How can I model a database structure to retain student information?

At a minimum, you would probably want to have at least two tables in your database, student and graded_assignment (or graded_test, if all grades are based on tests only).

student would have the student's name and id.

graded_assignment would have the student's ID (to tie the grade to a specific student), the total possible point value of the assignment, and the actual number of points earned by the student.

The total grade would be calculated through a query, something like:

SELECT s.name, s.id, SUM(g.points_earned) * 100 / SUM(g.points_possible) as percent_grade
  FROM student s
         INNER JOIN graded_assignment g ON (s.id = g.student_id)
 GROUP BY s.name, s.id
;

In reality, you would probably have a separate assignment table that would list information about each assignment/test/whatever, including the total points available, and the graded_assignment table would link back to that.

In all likelihood, you'd have a number of other tables. Students would be in one or more class; each class would have an instructor, who might teach multiple classes; assignments would be tied to a class. You might even have a scenario where an instructor teaches the same course to multiple classes, which might change what an assignment got tied to.

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.