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The Internal Assessment (IA) component of IBDP Mathematics comes in the form of a Mathematical Exploration. It is intended to be a student-selected topic submitted as a short report between 12 – 20 pages long. The purpose of the IA is to not only to assess the student, but to increase their understanding of mathematical concepts and develop a wider appreciation of Mathematics.
Cumulative Teaching Hours and Student Hours
The cumulative teaching hours as a guide for teachers is approximately 150 hours for Standard Level (SL) and 240 hours for Higher Level (HL). The duration of work for students is a cumulative 10 -15 hours.
Overall Weightage & Breakdown of Components
The Mathematics IA accounts for 20% of the total subject score. It is assessed based on 5 Criterion: Presentation (4 marks), Mathematical Communication (4 marks), Personal Engagement (3 marks), Reflection (3 marks), Use of Mathematics (6 marks). The maximum achievable score is 20 marks.
5-Criterion Assessment Framework & Tips
Presentation
To achieve the full 4 marks for Presentation, the IA report must be coherent, well-organized and concise. A coherent report means that the exploration is logically developed, easy to follow and achieves its aims. The structure of the report, comprising the introduction, body and conclusion should link well together. A well-organised report includes an introduction, aims and conclusions. Appropriate figures, diagrams, tables and graphs should be inserted accordingly to support the report. A concise report is not irrelevant and repetitive. Importantly, the use of technology is not required but encouraged, and will not be penalized.
Tip: Before commencing the actual writing of your IA, develop a plan. Create the “skeleton” or draft of your report, comprising an interesting and engaging Research Question, Introduction, Background, Method, Main Investigations, Results & Conclusion. Plan and organize your section titles, figures and tables to ensure they flow smoothly for the reader.
Mathematical Communication
Mathematical Communication that is relevant, appropriate, and consistent throughout is required to obtain full marks for this criterion. This includes notations, symbols, terminology, key terms, various forms of mathematical representation and deductive methods for proof.
Minor errors that do not impair clear communication will not be penalized.
Tip: After completing the main parts of your report, read them carefully. improve and standardize the mathematical representation throughout the report.
Personal Engagement
A high score in Personal Engagement is achieved when there is evidence of outstanding personal engagement of the mathematical topic chosen and making it their own. Importantly, it is not a measure of effort, but quality of engagement achieved by the student.
This Criterion is assessed in various ways including independent thinking, creativity, presentation of mathematical ideas, employing different perspectives. The report must be authentic as evident numerous times in the IA.
Tip: Do not try and copy other work found online or in other references. Develop your own motivation for the report. In addition, consider developing a useful and relevant report that is interesting to today’s reader. In a sense, develop your own investigation into your own interests and passions. The method and results obtained will be authentic and original to you.
Reflection
The Reflection Criterion is an indication of how well the student analyses, reviews and evaluates the exploration. Substantial evidence of critical reflection appearing numerous times in the report is required.
Tip: After completing your investigations and obtaining the results, spend some time to analyse these results and come to some meaningful conclusions that will allow the reader to understand your aim and insights better.
Use of Mathematics
The Use of Mathematics accounts for the largest component of the IA. To achieve the highest score of 6, relevant Mathematics concepts commensurate to the IBDP syllabus is required. In addition, thorough knowledge and understanding by the student is required.
Tip: Start strong. For those aiming for a higher score, select topics that are slightly more difficult compared to the IBDP Mathematics syllabus. Be careful not to proceed with extremely challenging or abstract topics which may require too much background knowledge. This will only make the report difficult for your peers to understand and create more confusion and difficulty in crafting a good IA report.
How to Choose an IA Topic
Students should conduct some research into interesting Mathematical topics that are commensurate with the IBDP difficulty level. Start by looking at your individual passions, interests, co-curricular activity and leadership involvement. There is much good Math to be found in these areas: Sports, Clubs and Societies. In addition, students can research into Mathematical topics that are inherent in the current IBDP subjects that they are pursuing. Whether it is the Sciences or Arts, very appropriate mathematical topics can be found in all areas.
For students who choose to pursue IBDP Mathematics Analysis & Approaches, perhaps a topic involving Calculus could be chosen. This includes optimization, rates of change, volume of revolutions, differential equations. Be careful not to select topics that are too difficult at the IBDP level to understand and apply.
· Engineering problems (Bridge, skyscrapers, 3D structures)
· Calculating sports parameters (frisbee math, rugby conversion math, tennis ace, volleyball goal, etc.)
· Surface and volume calculations (3D solids, irregular shapes, etc.)
· Growth rate/ Decay of biological and chemical compounds
For students who choose to pursue IBDP Mathematics Applications & Interpretation, maybe selecting topics involving statistics and probability could give you leverage. This includes permutations and combinations, game theory, statistical analysis, regression and correlation.
· Statistic analysis of individuals, teams, groups, or nations. (rankings, GPD, population, mortality rate, etc.)
· Biological markers, disease and virus analysis (COVID-19, breast cancer tumours, etc.)
· Regression and correlation approaches for better insight into trends.
Conclusion
The Internal Assessment is a unique coursework component of the IBDP that other high school accreditations do not offer. Students get the chance to complete this mini self-driven project to gain a better understanding of Mathematics in today’s world. Choose a topic that is interesting to you, so that you will not only enjoy the work, but also develop a naturally strong personal engagement and embark on a journey of discovery!
This article was written by Dr (PhD) Boon, a graduate from Imperial College London with a Masters in Nuclear Engineering and a PhD in Materials Science from National University of Singapore. He is also a highly sought after Mathematics tutor who has taught around the world and helped hundreds of students score a perfect 7 in IB Mathematics.
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