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. Please note, the IA is 20% while the written exam is a larger 80% of the overall grade. 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.

Enhancing Graphical Representation in Math IA:

1. Optimize space usage, scaling, and formatting for clarity. Be consistent in fonts, colors, and scale across similar graphs.

2. Craft descriptive titles and captions for each graph. Accurately label axes with units.

3. Display data accurately without distortions or misleading visuals. Prioritize aesthetics and accessibility.

4. Integrate graphs smoothly into textual analysis within the IA. Leverage graphing software appropriately.

Enhancing Graphical Representation in Math IA:
1. Optimize space usage, scaling, and formatting for clarity. Be consistent in fonts, colors, and scale across similar graphs. 2. Craft descriptive titles and captions for each graph. Accurately label axes with units. 3. Display data accurately without distortions or misleading visuals. Prioritize aesthetics and accessibility. 4. Integrate graphs smoothly into textual analysis within the IA. Leverage graphing software appropriately.
Key Guidelines for Mathematical Presentation for Equations in IB Math IA:
  1. Format equations clearly and precisely using alignment, spacing, and standard mathematical conventions. Be consistent in notation and layout.
  2. Ensure equations flow logically and support the mathematical argument made in the analysis. Define variables and terminology properly.
  3. Use equation editors effectively to produce readable math expressions complementary to the discussion.
  4. Reflect on formatting choices made to demonstrate consideration of quality presentation standards expected for Criterion B.
By adhering to these guidelines, you will ensure that your IA meets the high standards expected in Criterion B of the IB Math IA, demonstrating clear, coherent, and professional mathematical presentation.

Criterion C: Personal Engagement (+3)

Criterion C:
Personal Engagement (+4)

Expressing Genuine Interest and Deep Connection:
Merely stating an interest, such as “I have always been interested in…”, is not sufficient for a high score in personal engagement. Students should be genuinely interested in the topic and reflect this throughout the exploration in their logical reasoning, choice of methods, etc. They should connect their investigation to personal experiences or profound interests, showing how these have influenced their choice of topic and methodology. This deep connection must be evident in every aspect of the IA.

Mathematical Ideas in Personal Terms:
Students should present mathematical ideas in their own terms, exploring unfamiliar mathematics whenever possible. They should make the investigation their own, showcasing individuality and creativity by asking thought-provoking questions and choosing a novel research question. Independent thinking and creativity in collecting data or developing new methods are crucial.

Proactive Initiative and Critical Analysis:
Demonstrating initiative in selecting a topic with appropriate complexity and adapting known methods and protocols is recommended. In the IB framework, replicating (not copying) the work of others requires a critical and comprehensive understanding of their methodologies. This includes delving into research, mastering data collection, experimentation, and analysis techniques, and integrating these with personal insights. Such an approach ensures a profound engagement with the material.

Depth of Understanding and Authentic Engagement:
The IB values depth over breadth, expecting students to exhibit robust comprehension of their study’s foundational principles. Authentic engagement stems from articulating concepts in their own words, providing examples, and drawing connections to broader ideas. Students should aim to make every word resonate with the examiners, displaying a clear understanding of their work.

Uniqueness and Engagement Balance:
While uniqueness is encouraged, engagement can occur with both unique and common topics. It’s the student’s approach and connection to the topic that truly demonstrates engagement, not just the topic’s novelty. This includes reflecting personal engagement effectively in writing, maintaining authenticity, and offering tangible evidence of personal investment in the topic.

By approaching the IA with these considerations in mind, students can showcase their personal engagement effectively, ensuring their investigation stands out and achieves exceptional results in Criterion C.

Criterion D: Reflection (+3)

Criterion D:
Reflection (+3)

The examiner will assess how the student reviews, analyzes, and evaluates the exploration in the Reflection criterion. Reflection is essential and can be presented either in the conclusion section or woven throughout the investigation. Ideally, reflections should be interspersed throughout, with a strong emphasis in the conclusion to bring coherence and depth to the entire exploration.

Students are encouraged to critically examine their results. Discussing different approaches, explaining the chosen methodology, and exploring the significance of the results are crucial aspects. It’s beneficial to also consider potential future work, delve into the strengths and weaknesses of the methods used, and link these discussions back to the initial goals of the investigation. This approach helps in coming full circle, showcasing a comprehensive understanding of the topic.

Reflection should also extend to the student’s learning journey. It’s important for students to demonstrate their engagement and the extent of their learning throughout the IA process. Reflecting on challenges faced, the evolution of understanding, and how the investigation influenced their perception of mathematical concepts adds a personal dimension to the IA.

Further, students should consider real-world applications or broader mathematical contexts in their reflection. This adds relevance and depth, showing an understanding that extends beyond the confines of the IA itself. A structured and organized reflection, presented in a thoughtful and introspective tone, can significantly enhance the overall quality of the IA.

In summary, a well-crafted reflection in the Math IA should be deep, critical, and self-aware, demonstrating a student’s journey, learning, and growth. It should connect the mathematical investigation to broader contexts and personal insights, thereby exemplifying a high level of engagement with the subject matter.

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.

We provide a range of services to support students in need of assistance with their IA. Our dedicated team offers IB Math tutoring specifically tailored to help students excel in their IA projects. In addition, we also offer comprehensive IA services aimed at guiding students through the entire process. Whether you need guidance on topic selection, research methodology, data analysis, or simply want feedback and suggestions for improvement, we are here to assist you. Furthermore, our IB tutors offer detailed information about all the services we provide, ensuring that you have access to the resources you need to succeed in your IA. We are committed to helping you achieve your goals and wish you the best of luck with your IA!

What are the common mistakes in formulating a research question and outlining the aim of the study?

When formulating a research question and outlining the aim of a study, there are several common mistakes that one should be aware of. These mistakes can hinder the clarity and focus of the research, potentially affecting the overall quality of the study. Here are some of the most frequent errors:

  1. Poorly formulated research question: A common mistake is not having a well-crafted research question. A good research question should clearly state the variables that are going to be measured and the mathematical analysis that will be used in order to find the desired answers. It is important to strike the right balance between a question that is too broad and one that is too narrow. A clear and specific research question ensures that the study has a clear direction and purpose.
  2. Lack of specificity in the aim: Another mistake is not outlining the aim of the study properly. The aim should succinctly communicate what the researcher intends to achieve and should serve as a roadmap for the study. It is essential to be specific and avoid including any unnecessary background information. Vague phrases such as “relationship between them” or “building my understanding” should be avoided as they do not convey a clear sense of purpose. The aim should clearly state what will be done, such as coding a simulation to demonstrate a concept or determining the correlation between two variables.

Additionally, it is important to note that when formulating the aim, it should provide a clear roadmap of what will be done. If there are multiple steps or actions involved, it is beneficial to outline them in the aim. For example, the researcher can start by stating what they plan to do and then explain what they will do next to achieve their goal.

In summary, the common mistakes in formulating a research question and outlining the aim of the study revolve around lacking specificity, clarity, and focus. A well-crafted research question should describe the variables to be measured and the mathematical analysis to be employed, while the aim should be specific and provide a clear roadmap of what will be done in the study. Avoiding unnecessary background information and being concise are crucial in avoiding these common mistakes.

Extra points regarding Math IA you might find useful

Certainly! Here are several intriguing topics that students can consider for their IB Math IA investigations:

1. Simulating models to analyze and predict weather patterns.
2. Exploring the probabilities involved in a selected game such as Solitaire.
3. Investigating the mathematical principles behind the Global Positioning System (GPS) and its technological complexities.
4. Delving into mathematical theorems like Fermat’s Little Theorem or Goldbach’s Conjecture, highlighting profound unsolved problems in mathematics.
5. Using calculus to determine the volume and surface area of real-world objects like eggs, apples, or mangoes, with the possibility of employing simulation techniques for modeling.
6. Studying the structural designs of bridges to understand how they can withstand loading without collapsing.
7. Analyzing complex roots graphically to grasp their properties.
8. Exploring how guitar frets are arranged based on Pythagorean ratios.
9. Comparing the advantages between receiving a lottery prize as a lump sum or in installments.
10. Understanding how ISBN codes and credit card codes can be deciphered.

You can click here for a more comprehensive list

In order to conduct proper research for an IB Math IA, you should begin by thoroughly researching the topic you are interested in exploring. You should utilize various sources including research papers, publications, and journals to gather information and findings that will support your investigation. It is crucial to delve into the details of the chosen topic, ensuring a comprehensive understanding of how mathematics plays a role in real-world scenarios. By selecting relevant and understandable information, you can effectively analyze and present your research in your IB Math IA.


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