On Saturday 23^{rd} June, I attended my second ever #MathsConf, in Manchester. After attending #MathsConf14 in Kettering, I was completely hooked! For anyone reading who hasn’t yet been, I cannot recommend them more strongly – Mark (@EMathsUK) and the team @LaSalleEd do such a fantastic job of putting the day together, and it is by far and away the most effective CPD I’ve attended. With that in mind, I’m going to share some reflections on the day itself. (This is quite long – you have been warned).

**Session 1:**

I attended Jo Morgan’s (@mathsjem) session on looking at Indices in Depth. While I’ve read Jo’s posts before on her Topics in Depth series, I’d never seen her speak and I am just so glad I did! She began by explaining the rationale behind the project, which is that due to time constraints and other pressures, teachers typically cover topics at a superficial level, which Jo is keen to change.

She began by discussing how she used to teach the three laws of indices in one lesson, and how this was – on a surface level – successful (it even led to her being offered a job!). However, this meant that her students couldn’t answer more challenging problems, and her A Level classes still had gaps in their knowledge. This really resonated with me. Only two weeks previously, I had planned a ‘revision lesson’ for my top set Year 10s, in which I rushed through a few difficult examples, on the basis ‘oh, you’ll have done this in Year 9 – you should be able to apply that knowledge here’ and it was fairly disastrous. As such, I was really keen to think more carefully about how I introduce this topic.

The first key point that I took away from this session was Jo’s carefully considered examples and non-examples – rather than just showing pupils ‘this is how/why the rule works’, we also need to show them ‘how/why the rule does not work’, so that they can build up a more complete understanding. The other point that I found fascinating was the use of language surrounding this topic – I know from conversations with other attendees that I’m not the only one who has been referring to the ‘power’ incorrectly. More generally, I’m aware that I rarely (if ever) spend sufficient time in lessons looking at mathematical key terms and defining these effectively, so this is something that I want to continue to work on.

**Session 2:**

I attended Peter Mattock’s (@MrMattock) session on Revisiting Measuring. Pete is someone I’ve met previously and conversed with on Twitter, so I was absolutely delighted to get to see him speak. Now, I will be the first to admit that I’ve never really considered ‘measuring’ as a topic – it’s always seemed something that should have been covered in sufficient depth at a primary level. While I’ve explicitly taught ‘how to use a protractor’ and ‘how to use a ruler’, when necessary, I’ve not taken the time to think about what it actually means to measure.

We looked at how measurement is a tool of comparison – comparing something to a unit, and how we define what this unit is. I was so fascinated to learn about how various units have been defined and re-defined over time. I had absolutely no idea that a metre had once been defined as ‘one ten-millionth of the distance from the equator to the North Pole’, but now I am desperate to share this with my students.

My main takeaway was in terms of measuring/calculating areas. I’ve always introduced area from the perspective of ‘counting squares’, before moving onto formulae for areas of rectangles/triangles etc. The problem I’ve encountered with this is that the moment a formula is used, students seem to forget how this formula relates to the ‘counting squares’ approach – and so it becomes just another procedure to remember. Pete suggested creating ‘area rulers’ and using these as a way to promote a deeper understanding – I’m so excited to try this in my classroom.

**Plenary session:**

The plenary session of MathsConf15 was run by Simon Singh (@SLsingh), which I was so excited about! His book ‘Fermat’s Last Theorem’ was one of the first things that really made me interested in Maths, and I recently gave a talk on it for an enrichment session as school. In his session, he covered all sorts of interesting ideas – we were played a clip of Led Zeppelin before experiencing the same clip in reverse, which initially sounded like nonsense. Before playing the clip for a second time, he explained we would now hear some words about Satan, which, inevitably, we did. We had been tricked by the power of suggestion – a really useful reminder to remain critical and evidence-focused!

He also played us some clips from the documentary he made for the BBC about Andrew Wiles and Fermat’s Last Theorem. I’ve watched this before, but it is such a powerful film. I definitely want to spend more time with my students looking at just how beautiful and powerful Maths can be, and this provides a really nice starting point for those discussions. The documentary is still available online at:

Simon also discussed some of his most recent book ‘The Simpsons and their Mathematical Secrets’ with us, before sharing his latest project: The Parallel Project. This project is aimed at Year 7/8 students, and provides them with weekly challenges and puzzles, to stretch them beyond typical ‘school maths’. This is definitely something that I want to investigate further, as the puzzles are excellent quality and may be the catalyst some of my students need to fall in love with Maths!

**Session 3:**

Session 3 was on problem-solving with Clare (@abcdmaths). It was a packed session, with people sat on the floor. Clare (like me!) was making her Maths Conf debut – I think she did fantastically. We were encouraged to think about various tasks and if we would consider them as ‘problem-solving’ or not. This was a really interesting discussion – it goes without saying that we want our students to be excellent problem-solvers, but it’s really hard to identify what that actually means! I had an interesting discussion with Ashton (@ashtonC94), who suggested that a ‘problem’ is anything which students have not been taught explicitly.

For example, finding the radius of a cylinder when given its volume and height could be considered a ‘problem’, in that a student may not find it immediately obvious what they have to do. However, if a class have been taught a procedure to find the radius of a cylinder, and then complete 10 questions on it, then those would not constitute ‘problems’. In short – there isn’t one definition of what a problem is, as it depends on the student’s prior knowledge and all sorts of other things. Yes, there is a case that it must be a ‘non-routine’ question, but perhaps not if those ‘non-routine’ questions are taught directly.

The session has left me with a lot to think about and reflect on; I definitely want to do some more reading around how much of problem-solving is domain specific and how much is fairly general. Is there anything similar between solving a tricky circle theory problem or a simultaneous equations problem? I’m not sure yet, and will continue to think about this.

**Session 4:**

So, this was the session in which I made my #mathsconf debut! I was incredibly honoured to have been asked to present by Craig (@mrbartonmaths) alongside Ben (@mathsmrgordon). In it, Craig discussed how thinking about variation/examples has had a significant effect on his teaching, and Ben and I both presented an exercise which we had written and used in our classes. This culminated in the reveal of www.variationtheory.com, which I am so delighted to have been able to reveal after months of secrecy! I’m not going to go into much detail here, as I want to write a separate blog post concerning the exercise I shared, and hopefully respond to some of the criticisms that have surfaced.

Overall, I had the most fantastic time at #mathsconf15 – I learnt so much, and as before, left with new ideas buzzing around my head and things to take back to the classroom. A huge thank-you to Mark McCourt and La Salle Education for organising the whole conference so well – the whole day runs incredibly smoothly and it is just a dream to attend. If you’ve not been before, please look at attending! I promise you will have the best time.