In 1961, Beckman became Assistant Professor of Chemistry at Harvey Mudd College, where he also worked with Arthur Campbell on the NSF-funded CHEM Study program. He was also an active participant in Richard Popkin's "Science and Man's Goals" seminar, which re-kindled his earlier interests in philosophy. In the summer of 1964, Beckman attended an NSF course of study on the history and philosophy of science and mathematics, at the American University; and in the summer of 1967, he attended a course of study on contemporary issues in philosophy of science, at Stanford University, sponsored by the Council for Philosophical Studies. He spent his sabbatical year (1968-9) in London, England, as a visitor to the Department of Philosophy, Logic, and Scientific Methodology, The London School of Economics. In London, Beckman worked with Imre Lakatos and John Watkins.
While he was granted tenure and promoted to Associate Professor of Chemistry, in 1968, Beckman moved into the Humanities and Social Sciences Department, in fall 1970, as Associate Professor of Philosophy. In 1972, he was granted tenure in that department, and was promoted to Full Professor in 1979. He was voted Chair of the Faculty in 1984 but resigned after one year to become Chair of Humanities and Social Sciences, in 1985, serving as Chair until 1993. He resumed the Chair in the summer of 1998.
While his earliest interests in philosophy were centered on the philosophy of science, Beckman's teaching at Harvey Mudd led him into all areas of the history of philosophy and his research moved toward social issues and Continental philosophy. Today, he is strongly interested in the writings of Friedrich Nietzsche and Martin Heidegger. Aside from regularly teaching courses in the history of philosophy, he has developed courses on "Ethical Issues in Science and Engineering" and "Environmental Philosophy." Throughout the last decade, he has taught a course on "Indigenous People of the Western US," as a freshman seminar, and has become increasingly involved in Native American Studies. He has also been a leader, in the department, in applying the InterNet to teaching.
In 1999 Beckman helped gain college approval for two different multi-disciplinary programs, the Hixon Forum for Responsive Science and Engineering and the Center for Environmental Studies. At Commencement 2001, he received the Henry T. Mudd Prize for service to the college.