Conjecturing and generalising

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

An account of some magic squares and their properties and and how to construct them for yourself.

An article which gives an account of some properties of magic squares.

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.