A great deal is known about the difficulties learners have with understanding algebra. Here are some of those difficulties and what you can do about it:
1. Letters have many meanings. Most of them are not the meanings we give them in algebra. Letters are used in everyday life in lots of ways. Some of the ways we use words and the problem that creates are:
a. Letters are used to build words, so some learners believe that the letter b can only represent objects that start with the letter b, like bananas or bicycles. Just to confirm this for learners, scientists often use letters in this way, e.g. In e = mc2, e represents energy. In fact we can use any letter we like to represent a variable.
b. Letters are used to label specific things (eg. Room A, Groups of people, Options or choices). So learners can believe that letters in algebra represent a specific object and that two variables can never have the same value, eg. In , f and g cannot both be 6.
c. Letters are sometimes used to represent a special number. In e = mc2, c represents a specific measure, the speed of light 299,792,458 metres per second.
Another example is π, a greek letter.