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.

By Andy Day

INSET day yesterday. Hello teachers, I’m one of those people that come to your school on the first day back from holidays and interrupt your preparation for the coming term with power points of wisdom on how to teach.

I like to start by finding out something about what the teachers want, and what their beliefs about education are. Yesterday, one of the ideas that was mentioned – and generally agreed with – was ‘risk-taking’; the staff wanted their pupils to be willing to experiment and explore, and not to fear making mistakes, particularly in Maths. I agree with this aim, but… it’s ironic to hear it coming from teachers.

‘Look at all these things I don’t need!’ the philosopher Socrates is said to have declared as he stood before the many stalls filling the marketplace of Ancient Athens.

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).