Nat Miller

Faculty

Professor and M.A. Program Coordinator

Email nathaniel.miller@unco.edu
Phone (970) 351-2297
Location Ross Hall 2210D

Education

  • 2001, Ph.D. (Mathematics), Cornell University
  • 1999, M.S. (Computer Science), Cornell University
  • 1994, B.A. (Mathematics), Princeton University

Professional Experience & Affiliations

  • 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 Expertise & Interests

  • 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’sElements, for example) than traditional linguistic formal proofs. You can find some of my work here.
  • 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.

Publications

  • 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.