Presenting different points of view in maths is important. It's a colourful subject and learners approach it from all sorts of interesting angles. For example, write out four anonymous ways of looking at a concept on the board and then ask children what they think. Can they reach a consensus?
* I think multiplying two numbers together always makes a bigger number
* Multiplying by a fraction makes a smaller number doesn't it?
* If you multiply by zero then you'll get zero as a product
* It depends on what numbers you multiply together.
As children reveal their own thinking we are able to assess the level of sophistication they are working at and facilitate their learning from there. Ask children what share of a cake they would like: 30100, 28, or 15.
Children could then be given the following statement to discuss: "I'll have 30100 because that's miles bigger than any of the other fractions."
Sometimes there isn't a right or wrong answer. For example, "What number follows 1.5?" It could be 1.6 but it could also be 1.51.
Maths is not as black and white as some people seem to think
John Dabell is a numeracy consultant and teacher trainer