Mathematics need not be too complex or too simplistic for pupils to learn. The balance is found somewhere between mastery and basic knowledge of the more important processes here. For many students the subject is going to be really too complicated for comfort and that means even the academic curriculum could be lacking.
The process is still very awkward for most purposes, requiring people to do both long calculations and shortcuts. How to teach math again is a balance that should be composed of simpler shortcuts as well as the basics of complex items. This is for things that are usable for students and not forgotten after a few years at work.
Work is most often than not something that requires you to have good knowledge of basic mathematics. These are arithmetic equations you can do on your mind, more and you will not be able to contain much of the knowledge. You will have need of more notes, more calculating devices and time when you have to do complex equations.
These are really more or less things which the experts should be aware of and do. And there is not a lot of need for these because of how there are few positions that may offer good incomes to, say, a trained physicist. The complex math should be left to these and not to the general run of students, who still labor under harder items for geometry, trigonometry, physics and algebra.
The process of teaching however is something that mentors have to digest well especially for math. Not a lot of teachers are themselves math experts but they have to fit into this role well if they are to be effective. More often than not they will have a sneaking suspicion that they are not, because of the looks in the eyes of pupils.
These are either terrified or blank when confronted by the square root of a trinomial. It is not fun to imagine this concept and the blank stares means that there is more dangerous of students being the passive types resigned to the fate of failure. Interest is something that should always be present in this kind of teaching.
Many are finding out to their amazement that reviews of what folks learned through all the years they have been dealing with subject can turn out failures. This means that there are really things which are not digestable in most instances. The teaching is a failure when you are able to see this effect.
For most students, passing through the subjects here will be a thing they crave. Preferably by not taking too many exams or at least having the square root of the trinomial explained in more colorful and imagistic terms. There is a sense that math is a really alien subject for the human mind here.
The geniuses on this level are those who may not even be integrated in normal society. These are often geeks and nerds who will not know what to do with their lives without numbers and equations. This is thing that points to the fact that math may be more alien to most if not all students.