... pointsin these courses for pre-service teachers, the instructor should take a fewminutes to explain some of the (real) core applications of mathematics, soas to break the mind-set that mathematics ... of them.” If either of these were ever true, they are certainlynot true today, as mathematics has grown in breadth over the centuries. Itis impossible to “define” mathematics today. About the ... in the four course sequence that we recommend.This discussion reflects the mathematics that students need to know, and consequently the core mathematics that pre-service K - 8 teachers must know, ...