Ib Maths Exploration

Many IB students find themselves uncertain where to go with the exploration. They have spent many years answering closed exam questions in Maths, where there is a clear correct answer. All of a sudden, they are told to write something about maths - where to even start!? Having moderated Higher Explorations for the IB and looked after exploration moderation within the department, I have some insights to offer.

First things first

We must understand what the exploration is - it is not about answering questions, nor about doing difficult maths. It is about using maths to solve a problem, and writing about it. If you look at how it is scored, only 6 marks out of 20 are for using maths. That gives you an idea of how your work should be structured.

Choose an aim

Your aim defines your work. You need a specific aim that you can actually achieve, using maths you know, in the time you have, that is relevant to you. Your aim should be stated at the start of the work, and at the end you should make clear that your aim is complete.

Good areas of maths to choose include optimisation, modelling in a financial or engineering context, probability and statistics.

Investigations of common problems such as the Golden Ratio are bad. There are many websites about these areas, it is almost impossible to do anything new or personal.

Think about something personal to you

You really need to model a situation relevant to you, using maths, and solve a problem. So what interests you? I`ve seen work done on hockey, swimming, politics, and the shapes of flasks. All of these made excellent explorations, because the student was analysing a situation personal and relevant to them. Textbook problems never make good explorations - again, it`s not an exam.

Create your model

Look at how maths applies to your question, how can you model it. You might be using volumes and surface areas, trigonometry, kinematics. You will likely be creating a function, maybe differentiating it. Your situation needs to be simplified so that maths can be applied to model it. This creates a good reflection point - what are the limitations? What effect will they have?

Solve your problem

Do the maths, get the answer. Check it through, present it well, explain it so that the marker can see that you have understood it.

Personal engagement

As I`ve mentioned, the work needs to be personal to you. To show this within the exploration, make clear what you have done. If you`ve collected data, say so and provide a little detail on how you collected it. If it`s on your hobby, put in some pictures of you doing the activity. If it is a variation on a standard problem make it very clear how you`ve made it your own. In the case of the flask exploration, the student took photos of his own and his family`s flasks, and discussed how they fit his model.

Reflection

This means a range of things. For top marks, your reflection should be critical and appear throughout the work.

Here are some questions you could ask yourself to help you to come up with some reflection points:

• How reliable are my results?
• What might limit the accuracy of my work? What impact would it have?
• What have I learnt by doing this?
• What further work could be done?
• Who would care about this - are there any other implications?
• Is there an international dimension?
• How else could this be applied?

How much help can I have?
You should be discussing your exploration with your teacher throughout the process, and you can discuss it with anyone at any time.What you can`t do is have someone do the work for you, or plagiarise other work. The IB are very alert to the possibility of people copying some or all of their explorations, and are very strict if it is found.You should have one draft formally marked by your teacher, who will indicate where errors are (but not correct them) and will give general feedback on how to improve.
Finally
Before handing in the final version, proofread it. Look for anything that isn`t clear, doesn`t make sense. Pick out typos, bad mathematical presentation, maths errors. Is it sensibly organised, can it be read from start to finish and make sense?
Then, I suggest that you swap your work with another student, and proofread each others. They are supposed to be written to be read by your peers, so you should be able to read each others and understand them.
Finally finally, don`t spend hours and hours on this at the expense of exam work or other subjects. Get it done as well as you can, get it handed in, forget about it and focus on the other 80% - those exams!