The Maths Workshop course on the Pembroke-King’s Programme is not delivered as one might expect maths to be taught. Instead of relying on didactically lecturing on theories, the Maths Workshop that Mate Balogh oversees seeks to teach mathematical thought with a focus on problem solving.
The course is explicitly aimed at non-mathematicians with an interest in problem solving. This means that most of the students have never thought about the topics covered (infinities, mathematical games, finite mathematics, impossibility proofs) and so are able to discover entirely new areas of mathematics by solving interesting puzzles.
The problems are organized into chains that start out with somewhat simpler entries, but later problems expand and build upon ideas and methods introduced previously before leading to powerful mathematical theorems. There are often many different ways to come to a solution and so the students are able to find the path that is most natural to them. The aim is that in thinking about problems and coming up with solutions by themselves instead of looking at pre-prepared proofs the students will achieve a more complete understanding.
Although this style of learning has a long history and strong tradition in Hungary, it is entirely different from what students on the Pembroke-King’s Programme are likely to have experienced before.
The overall hope is that students get a solid grounding in the specific areas covered over the course of the workshop. More than that, Mate said, we hope that students also absorb the principle of building towards more complex ideas by gaining a solid understanding of the simpler, related thoughts first. Solving related problems and thinking about variations is a great way to ensure that they understand the sequence as a whole and not just a number of disconnected results that they try to remember.
The best moments of PKP are always where we see the enjoyment of discovery on the students. When their eyes light up after solving a particularly interesting and difficult problem or when all the pieces fall into place during a discussion. – Mate Balogh