The Exploration

The exploration is an opportunity for students to explore an area of Mathematics of their choice. There are three broad approaches students take.

1) Some students choose a topic from the course which they wish to apply to a certain scenario. For example, performing a statistical analysis of some data they have either collected or researched to reach a conclusion. Or perhaps using calculus and volumes of revolution to model a vase. Or using differentiation and graphical methods to find the optimal solution to a particular problem.

2) Some students choose a topic from the course, that they wish to explore further, beyond what was covered in the course. Perhaps an AASL student is interested in how the Binomial Theorem can be applied for non-integer powers. Or an AAHL student wishes to explore how the counting methods they have learned can be extended to scenarios where people are sat in a circle. Or an AISL student might want to explore the applications of t-testing beyond that which is course.

3) Some students choose a topic to explore which is from outwith of the course entirely. This can often involve something from the 'other' course. That is, and AA student might choose to explore statistical testing or Voronoi diagrams which are in the AI course. Or a SL student might want to explore complex numbers or differential equations, which are only in the HL course. Other students choose topics that are not in any of the courses to explore, such as group theory, the travelling salesman problem or Cantor sets.

Students spend time in class looking at the criteria, looking at examples of past explorations, considering what makes these good or bad, and coming up with their own ideas for their exploration. The teacher will guide students towards topics that will work well, and will support all students throughout the process.

In the summer term of the first year of the IB, 3 weeks of lessons will be dedicated to students working on their exploration. This is a chance for them to do the actual mathematics with support from the teacher, and to start writing up the exploration. It is best if students use this time wisely, to get support with things like formatting mathematical content, using mathematical software and completing the mathematics.

At the end of this 3 week block, students will hand in the draft of their exploration. This is the only time the teacher is allowed to look through the full written piece and give formal written and verbal feedback. It is very important that students hand in a draft that is as close to complete as possible, in order to get the most useful feedback from the teacher.

Between 10 and 15 hours of class time are allocated to working on the exploration. This includes looking at the criteria, discussing ideas, and the 3 week block of working on it in class.

Autumn Term Year 1

Students will be introduced to the basic requirements of the internal assessment, might get a chance to see some examples, or view the criteria. In HL they will do a couple of short tasks towards developing the skills of typing mathematics and exploring topics.

Spring Term Year 1

Students will spend a bit more time looking at the criteria and examples, and will start generating initial ideas for topics for their exploration. These will be discussed with the teacher, and by the end of the term all students should have a chosen topic.

Summer Term Year 1

Standard Level Courses - in SL courses, students will spend 3 weeks at the start of the term working on their exploration, and hand the draft in before the end of year examinations. After the half term, they will receive feedback and the final exploration is due before the end of the school year. It is complete by the end of the first year of the course.

Higher Level Course - in the HL course, students will spend 3 weeks after the end of year examinations working on their exploration, and will hand their draft in before the end of the school year.

The Exploration is assessed against 5 criteria:

• Criteria A - Presentation

How well organised the exploration is, and how coherent it is. Is it easy to follow, and is the aim clear?

• Criteria B - Mathematical Communication

How well the student communicates their mathematics. Do they use correct notation and terminology? Do they use different forms of representation of their ideas (graphs, tables, equations, etc)?

• Criteria C - Personal Engagement

How much has the student engaged with the mathematical topic and the process of the exploration. This is marked of evidence in the exploration, not on what the teachers see them do in class. Has the students explored something new to them? Have they looked at it from different persepctives? Have they explored the topic fully, or just scraped the surface?

• Criteria D - Reflection

How well does the student reflect on the results of their mathematics, and how this leads to further analysis. Does the student explain what they mathematics tells them? Do they compare different methods or approaches? Do they reflect critically on any limitations of their exploration? Do they consider what should come next at each stage of the exploration?

• Criteria E - Use of Mathematics

This is the only criteria which has a different rubric for SL and HL courses. It assesses how well the student understands the mathematics they have used, and whether it is relevant to the aim of the exploration. Students must not just get the correct answers, but also demonstrate understanding of the mathematics to score well in this criteria.