More on fractions

The next problem with fractions is that pupils are taught the words “numerator” and “denominator” for the top and the bottom of the fraction, which they learn dutifully, but which mean nothing to them. They do not realise what the numbers signify. They do not realise that the word “numerator” means “how many”; they don’t realise that “denominator” means “what sort of thing” (as in denomination relating to currency or religion). This lack of understanding hampers the pupil as the rules they are expected to learn for manipulating the fraction are both opaque and arbitrary. Once they understand the meaning of these two numbers then the reason why they have to jump through the hoops they do to manipulate the fraction becomes apparent, and much more understandable.