The gap between secondary school and university mathematics

It seems self-evident that there is a significant gap between secondary school and university mathematics, even though the gap may take different forms, which vary with different education systems in different places and at different times. This paper attempts to capture some common forms of this gap, and in particular, it discusses some core factors that are directly related to the nature of mathematics. Further, it also attempts to find ways to bridge the gap more easily and surely for students.