What is the column method?

Column method of addition and subtraction is the method where numbers are 'carried' and 'borrowed'. It is set out like this:
 

This is a quick and efficient method for working out addition and subtraction, but the downside is that a child could use this method without having any awareness of place value (that is: they would not understand that the 3 in the above number is not 3, but in fact 30). It also means that they are not learning to add and subtract multiples of 10 or 100 (for example: 30 + 90, 120 - 50 etc). In order to help children understand these concepts, teachers often use partitioning for addition and a number line for subtraction.