Use mathematical representations to unlock understanding – these can both clarify the meaning of a concept and provide access to the structure of the mathematics in a problem. Use ideas of variation theory to draw attention to key concepts.
Celebrate and build on what students already know. This requires formative evaluation so that students can develop their understanding from where they are. Drawing on the thinking of peers is an important part of the process, and helps to build a supportive and collaborative community.
It is important for students to have insight into fundamental mathematical ideas and concepts to help them make connections across the curriculum. This simplifies the amount that they need to learn. Emphasise the links between mathematical concepts (for example, factors and multiples, multiplicative reasoning, ratio, trigonometry).
Cover key content in depth to attain understanding and fluency that can be applied in different contexts. Fluency is not just about knowing facts and procedures, but also how and when to use them (for example in solving multi-step problems). Students practise important skills by drawing on both newly developed and previous understanding.
Build a supportive and collaborative community in which peers and the teacher support one another, misunderstandings are accepted, and the class works together to resolve these. The expectation is that everyone can understand important basic principles and come to use these with developing confidence.