Effective teachers understand that the tasks and examples they select influence how the students come to view, develop, use, and make sense of mathematics.
Requiring students to think deeply about mathematical ideas will ensure that conceptual understanding is developed and that higher ordering maths thinking is achieved. Teachers therefore need to be able to design, select and sequence mathematical tasks, both for teaching and for practice, that support the development of big ideas of mathematics rather than isolated strategies and skills. Tasks should challenge students to explore concepts (not simply ‘get the right answer’), to be able to generalise and to develop ideas about the nature of mathematics. Independent tasks should be well chosen to achieve this and not simply be time fillers.
Many of the short term interventions that teachers have implemented to accelerate learning in mathematics have focused on developing aspects number knowledge and related skills because these have been identified as foundations upon which to build. Some of these interventions are in addition to and complement the regular classroom programme in which the development of mathematical concepts and processes is a priority.
See, say, do
A powerful teaching model is based on recognising that there are six things that students need to understand before they can be said to understand the meaning of 2 digit numbers.
Process to See, Say, Do (Example)