The Common Mathematical Needs of Students in Mathematics, Science and Engineering
Preparation for University Mathematics
To provide a context in which to discuss the impact of computers and computer science on curriculum and methodology, it is necessary to agree first, in general, on the appropriate mathematics for the secondary school student and then to consider the university curriculum. Since there are significant differences between different parts of the world on when secondary school ends and university instruction begins, the comments which follow will have to be interpreted in the local context.
Algebra has traditionally been an important subject in high school. Since elements of abstract algebra are likely to become increasingly important in mathematics education, it is clear that algebra will remain of central importance in the secondary school curriculum. The important thing, however, is not to have students achieve great manipulative skill in algebra (e.g. in polynomial algebra) but rather to teach them to consider algebra as a natural tool for solving problems in many situations. Nevertheless, the ability to use formulas and other algebraic expressions will remain necessary.
In recent years there has been a trend toward replacing much of Euclidean plane geometry with those aspects of geometry more closely akin to algebra. This is useful as a preparation for university mathematics but there is much feeling among mathematics educators that the loss of Euclidean geometry is a sad development.