We've been home educating our children for the past few months and experimenting with an autonomous, child-led, approach. So we're wondering quite a bit about how maths fits into autonomous learning...

What's maths really about? What's maths for? What maths do we need in real life?

Does maths have inherent interest or beauty? Some maths doesn't, e.g. solving quadratic equations or multiplying fractions. And why do we need this stuff anyway?

Can we learn maths by considering interesting problems, big ideas, real world things, rather than working in the traditional school approach with foundations and bite sized steps?

**I think so. Here's what I'm trying...**

Pose a Big Maths Question (see below), perhaps with an initial example, and leave the kids to investigate. Consider giving some hints, but basically let them explore, make mistakes, go down blind alleys and so on.

The theory is: the exploratory journey is at least as valuable as getting the 'right' answer. And there may be more than one right answer.

**And maths games?****I'm also experimenting with some maths games, the first of which is The Confused Shopkeeper.**

## Big Maths Questions

### What makes things float?

Examples:

- Drop some modelling clay in water and watch it sink. Now shape it into a boat and see it float. Why does it do this?
- Compare an apple with an egg -- why does one float and one sink?
- What about other things around the house?

A boat made from Polydron, wrapped in cling film. Surprisingly stable

A coracle frame made from cardboard, and then wrapped in cling film and floating, fully loaded!

Hints:

- Is it something about the weight of the object? But why did the clay sink AND float?
- What about the displaced volume of water? How would you measure this?
- If you note the weight in grammes and displaced volume in mililitres what do you notice about the things that sink, and those that float?

### What makes things stable in water?

Examples:

- Take the clay boat from above and add some weight to one side, what happens?
- Take a floating dish with a flat base, add some marbles, what happens?
- How might you make things more stable in water?

##
Some *Real* Maths sites

- http://en.wikipedia.org/wiki/A_Mathematician's_Lament
- The Manifesto on http://www.cut-the-knot.org/manifesto/index.shtml
- http://blog.mrmeyer.com/
- http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
- http://www.mrbartonmaths.com/whatuse.htm