One of the difficulties in any teaching of mathematics is to bridge the
divide between the abstract and the intuitive. Throughout school we
encounter increasingly abstract notions, which are more and more difficult to
relate to everyday experiences. The subtraction of two apples from six is
simple; but the subtraction of six from two causes some ripples of uncertainty.
The division of twelve by three can be related to the sharing of sweets
amongst siblings; but the division of twelve by five takes us a little out of our
depth. Fortunately the introduction of negative numbers takes care of our
apples and rational numbers mollify our sweets.