Our event in Birmingham kicked off with an opportunity to meet other scholars and alumni. Over a very nice coffee and cake, I had a chance to meet Kyle, Abi and Victoria. Kyle and Abi are both alumni and it was great to get their reflections on what went well and not so well in their training year, as well as their thoughts about teaching a few years down the line.

Victoria and I are trainees from different ends of the country (London and Bolton) so the Maths Scholars’ event was an excellent opportunity to meet and share stories from very different settings. Ironically, our stories shared some common threads (difficult topics, behaviour management and classroom engagement!)

The first speaker at the event was Aidan Gollaglee. Aidan works with the Maths Hub team in London. The focus of his talk was how we introduce trigonometry to our students. I had taught trigonometry to a Year 9 class five days before the talk, so this was an excellent opportunity to reflect on an alternative approach.

He asked us to consider different ways of engaging our classes in what sin, cos and tan really mean. Teachers often dive straight in to SOH CAH TOA without stopping to explain what each of the trigonometric functions does. Many students, Aidan observed, miss the point that they are simply ratios between two sides.

He pointed us towards Desmos as a useful tool for introducing trigonometry. A diagram on Desmos clearly shows the students what happens when we change the side lengths or the angle. The students see that the ratio of the sides is linked to the angle. Along similar lines, he suggested using the unit circle much earlier than it appears in most schemes of work.

Aidan suggested that our students can grasp the role of sin and cosine quicker using the unit circle (seeing that sin and cosine give the vertical and horizontal height, respectively). This gave me interesting food for thought. I reconsidered how engaged my students were with my trigonometry lesson. I reflected on the fact that I aimed for success in using the functions to find side lengths over using a manipulative tool like Desmos. I see the merits of both and am considering using Desmos if I teach trigonometry next year.

The second speaker was Bernard Murphy, who spoke about Problem Solving. Bernard introduced us to two different styles of problems – Area mazes and Langley’s triangle. They both confounded, frustrated, but definitely engaged, the Maths Scholars in the room. The purpose of the activity was three-fold.

Firstly, I understood, first hand, how students feel when they are problem solving in my lessons. I often forget how hard it can be to know where to start on a problem as a novice. Secondly, the activity demonstrated how powerful it is to let students struggle and achieve themselves. I am quick to intervene as a teacher when students are struggling, but Bernard demonstrated that more can be learned by allowing a significant degree of struggle (and thought)!

Thirdly, the activity demonstrated how important teaching method selection is for problem solving. For Langley’s triangles, it was clear after Bernard reviewed the first problem that we would need to add lines to the diagram. Importantly, Bernard encouraged us to ask ‘why did I not think of this before’ and ‘how can I think of this next time’. I found this session really engaging (if a little frustrating at times)!

Finally, we heard Tig Williams speak on how we can use maths with computing. A really engaging speaker, Tig encouraged us to look at how the computing students are studying in Year 4 can be combined with maths students are studying in Year 8. For instance, I can see how Scratch could be used to introduce properties of internal angles in shapes.

Using the Scratch program makes it clear to students how the code (mathematical rule) links to the visual representation of the shape. It would also be possible to allow students to inquire their way towards the rule we want them to learn by asking them to build a code that makes a shape on screen. This would engage students who like computing alongside those who typically enjoy maths.

Overall, I am really glad that I attended the event in Birmingham. It brought together speakers, scholars and alumni who are all passionate about maths into one room to discuss how we can optimise our maths teaching. I took lots away from the event and cannot wait to try it in my teaching!

**By James Rolls **

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