One way of considering the problem-solving process in maths can be determining the issue that takes it beyond a routine question, considering the available options which may be based on previous experience, and choosing an action to start making progress.
Non-routine problems are a major aspect of applying maths in real-life. They’re also a key component in assessment at A level and in university admission tests.
We’re running a face-to-face Year 12 Problem Solving Conference in Hertfordshire on Monday 18 July 2022 for A level Mathematics students who are aware that they find unfamiliar problems a particular challenge. The conference is designed for students who aren’t taking A level Further Mathematics.
Alternatively for students who will be in Year 13 next year and may be looking to take the MAT or the TMUA in November 2022, or the STEP in 2023, we’re currently planning a specific autumn term Higher Level Problem Solving series to help them with preparations for these exams. These events are planned to be weekly two-hour classes running from September to November. There will then be a separate series for students who wish to continue with STEP preparation from January onwards. Applications are due to open later this term, so keep an eye on the East of England regional events page.
In addition, our regular classes for new Year 12 students are planned to start at the end of the autumn term or the start of the spring term, so again keep an eye on the East of England regional events page. In 2021-22, our higher level problem solving classes generally met fortnightly online over about seven months for twilight sessions from 16:30 to 18:00. Students used an interactive platform with the capacity for students to engage with chat boxes and polls, write on screens, and use their microphone. Students worked in breakout rooms to collaborate on questions for a good proportion of the time. It was delightful to hear students reason things out together and watch them produce solutions on shared whiteboards.
Year 12 students have learnt new theory, tackled admission test papers, and worked through short questions like this:
Sally has a left sock, a right sock, a left shoe and a right shoe. In how many ways can Sally put on her socks and shoes if each foot’s sock must go on before each foot’s shoe?
Year 13 students have engaged with a range of ideas, starting with techniques that support academic interviews in maths, moving on to some of the additional theory for university admission tests and, more recently, considering STEP questions to prepare for the exams that some students took in June.