Monsma has taught broadly in interdisciplinary humanities programs, and his main teaching interest is in core texts and core education. He has taught math and science courses, with an emphasis on these disciplines as liberal arts. He currently teaches courses in philosophy, political philosophy and literature. He has a special interest in developing courses for AUIS on the thinkers of the golden age of Islamic philosophy. His dissertation project explored the metaphysics of French philosopher René Descartes, and more generally the relations between science and religion, and their competing claims to set down a foundation for understanding the world. He has expertise in ancient Greek philosophy, early modern political philosophy and the novels of Evelyn Waugh. He is currently writing about Shakespeare's comedies. He heads the Core Program at AUIS.