Math IA is required for Mathematics Analysis and Approaches (HL and SL); Mathematics Applications and Interpretation (HL and SL) . Math IA accounts for 20% of the overall score. It is mandatory, meaning that the students will not receive a grade for the whole subject if they do not perform it. The official guide states that 6 to 12 pages are enough. However, the report can go up to 20 pages, and the students will not get any penalty for writing a more extended investigation as long as they satisfy the rubric and are concise.

It should be highlighted that the goal of IA is exploring ideas, not writing a formal research paper! It is recommended that students spend around 10-15 hours of class time and one-on-one teacher meetings plus around 10-15 hours working individually. According to our experience, it usually takes around 20 hours or more of focused work to produce the desired results.

IB recommends that students find their own stimuli with the help of the teacher. However, teachers sometimes provide a list of stimuli from which the students choose the ones to which that they can relate.

In our experience students spend far more time than what is necessary and take too long to get started with an idea. Remember that the IA is worth 20% and the written exam 80%. Spending the extra hours on the IA to get another mark or two could be better spent on practicing exam questions on topics which you have covered off the syllabus.

Each exploration is assessed against five criteria as follows:

Criterion ACriterion BCriterion CCriterion DCriterion E
CommunicationMathematical presentationPersonal EngagementReflectionUse of Mathematics
Criterion ACommunication4
Criterion BMathematical presentation4
Criterion CPersonal Engagement3
Criterion DReflection3
Criterion EUse of Mathematics6

The final mark is achieved by adding all the marks (no fractions or decimals are acceptable, and the score will be rounded down if necessary). Even though criterion E has the same score for SL and HL, but the descriptors of them are different and are discussed in the following sections. All criteria are treated separately, meaning that achieving a high score in one of them does not guarantee a high score in the other sections or the other way around. In both HL & SL, the maximum score that can be achieved is 20.


Criterion A: Communication (+4)

Criterion A:
Communication (+4)

According to IB, “This criterion assesses the organization and coherence of the exploration. A well-organized exploration contains an introduction, has a rationale (which includes explaining why this topic was chosen), describes the aim of the exploration and has a conclusion. Coherent exploration is logically developed and easy to follow.”

This criterion is about writing a well-structured IA. In the introduction students should clearly state why they have chosen the subject, talk about the context of the exploration, and straightforwardly describe the project’s aim. It should be concise and also easy to follow.

The paragraphs in the body of the report can be results followed by discussion or “results and discussion” as a whole. This section is the meat of the whole exploration.

Students should show all their work. They should include all the equations. The explanations should be concise, complete, and easy to follow. The number of data points should be enough for quantitative work. Data can be collected using research, observation, or survey. Data taken from other references should be cited. Any data that is not strictly necessary in the main text should be put in the appendix.

The conclusion brings everything from the whole IA back together in a condensed manner! Students should clearly explain how the processes connect to prove or reject the hypothesis. Was there something that could have been done differently to make the whole exploration better? Were the models used in the exploration reliable? Does the student have any recommendations for a possible future project? Students need to define a clear focus and/or question for their exploration.

Criterion B: Mathematical presentation (+4)

Criterion B:
Mathematical presentation (+3)

To get a full score in this criterion, students should use appropriate mathematical language that includes standard and correct notations, symbols and terminology. They should define key terms accurately when introducing them. They should not limit themselves to one type of representation but use different types if possible, including diagrams, tables, charts, formulae, models, and graphs. In that way, they show the examiner that they can look at the data from different perspectives and interconvert and interpret them coherently and also show that they can use technology effectively.

Some of the common mistakes in this section include rounding errors, neglect of significant figures, not defining key terms, difficult-to-read charts and graphs, unclear labels on the axes of graphs, and the misuse of terms.

Criterion C: Personal Engagement (+3)

Criterion C:
Personal Engagement (+4)

Expressing their interest in the introduction and giving a personal connection or showing curiosity will not be enough to get a high score (or any score) in this criterion. Saying that “I have always been interested in…” will not cut it!

Students should be genuinely interested in the topic, and it should be reflected throughout the exploration in their logic, choice of methods, etc.

The students should present mathematical ideas in their own terms. They should ask questions and explore unfamiliar mathematics if possible. They should make the investigation theirs and show it in several instances throughout the investigation.

Students should show independent thinking by choosing a novel research question, showing creativity in collecting data or coming up with new methods, and understanding the strengths and limitations of their investigation.

Students should display initiative by choosing a topic with suitable complexity. They will use known methods and protocols, but it is recommended that they adapt them if possible.

The examiners should feel the students’ complete engagement in the exploration. They should feel that the students understand every word that they have written!

Criterion D: Reflection (+3)

Criterion D:
Reflection (+3)

To check this criterion, the examiner will assess “how the student reviews, analyses and evaluates the exploration.”

Reflection can be done in a conclusion section or spread throughout the investigation. If students want to limit it to the conclusion section, then a strong reflection is necessary. Having the reflection interspersed throughout the investigation while emphasizing it in the conclusion section is the best approach.

Students should not shy away from being critical of the results. They can talk about different approaches that they could have used and why they have chosen this specific one. They should talk about the significance of their results. They can talk about what can come later as future work; they should discuss their methods’ strengths and weaknesses and link the whole thing to the goals of the exploration to come full circle!

They should show that they have engaged and learned quite a lot while doing this IA.

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Criterion E: Use of Mathematics (+6)

Criterion E:
Use of Mathematics (+6)

Even though both SL and HL students can be awarded a score of six for this criterion, the descriptors are different.

The mathematics used in the exploration should be at the same level of difficulty or higher. Making mathematics complicated when simple math will do will harm students’ scores by making the methodology irrelevant!

In SL, “correct” math that has some occasional insignificant errors can result in a 6, but to get a 6 in HL, the math needs to be “precise,” meaning it has no errors.

Using technology is recommended, but students should prove that they know what they are doing.

“If the mathematics used is relevant to the topic being explored, commensurate with the course’s level and understood by the student, then it can achieve a high level in this criterion.”

HL students should show a deeper level of understanding throughout the IA. It is recommended that the sophistication be in the HL syllabus, but if it is in the SL syllabus, it can still get a high score if the math is used in a sophisticated way that is beyond the level of an SL student.


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