How can I model a database structure to retain student information?
You need to normalize the design. A column can, under sane circumstances, only hold a datum (singular).

So something like this 

CREATE TABLE student (
  studentid int AUTO_INCREMENT PRIMARY KEY
);
CREATE TABLE class (
  classid   int AUTO_INCREMENT PRIMARY KEY,
  classname text
);
CREATE TABLE student_class_grade (
  classid   int REFERENCES class,
  studentid int REFERENCES student,
  grade     float
);


This is super simple, so each student has a studentid, each class has a classid, and you can put as many entries as needed for stupid_class_grade. This doesn't account for the extra complexity needed for weighing tests and homework differently in the same class.