"*These 36 credits must include courses in single and multivariable calculus, linear algebra, and at least two of the following four more advanced subjects: abstract and/or applied algebra; analysis or advanced calculus; geometry, including non-Euclidean geometry; probability and/or statistics. "
Real Analysis and Abstract Algebra are core introductory math major courses, not advanced courses. If you cannot do proofs, then you are still doing arithmetic. A degree without significant coursework beyond these classes is not a math degree. Its engineering mathematics of some sort.
And almost all of the MAT curriculum deals with non-abstract math.
A mathy kid will be ready to move beyond applied math prior to HS and your typical MAT curriculum will not equip the teacher to do that.
This is why we have reports of teachers dropping proofs from Geometry and then omitting critical stuff like right triangles as well. They cannot teach the abstract stuff and then are not literate enough in applied math to know what is critical.
