Computer Environments for the Learning of Mathematics

Computer software for the learning of mathematics, as distinct from software for doing mathematics, needs to be designed to take account of the cognitive growth of the learner which may differ significantly from the logical structure of the formal subject. It is therefore of value to begin by considering cognitive aspects relevant to the use of computer technology before the main task of focusing on computer environments and their role in the learning of mathematics. The growth of (mathematical) knowledge The human brain is remarkable in its ability to store and retrieve complex information, but it is correspondingly limited in the quantity of independent pieces of data that may be manipulated in conscious short-term memory. To minimise the effects of these limitations, one method is to ‘chunk’ the data by using an appropriate representation which is more easily manipulable. For instance, standard decimal notation is a compact method of representing numerical quantities of any size, with corresponding routines for manipulation; algebraic notation can be used to formulate and manipulate certain types of data for problem-solving; graphical representations are appropriate for other tasks, such as representation of complex data in a single gestalt.