Students can legitimately use calculators, spreadsheets, CAS software, regression tools and statistical packages.

But a screenshot of software output is not, by itself, evidence of mathematical understanding.

Weak evidence

Polynomial regression gives y = 2.17x³ − 5.6x² + …

Stronger evidence

The student explains:

why polynomial regression is suitable
what the coefficients or parameters mean
what domain is appropriate
how well the model represents the data
what limitations the model has
why another model might be more appropriate

The software can perform the calculation.

The student still needs to demonstrate the understanding.

At HL, teachers should also consider precision, sophistication and rigour, but this should not become a search for university-level mathematics simply for its own sake.

3. Annotate evidence, not praise

Teacher annotations play an important role during moderation.

The 2026 examiner instructions specifically note that comments and annotations should help the moderator understand why particular achievement levels were awarded. They also state that it is essential to include a comment for each assessment criterion so the examiner can understand the teacher's evaluation.

This means annotations such as:

Good.
Nice graph.
Excellent.

are not particularly useful.

Instead, annotate the reason that the passage matters.

For example:

B: variables defined consistently.
C: independent decision changes direction of exploration.
D: limitation identified and its effect on conclusion considered.
E: technology output interpreted mathematically.

A useful principle is:

Annotations locate the evidence. Criterion comments explain the judgment.

You do not need to annotate every paragraph.

Focus on evidence that helps justify the achievement level, especially where the mark is borderline.

4. Write comments that justify the achievement level

A strong criterion comment should do three things:

Evidence

What did the student actually do?

Judgment

How does that evidence relate to the descriptor?

Boundary

Why does this achievement level fit better than the one above or below?

For example:

The student defines variables clearly and uses appropriate notation across most of the exploration. Graphs are generally labelled correctly, although notation for the model parameters changes repeatedly in the final section. Mathematical communication is therefore relevant and appropriate but only mostly consistent. B3 is the better fit than B4.

That is far more moderation-friendly than:

Good mathematical communication. 3/4.

The first comment allows another marker to reconstruct your reasoning.

5. Be especially careful with borderline marks

Most difficult marking decisions occur at descriptor boundaries.

Four questions can help.

Frequency

Is the evidence isolated, occasional, repeated or sustained?

Quality

Is it superficial, meaningful, substantial, sophisticated or rigorous?

Consequence

Does the evidence actually affect the development or interpretation of the exploration?

Dominant descriptor

If you could choose only one descriptor to characterize the student's performance, which is the better description?

This is particularly useful for boundaries such as:

A3 vs A4: Is the exploration genuinely concise?
B3 vs B4: Is mathematical communication consistent throughout?
C2 vs C3: Are there numerous high-quality examples of authentic engagement that drive the exploration creatively?
D2 vs D3: Is critical reflection substantial?
E5 vs E6: Is thorough mathematical understanding demonstrated consistently?

6. Do not invent additional penalties

Teachers should assess each criterion according to what that criterion actually measures.

Suppose a student's graph has no axis labels.

That may affect Criterion B because it weakens mathematical communication.

It does not automatically mean the student should also lose marks for Reflection and Use of Mathematics.

Likewise:

an exploration is not automatically penalized simply for being short
technology is not inherently a weakness
using only one type of graph is not automatically a problem
advanced mathematics is not automatically required at SL
personal interest alone does not automatically earn Criterion C

The important question is always:

What does this evidence actually demonstrate under this criterion?

7. Standardize before finalizing marks

If several teachers teach IB Mathematics in the same department, standardization is essential.

A simple process is:

Two teachers independently mark the same exploration.
Compare marks criterion by criterion rather than beginning with the total.
Identify the evidence that produced each judgment.
Discuss any descriptor boundaries where marks differ.
Agree on what evidence the department expects at each level.
Apply that standard consistently to the remainder of the cohort.

IB itself uses a similar calibration philosophy in its professional-development marking resources. Teachers work with actual explorations, review moderator annotations and feedback, assign marks, and compare their judgments with senior-moderator standards.

A particularly useful standardization question is:

What additional evidence would we need to see to move this exploration one achievement level higher?

That keeps the conversation focused on the descriptor rather than on individual teacher preferences.

A final checklist for IB Maths teachers

Before submitting your marks, make sure that:

You have read the exploration as a complete mathematical argument.
You have assessed each criterion independently.
Your marks are based on observable evidence.
You have considered adjacent achievement levels in borderline cases.
Your annotations identify relevant evidence rather than merely praising or criticizing.
You have written a justification for each criterion.
You have not rewarded effort or enthusiasm that is invisible in the submitted work.
You have distinguished mathematical sophistication from mathematical understanding.
You have considered whether technology-generated results are actually understood.
Your comments would allow another experienced teacher or moderator to understand why the achievement level was awarded.

That final point is a useful test of the entire process.

If another IB Mathematics teacher can read your annotations and comments and reconstruct the reasoning behind your marks, your marking record is doing its job.

A note about the 2029 course

This guidance applies to the current exploration criteria.

For first assessment in May 2029, the mathematical exploration remains the internal assessment task, but the criteria change. Both AA and AI, at SL and HL, will use the same four criteria:

A: Problem Specification, 4 marks
B: Abstraction, 6 marks
C: Computation, 4 marks
D: Interpretation, 6 marks

The revised courses begin first teaching in August 2027.

Free resource for IB Maths teachers

For teachers who want a more detailed marking reference, we have also developed a How to Mark the IB Maths IA guide covering:

borderline achievement-level decisions
criterion-specific annotations
moderation-ready comments
examples of strong and weak evidence
SL and HL Criterion E guidance
sample marking commentary
a final marking checklist

It is designed to be kept alongside the exploration while marking, rather than read once and forgotten.

How to Mark the IB Maths IA: A Practical Guide to Assessing the Mathematical Exploration