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Several years ago, we devised a structure for a problem-solving session for Year 12 students. The essential components are:

  • a group of Year 12 A-Level Mathematics students covering all levels of attainment,
  • a group of trainee mathematics teachers (referred to as Associate Tutors, or ATs, here), and
  • a set of genuine mathematical ‘problems’ – distinct from routine ‘questions’ where the means of solution is apparent and familiar to students.

These sessions have been successful because the focus is on problem-solving rather than revision, and students work in small groups, collaborating closely with each other and their AT mentor.

This year’s events used trainee teachers from two local HE partners: Liverpool John Moores University (LJMU) and the University of Chester (UoC).

We have found over the years that the key to success is to give Ats the freedom to devise their ways of working. The problems we use are tried and tested to ensure accessibility for all students, but we trusted our ATs to develop creative ways of enabling collaborative working. Desmos, shared whiteboards, and a sensitivity towards encouraging students’ confidence in speaking about their work meant that the vast majority of students could get involved in productive ways.

An equilateral triangle is inscribed in the triangle
“The uni reps were really good – they didn’t jump straight into the deep end of geometry like I thought they would which made me feel less nervous, but then they also challenged us and let us work together.”

After feedback from an online version of this event held during the pandemic, we have tweaked the design of the competition, which is always a favourite, so that it is now held in two parts: the first part at the start of the day, and the second, longer part – in the same teams and continuing with the score achieved earlier – for the finale.

Question 7) Find rational numbers W, X, Y, and Z which solve this equation:
“I enjoyed how the event was ordered in a way that I was excited for the competition at the end and I feel that the classes at the start really rejigged my memory!”

Overall, the event was as much of a success as always, really enjoyed by all involved, and particularly a fabulous learning opportunity for our ATs, for whom opportunities to work with this age group are often limited whilst on placement.

by Martin Bamber

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