The main goal of the teacher is to teach the student how to think. In order to be an effective teacher of thinking, the teacher must be present when the student attempts to think. It follows that the chief classroom activity should be students thinking, not teachers lecturing. Moreover, a given body of information can be conveyed more permanently and effectively to the students if they are actively engaged in thinking about it. Students can cooperate by asking questions, thinking out loud, and voicing mental corrections to the teacher's statements.

See NSSE for a report on how student engagement improves performance, especially especially for "those who come to college less well prepared academically or are from historically underrepresented racial and ethnic backgrounds".

Courses I have taught:

- Historical record
- Math course catalog, Spring, 2007
- Spring, 2007, Math 199 CHP, "The Art and Practice of Mathematics", MWF 10-10:50, Room 441, Altgeld Hall.
- Spring, 2007, Math 535 D1, General Topology, MWF 11:00-11:50, Room 159, Altgeld.
- Fall, 2004, Math 198, Freshman Seminar, The Art and Practice of Mathematics, Room 345 Altgeld Hall, time table.
- Spring, 2004: on half-pay sabbatical leave, not teaching.
- Fall, 2003, Math 248, Fundamental Mathematics (Advanced Composition).
- Fall, 2003, Math 401, Abstract Algebra, I.
- Spring, 2003, Math 416, Topics in Algebra, Algebraic K-theory.
- Fall, 2002, Math 407, Group Representation Theory.
- Fall, 2002, Math 198, Freshman Seminar, The Art And Practice of Mathematics.
- Spring, 2002, Math 130, Calculus and Analytic Geometry, II.
- Fall, 2001, Math 120, Calculus and Analytic Geometry, I.
- Fall, 2001, Math 416, Algebraic Geometry, II.
- Spring, 2001, Math 198, Freshman Seminar, The Art And Practice of Mathematics.
- Spring, 2001, Math 422, Algebraic Geometry.
- Spring, 2000, Honors Math 315, Linear Transformations and Matrices.
- Spring, 2000, Math 402, Abstract Algebra, II.
- Fall, 1999, Math 198, Freshman Seminar, The Art And Practice of Mathematics.
- Fall, 1999, Math 401, Abstract Algebra, I.
- Spring, 1999, Honors Math 315, Linear Transformations and Matrices.
- Spring, 1999, Math 431, Algebraic Topology.
- Spring, 1998, Math 321, Symbolic Algebra.
- Spring, 1998, Math 422, Algebraic Geometry.
- Fall, 1997, Math 120, Calculus and Analytic Geometry, I.