Methodology of Teaching Mathematics

A methodology will lack the precision of a technique but will be a firmer guide to action than a philosophy. Where a technique tells you 'how' and a philosophy tells you 'what', a methodology will contain elements of both 'what' and 'how'.

Religion, aesthetics, ethics, and science are all ways in which human beings seek order in the natural world. Science differs from these other ways of knowing and learning because the scientific process uses the scientific method, a standard series of steps used in gaining new knowledge that is widely accepted among scientists. The steps of the scientific method are often applicable to other situations, and begin with observation.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.