Question: How do you introduce new concepts in Maths?
One Answer: You demonstrate and explore them in a concrete way, then get students to represent the concept pictorially, then record it numerically – from the concrete to the abstract, in other words. So if you were introducing fractions, you’d get students to cut up a cake, then draw or arrange pictures of cakes cut up, then use digits to record the process.
That all makes sense to me, and apparently it’s the main principle behind Singapore Maths, the curriculum and methods that started in Singapore and have been followed by schools around the world attracted by the country’s performance in Maths teaching.