27/07/2011
What does it mean to be functional in maths?
 To be able to solve problems
 To be able to apply their knowledge and skills
Sue Hough and Paul Dickinson
MMU
s.hough@mmu.ac.uk
p.dickinson@mmu.ac.uk
Two meanings for ‘understand’
 To have the confidence to be able to tackle an unfamiliar problem in an independent way
 To have a sense about whether they are right or not.
What kinds of understanding do we promote in this country?
 A student at Level 8 can understand that ‘….relational understanding……knowing both what to do and why’
‘Instrumental understanding……rules without reasons……the possession of a rule and the ability to use it’
(Skemp 1976)
An approach based on Realistic Maths Education (RME)
x2 – 9 = (x – 3) (x + 3)
 Work out 1/3 + 1/5
How do you know you are right?
Some examples
 Well researched activities encourage pupils to move from informal to formal representations
 Trigonometry
 Use of context is sustained throughout, not only as a starting point but as a way of developing a student’s understanding
 Use of models to support pupil development
 Progress towards formal notions seen as a long‐term process.
 Irrational numbers
 Volume 1