Working mathematically is about more than knowing facts, recalling definitions and applying techniques to familiar problems. I teach a course at the University of South Australia to develop problem-solving skills in pre-service maths teachers (primary and middle school). We focus on mathematical processes, not any particular branch of mathematics. We learn and practice strategies for: getting started, attacking the problem, and reflecting on and extending our work. The aims are to: develop students’ mathematical thinking skills so that they can tackle unfamiliar problems with confidence, help them experience the joy in asking and answering their own questions, and orient them towards the ways in which mathematicians work. In this session we’ll sample some good problems for uncovering aspects of problem-solving, and talk about specific strategies for progressively developing oral presentation and mathematical writing skills. We’ll also tackle the thorny issue of assessment, including how to support students to undertake in-depth mathematical investigations of their own choosing. My goal is that you’ll find one or two specific ideas that will help in your current teaching.