2012–present: Professor, University of Northern Colorado
2007–2012: Associate Professor, University of Northern Colorado
2001–2007: Assistant Professor, University of Northern Colorado
1994–2001: Graduate Student/Teaching Assistant, Cornell University
Research/Areas of Interest
Reasoning with Geometric Diagrams - It has long been assumed in mathematical communities that diagrams can be properly
used only as aids to human intuition which have no place in formal proofs, reducing
diagrams to second-class citizens of the mathematical world. My research aims to
show that diagrams can be used rigorously and fruitfully in formal mathematics, and,
indeed, that the formal proofs that one gets using diagrams are more understandable
and correspond better to normal informal proofs (of the kind that one finds in Euclid's
Elements, for example) than traditional linguistic formal proofs. You can find some of my
The Teaching and Learning of Mathematics using Inquiry-Based Methods - Most of my teaching is done using inquiry-based methods, and I have had several
publications and presentations in this area. You can find some of them here.
Miller, Nathaniel, “Teaching Inquiry to High School Teachers Through the Use of Mathematics
Action Research Projects,” Primus, to appear.
Miller, Nathaniel, “The Philosophical and Pedagogical Implications of a Computerized
Diagrammatic System for Euclidean Geometry” in Gold, Bonnie, ed., Using the Philosophy of Mathematics in Teaching Mathematics, MAA Notes Series, to appear.
Miller, Nathaniel, “Teaching Writing and Proof-Writing Together,” in Schwell, Steurer,
and Vasquez, eds., Beyond Lecture: Resources and Pedagogical Techniques to Improve Student Proof-Writing
Across the Curriculum, MAA Notes Series, Vol. 85. MAA Press, Washington, DC, 2016.
Miller, Nathaniel, and Nathan Wakefield, “A Mentoring Program for Inquiry-Based Teaching
in a College Geometry Class,” International Journal of Education in Mathematics, Science and Technology, Volume 2, Issue 4, 2014, p. 266–272.