This paper examines how particular teaching and learning strategies are related to student performance on specific PISA test questions, particularly mathematics questions. The report compares teacher-directed instruction and memorisation learning strategies, at the traditional ends of the teaching and learning spectrums, and student-oriented instruction and elaboration learning strategies, at the opposite ends. Other teaching strategies, such as formative assessment and cognitive activation, and learning approaches, such as control strategies, are also analysed. Our analyses suggest that to perform at the top, students cannot rely on memory alone; they need to approach mathematics strategically and creatively to succeed in the most complex problems. There is also some evidence that most teaching strategies have a role to play in the classroom. To varying degrees, students need to learn from teachers, be informed about their progress and work independently and collaboratively; above all, they need to be constantly challenged.