Don't store multiple values in the student_id field, as having exactly one value for each row and column intersection is a requirement of First Normal Form. This is a Good Thing for many reasons, but an obvious one is that it resolves having to deal with cases like having a student_id of "1245".
Instead, it would be much better to have a separate table for storing the student IDs associated with the records in this table. For example (you'd want to add proper constraints to this table definition as well),
CREATE TABLE mytable_student_id (
mytable_id INTEGER,
student_id INTEGER
);
And then you could query using a join:
SELECT * FROM mytable JOIN mytable_student_id
ON (mytable.id=mytable_student_id.mytable_id) WHERE mytable_student_id.student_id = 245
Note that since you didn't post any schema details regarding your original table other than that it contains a student_id field, I'm calling it mytable for the purpose of this example (and assuming it has a primary key field called id -- having a primary key is another requirement of 1NF).