The latest meeting of my school’s Sixth Form Mathematics Society has just finished and, as usual, I am clearing various bits of detritus from the carpet. Crumbs from those chocolate biscuits named after a well-known German mathematician and philosopher are strewn everywhere. And piles of paper are covered in some very serious maths indeed: convergent and divergent series; an explanation of the work of Hilbert and Cantor; the St Petersburg paradox and more. The students have been discussing infinity.

All teachers are aware of the pressure to get through a syllabus and still (miraculously) have enough time for revision and exam preparation. Yet we know that some of the very best lessons are the ones where discussion and exploration take an unexpected turn, or wander off into more esoteric territory beyond the syllabus. Student feedback in my school certainly supports this and teachers here try to broaden investigations as often as possible. Of course, there isn’t enough time in the week to do everything - and this is where our maths societies come in.

The Junior Maths Society meets occasionally as an after-school activity, and the sorts of things they get up to will be familiar to teachers everywhere. Games, puzzles, code-breaking and origami are typical.

The Sixth Form Maths Society is a bit different. One of several academic societies in the school, it takes the form of semi-regular meetings (a few per term), which are chaired by a member of staff but run by students themselves, who each prepare and present short nuggets of information on a common theme. The presentations are informal but the themes - also chosen by students - can be very ambitious. Over the past three years the society has discussed subjects such as zero, quantum mechanics, encryption and prime numbers.

If this sounds a little academically elitist and relevant only for the most able students, consider the attendance: a gathering of 20 or more children is normal and this sometimes includes students who do not study maths at all. The fact that the students themselves have responsibility for preparing and leading the discussions is very important - no one in the room is expected to be an expert and everyone is listened to.

The society has done much to raise the profile of maths within a school that is widely known for its arts teaching. University applications for Stem (science, technology, engineering and maths) subjects are very strong and the number of our students who go on to study them at the very top institutions has increased over the past few years.

Every other year, we give our students the opportunity to purchase Sixth Form Maths Society hoodies (the latest features an Enigma cipher), so each cohort has their own sense of ownership and feels like part of the community. A Twitter feed disseminates news about the society, as well as interesting puzzles and mathematical information, to the rest of the school and anyone else who subscribes.

This is not engagement in maths by stealth, it is engagement in the subject purely for its own sake, and that is why it is so successful. Clearing up a few crumbs from the carpet is a small price to pay.

Michael Truss is head of academic enrichment and head of maths at Bedales School in Petersfield, England. The Bedales Sixth Form Maths Society can be found on Twitter at @BedalesMaths

Top 10 post-16 maths resources

1. Stat attack

Ideal for setting as homework or as a revision task, this collection of worksheets with solutions can be used to recap a range of statistical topics.

2. Maths with mates

This set of resources to support work on the index laws focuses on a peer- to-peer activity in which students learn something and then teach it to their group.

3. Equation exercise

These presentations and supporting worksheets offer a plethora of exercises to reinforce students’ understanding of a range of maths topics.

4. Algebra assistance

Work on students’ algebra skills using these editable handouts that include problems to solve on substitution, algebraic operations and equations.

5. Trig points

These student-friendly notes on the sine and cosine rules are useful to support trigonometry.

6. Making maths active

This collection of inventive problem-solving activities, ranging from treasure hunts and differentiated balloon games to mini-relays, will keep even the most able students in your class motivated.

7. Revise the rules

These checklists take students through key areas of mechanics and statistics and ask them to rate their confidence in each - a great way to focus their minds before revision begins.

8. Close focus

This presentation provides the perfect way to scaffold independent revision: students select their topic and area of study before answering a series of questions.

9. Pure knowledge

A group of well-presented worksheets that make excellent end-of-topic summaries for 11 areas of pure maths.

10. Deft decisions

Liven up your revision sessions with this quiz of four different rounds related to decision maths, including questions on definitions and quick calculations.