More than abstraction, it is the vagueness and ambiguity and the general feeling of handwaviness in the way mathematics is taught which perhaps is the bigger pr

More than abstraction, it is the vagueness and ambiguity and the general feeling of handwaviness in the way mathematics is taught which perhaps is the bigger problem. Take a concept of vector it is unclear from the way it is taught if it has an endpoint, that is if it is anchored to a point in space.