Real Maths?

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?

  • 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!

  • 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?

  • 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

Scratch Club Review

What went well in Scratch Club at my local primary school?

Reading back to my first post on Scratch Club Plans, I had in mind myself as a teacher, someone who would deliver lessons and impart knowledge to the students. I spend a fair bit of time looking at what to teach the kids next, and working out ways to present this info in bite sized chunks.

But later I recognised that the students had their own interests and agendas, and that these provided their motivation to learn, with each student preferring their own path.

Recognising this, I created the Scratch Club Badges as a way to explain the many aspects to Scratch programming and provide a way for each student to pick their own way through the subject. This worked as a way of giving each individual something to aim for that interested them, but it had a side effect of producing some competition/arguments amongst the students with them spending a bit too much time comparing themselves to each other.

Things that worked well

  • Students can work on anything that interests them, and spend as long as they like on any area of Scratch
  • Students can talk to each other, walk around to see what others are doing, copy ideas as they wish
  • Students are encouraged to help each other
  • Final demos, at the author's request, of their work
  • Initial demos of ideas from me at the start of sessions, e.g. to show something new and inspire them to try

What I'd do differently next time

  • Kick off with the rules, or rather lack of the usual school rules … e.g. OK to explore your own interests, walk around, talk to each other, copy ideas
  • Try to get at least an hour, or preferable hour and a half for each session
  • There's no need to prepare so many lesson plans, but get some feature demos ready for each lesson