Mini Explorations

Preparing Students for the Exploration

In the Internal Assessment portion of the May 2019 Mathematics SL Subject Report, the first comment in the section Recommendations and guidance for the teaching of future candidates stated that “Candidates would benefit from more practice and exposure in writing mathematics.”

And in the May 2023 Mathematics SL Subject Report, the following recommendation appeared: "Mini explorations can be used to guide learners to interpret assessment criteria and work on mathematical communication using technology..."

I strongly agree with both of the recommendations above. The truth is that the majority of students – even near the end of their secondary school education – have had very little or no experience in writing a paper that focuses on exploring a mathematical topic which includes some degree of creative and independent thinking. Producing such a paper – especially one that is 12 to 20 pages – is a challenging task even for the brightest students. The task can be made less daunting and more manageable (maybe even enjoyable) for students if they have an opportunity to complete at least one shorter writing task designed specifically for them to gain some insight, skills and feedback on writing about mathematics before they do their Exploration.

Some teachers may consider having their students complete a full practice Exploration (12-20 pages with a bibliography, etc.) to prepare for the real thing. If there is sufficient time in the schedule, this would be very beneficial for students. However, my experience is that students generally do not have the time and energy to write a full practice Exploration and then later write a second different Exploration for their final IA.

Instead, I have students complete an extended homework assignment that I call an “investigation” (see below) to prepare them for writing an Exploration. It is essentially a Mini Exploration but I do not call it this with students because I do not want to give them the impression that it is simply a shorter version of a full Exploration because it is not. I do not use the Exploration criteria to assess these investigations and the students do not choose their own topic nor do they need to find any source material. These investigations ('mini explorations') require students to reflect, explain, justify and comment as they carry out mathematical methods to obtain results with an investigative, explorative approach. These are aspects of the investigation assignment which are not typically included in mathematics assignments - one of the reasons that students are not well prepared to take on the Exploration.

I typically give students about one week to complete one of these investigations. I stress to students that to get the most out of the assignment they must work on it completely on their own and are not to discuss any aspects of the assignment with another student. I strongly encourage them to ask me questions - and if a student is stuck on a part of the investigation, I will provide appropriate hints to help them move forward on the assignment.

I currently have written one SL investigation and one HL investigation – and there is a separate Answers / Teachers Notes document for each. I use a set of four criteria (modified from the Exploration criteria) to assess each student’s work. Both of these investigations have a calculus focus being that they are essentially optimization investigations, but other parts of the syllabus also play a part. I am writing some more investigations which will have a non-calculus emphasis. As always, any feedback will be much appreciated.