The computer is an essential tool for the teaching of Numerical Analysis, since even simple methods involve complicated arithmetic. However, lecturers have been finding difficulties in formulating courseworks for undergraduate courses because the computing aspects tend to consume a great amount of the student's time, and hence divert his attention from the mathematical principles of the exercise. This project therefore instigated an investigation into how the learning of Numerical Analysis may be improved. After having established a learning model for Numerical Analysis, an assessment of the conventional teaching methods was performed, showing that these are not effective in furnishing the student with practical experience on the subject. A national survey of Numerical Analysis courseworks manifested that some lecturers attempted to overcome this problem by replacing the traditional coursework with interactive computer programs. The possible roles that may be assigned to the computer as an interactive teaching device were thus examined, leading to the conviction that the computer's. function must rest in, providing all students with the opportunity to easily execute the numerical methods, and to stimulate them to undertake a thorough critique of their subject. The educational objectives given to the teaching programs are: initiate or increase the amount of student- lecturer communication¡ produce all aspects of problem solutions; maximise the student's enthusiasm; accommodate all students; exhibit a user-friendly disposition; require no pre-usage training; involve no machine dependent code; be useful in all practical learning situations. A study of the programming features which are necessary for the real isatian of these objectives revealed that the methodology for designing the man-machine interaction for educational software requires further research and development. Through the development of three teaching packages (on ordinary differential equations, I inear simultaneous equations, and numerical integration) it became possible to derive a methodology for the design of the man-machine interface for simulation-type programs, whose design elements, which fall in one or more of the categories of learner control, motivation, and informative representation, are explained in terms of the psychological theories of learning. The methodology is proposed on the basis that the experiments carried out in real classroom situations proved that the form of the man-machine interaction enabled the programs to fulfil their educational objectives. Furthermore, it was discovered that the teaching programs have several advantages over the traditional coursework technique, in that they enhance the student's knowledge of Numerical Analysis to a greater extent, as well as increase the amount of student-lecturer contact, without expending more of the student's time.