Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyze and change the world.

Mathematics is beautiful, develops the mind, underpins the study of other subjects, is a necessary component of many jobs, is necessary to be a successful citizen; it is historically of great significance; and, finally, it is unique amongst human intellectual development. Perhaps any one of these points would be sufficient reason alone for the compulsory study of mathematics. Collectively, they make it clear that compulsory mathematics education is vital for our progress and development.

There are some students that really struggle also with these courses and that never really grasp them to the level where they will be able to actually apply whatever is taught outside the class room. This is certainly, to at least a part, due to a failed approach of teaching, but perhaps not always. In all cases, for these people struggling, it would probably be better to not take the courses at all, since all they get out of it is a lowered self-esteem.

Allowing these courses to be electable, though, would probably have a lot of people skipping them, just because they are perceived as hard and unnecessary (as it is not quite apparent that you will need them) and that is likely a large loss to the society at large. Therefore, it is likely better to keep them as required courses and try to address the problems that certain individuals face, in more directed ways.