Kat, Obama did not teach at Harvard. He graduated from Harvard Law School and was President of the Harvard Law Review. He taught at the University of Chicago Law School.

From his resume,
1993-2004 Visiting Law and Government Fellow, then Senior Lecturer, in Constitutional Law at the University of Chicago Law School. Taught courses on the due process and equal protection areas of constitutional law, on voting rights, and on racism and law. Helped develop a casebook on voting rights.

Obama's resume is online here:

http://obamasresume.org/