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.

One of our experienced specialists, Andy Day offers a simple activity to test children's reasoning abilities.

Reasoning and Problem Solving

When the new Australian curriculum goes live in 2015, teachers across the country are being asked to – among other things – get students thinking mathematically. Two of the four proficiency strands are Problem Solving and Reasoning, (the others being Understanding and Fluency).

When I told people that my work with philosophy for children had moved me into mathematics for children, and how we teach it, a lot of them were surprised. They are still surprised when I insist that philosophy and maths are closely related. For many, those two subjects would seem opposite ends of the spectrum: at one end is cold hard mathematics with its truths set in stone, and the other is philosophy, as vague and elusive as a puff of smoke. But this is to misunderstand them both.