IB Mathematics: Analysis and Approaches SL
Form 1 of 4
The internally assessed component in this courses is a mathematical exploration. This is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection. A student should develop his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow all students to develop an area of interest for them, without a time constraint as in an examination, and will allow all to experience a feeling of success.
In addition to testing the objectives of the courses, the exploration is intended to provide students with opportunities to increase their understanding of mathematical concepts and processes, and to develop a wider appreciation of mathematics. These are noted in the aims of the courses, in particular aims 6–9 (applications, technology, moral, social and ethical implications, and the international dimension). It is intended that, by doing the exploration, students benefit from the mathematical activities undertaken and find them both stimulating and rewarding. It will enable students to acquire the attributes of the IB learner profile. It is expected to take 20 hours.
The first step is to Choose a topic.
Choosing a topic
- Identifying an appropriate topic
- Developing a topic
- Devising a focus that is well defined and appropriate
- Ensuring that the topic lends itself to a concise exploration
Students sometimes find it difficult to know where to start with a task as open-ended as this. While it is hoped that students will appreciate the richness of opportunities for mathematical exploration, it may sometimes be useful to provide a stimulus as a means of helping them to get started on their explorations.
Possible stimuli that could be given to the students include:
sport | archaeology | computers | algorithms |
cell phones | music | sine | musical harmony |
motion | e | electricity | water |
space | orbits | food | volcanoes |
diet | Euler | games | symmetry |
architecture | codes | the internet | communication |
tiling | population | agriculture | viruses |
health | dance | play | pi (π) |
geography | biology | business | economics |
physics | chemistry | information technology in a global society | psychology |
A possible mind map for the stimulus “water”
During introductory discussions about the exploration, the use of brainstorming sessions can be useful to generate ideas. In particular, the use of a mind map has been shown to be useful in helping students to generate thoughts on this. The mind map below illustrates how, starting with the stimulus “water”, some possible foci for a mathematical exploration could be generated.
