Because mathematics is sometimes
messy and ambiguous, it is important to help children recognise these aspects
of mathematics. Mathematics is also logical and conveys precise meanings.
Take, for example, the notion of fallen leaves covering an area of ground.
The leaves will have fallen in a ‘random’ fashion. Some leaves will overlap
and there will also be gaps between them. This is an important discussion
point in order to raise children’s awareness of the need for using like
units in order to measure an area and convey this measurement to others.
This leads eventually to using standard units that will cover the surface
without gaps. This process of moving from a mess to a tidier structure
is the process of formalising mathematics, of making sense of the world;
this is the basis of mathematical modelling.
The two ideas offered here
are aimed at children's understanding of area and perimeter. The essential
ingredients are that the tasks, through their initial simplicity, are accessible
to children at Key Stage 2 and above. Within the tasks we offer, there
exist opportunities for ever-more complex and differentiated outcomes.