Well, usually I’d defer to a math professor, who has likely gotten dozens of students into graduate school and may even have some graduate students of his own depending on the kind of school your son attends. Your son may want to talk to other math professors at his college if he’s not sure if this is a matter of opinion vs. an actual requirement.
I’m not in math - and math is a bit different because the foundational knowledge required to do research is so much higher than in other fields - but generally speaking, it’s usually in the middle. Most U.S. college students looking to go to graduate school should take a wide range of foundational coursework in their area, but by the time they get to their junior or senior year, should be able to identify a specific area in which they are interested and concentrate a certain number of classes (3-5) in that area.
@xraymancs and @boneh3ad may be able to offer more guidance here.