Mathematics is a hierarchical subject that continually builds upon what has gone before. The assimilation of earlier material is essential if it is going to be possible for students to be taught and learn new mathematical ideas. This indeed is the view adopted by the benchmarking group developing national standards for the teaching of undergraduate programmes in Mathematics, Statistics and Operational Research (MSOR) within the UK. The draft statement from this group makes a very important observation about the learning of mathematics:
The subjects included in MSOR are largely cumulative: what can be taught and learned depends very heavily and in considerable detail on previously learned material. This applies to MSOR very much more than to many other disciplines. An MSOR programme must be designed to follow a logical progression, with prerequisite knowledge always taken into account. Advanced areas of pure mathematics cannot be treated until corresponding elementary and intermediate areas have been covered. Development of application areas can often be done in parallel with other work, but it is always necessary to ensure that the required methods and techniques have been dealt with.
(Quality Assurance Agency for Higher Education, 2001:6, Section 2.1.1)