Doing a Higher Level (HL) Math Exploration for IB

From the Editor’s Desk

10th December 2023

Mathematics in the International Baccalaureate (IB) diploma is divided into Higher Level and Standard Level. Both Higher Level and Standard Level Mathematics require the writing of a Math Exploration, which is considered an Internal Assessment for the subject, making up 20% of the grade. This article concerns the Math Exploration at the Higher Level for the IB diploma.

1. Choosing a topic

Students should choose a topic which they are at least remotely interested in, as they will be doing a lot of research on it. Dry topics would be less enjoyable for certain students. For example, a potential topic is the use of the Taylor series to develop a better Newton Raphson formula so that the student can better estimate the roots of transcendental functions. (In short, there is a formula to estimate roots which use a function and its derivative to do so.)

In the topic mentioned above, there is a problem and a mathematical solution. If the student is unable to think of problems in Mathematics, they could ask their tutor to point them to some useful ideas and conduct further research along those lines to select a topic.

2. Make use of technological tools in your Math Exploration

A Math Exploration involves independent research, and students should make use of technological tools (such as those which involve simple programming skills) to aid them in their investigation. It would be far easier to outsource some of the heavy calculations to a computer instead of undertaking them all on paper, especially since the presentation of the data would also be neater. In the context of the topic mentioned above, the student could use a loop to calculate the roots of the functions. Some of this knowledge may be useful in university as they could be a repeat of the topics the students have learned in their independent study.

3. Keep track of your calculations properly so you can check for mistakes

A common mistake made by students is their lack of neatness in their calculations, resulting in them making many small mistakes which further compound as they go along. It is far more difficult to check messy work as compared to neater work. Students who use tools such as scientific calculators to make calculations, for example, may find it much harder to keep track of their calculations (along with there being the possibility of making typing errors) and would find themselves getting wrong figures. This results in a high amount of time wasted double and triple checking their calculations. Again, students should find a solution to keep track of these calculations, such as a code which could do the same task much faster and easier than we can.

4. Do preliminary research which is robust and detailed

Students should read up on the theory behind their topic as much as possible so that they can explain what they are doing effectively. The theory should not sound as though as it has been regurgitated – in fact, students are recommended to pick a topic that they are personally interested in so that they can have a good rationale for why they have chosen the topic and how it applies in their daily lives. The IB diploma encourages risk-taking and learning outside the box, which is the basis for the exploration in this assignment.

5. Display your data in an interesting manner

Students should be reminded that their results are the most interesting part of the assignment, and they should be displayed in a colour-coded graph or a table to ease the marker in their understanding. Some students have the misconception that their Math Exploration needs to be bombastic and difficult to understand. However, this could not be further from the truth. The more the marker understands the student’s argument, the easier it will be to assess and if the argument is robust enough, high marks will be awarded for it.