Before beginning any class it is important to explain to the students why they need to learn that material. If the students understand that it will affect them and their lives then they will accept it more readily. If they have no idea why they need it or if the reason is simply that they will have a test on it or it's on the report card, then the lesson will be less effective. They may or may not learn the material but they will not internalize it. They will want to reject the material as soon as possible.

Granted in some subjects it is impossible to explain why students should study that material. The teacher will have to overcome that problem.

In some subjects such as advanced issues in the sciences or in mathematics that may indeed not have a bearing on the future lives of students the administrators may consider then limitint those courses to students who want to take electives. Others perhaps should not study these courses.

With mathematics more than any other subject, I have heard the excuse that it helps people think. This is also the reason for teaching advanced courses. This is unfair.

Many other things help people think besides mathematics, and many other ways of thinking besides mathematical thinking are arguably just as important.

A student who has to do endless series of mathematical problems just because in the hope that it will help them think will not be convinced and will reject the assignment.

Let's look at it in another way. It is also argued that Gemara helps people think. If there is a limited amount of time to spend in school, then the manner of thinking for Gemara studies may be of greater importance than for mathematical studies and its need can certainly be justified much more easily.

One way to test whether students understand the need for a subject is by questioning why they are studying it. If they struggle to offer valid, justifiable reasons, to the teacher or to themselves, then there is a problem that needs to be corrected immediately before attempting to teach any new material.

If on the other hand the students can explain why, but they give incorrect reasons, then you may be able to agree with some of those reasons perhaps and develop additional ones.

Ideally, the students may feel or realize that the subject has importance for their future.

At any rate, this issue must be clarified in the beginning stages of a child's studies of any subject.

Of course, the older the child, the more that he can formulate questions. It is thus more important for the teacher to have reasons for studying the subject. Indeed in kindergarten or the early childhood years the issue of what they're doing in class rarely comes up, so it is not as important.