Quarter system classes will not cover the same material in less time. They do allow students to have a more varied with less of a subject. Your D can do both majors. Many math departments will work for her because she isn’t heading to a math PhD. She needs to look closely at what is offered in the teacher education path. A friend’s son went to Emory, originally a Psych major, switched to education. But- no student teaching and unqualified to teach. She may do best in a setting with many other math majors that are heading in many different directions with the major. Part of her decision will be to choose a stellar math program school to be exposed to areas of math she may find interesting even if she never uses that specific knowledge in a classroom. Perhaps being among a bunch of highly intelligent math nerds will help her understand her students who one day go the math route and their thinking processes. I know my good math teacher had students much better than he was in math and was able to understand their reasoning. Like every occupation, math teaching will have its boring routine with most students punctuated by the few with interest and insights.