Are there good problems to teach?
Our students come from diverse backgrounds and very rarely have a
history of connection with the mathematical sciences through family or
friendship networks. In this respect, the issue of enculturation into the
productive professional disposition required of a mathematician is an
added aspect of their education that we build upon through a module on
Problem Solving (level 5). In the past academic year, we used the history
of mathematics to structure our exploration of problem-solving techniques
and methods.
The Problem Solving module has continuously evolved since its
introduction in 2014, as the team have focused it to develop the
mathematical proficiencies expected of maths graduates (conceptual
understanding, procedural fluency, adaptive reasoning, strategic
competence, and productive disposition).
In this talk, we analyse our teaching methods employed in the Problem
Solving module to test our assumptions about assessing for mathematical proficiency. This led us to further question how teaching students to
create new problems may be one proficiency category that is usually
missing from mathematics curriculum at HE level. We give an alternative
addition to problem solving curriculum by learning from deconstructing
some of the techniques used by designers of mathematics problems as
developed within the International Mathematics Olympiad movement.