Math is about learning how mathematical language is applied to problems. She is incorrect about how the math is applied. Ergo she is wrong. Her intuition is

Math is about learning how mathematical language is applied to problems. She is incorrect about how the math is applied. Ergo she is wrong. Her intuition is on the right track. The only "whole" in this case is the entire set of students (or seats or whatever it is that is being talked about).