Lois Kailhofer
Associate Professor | Milwaukee School of Engineering
Milwaukee, WI, UNITED STATES
Lois Kailhofer is currently interested in cognitive research related to teaching and learning.
Education, Licensure and Certification (3)
Ph.D.: University of Wisconsin-Milwaukee 1999
Dissertation title: A Partial Classification of Inverse Limit Spaces of Tent Maps with Periodic Critical Points
M.S.: University of Wisconsin-Milwaukee 1992
B.S.: Mathematics and Physics, University of Wisconsin-Madison 1989
Biography
Dr. Lois Kailhofer received her undergraduate degree in math and physics from the University of Wisconsin – Madison. She received her Masters and Ph.D. in mathematics from the University of Wisconsin – Milwaukee. Her Ph.D. work was in dynamical systems. She currently teaches the math education courses for future elementary and middle school teachers. She also teaches geometry and algebra. She is currently interested in cognitive research related to teaching and learning.
Areas of Expertise (5)
Symbolic Dynamics
Dynamical Systems and Geometric Topology
Cognitive Theory
Pedagogical Practices
Topological Dynamics
Affiliations (3)
- National Council of Teachers of Mathematics : Member
- Wisconsin Mathematics Council : Member
- American Association of University Professors : Member
Selected Publications (4)
Assessing Student Learning Outcomes Across a Curriculum
Assessing Competence in Professional Performance across Disciplines and Professions2016 Disciplinary and professional competence in postsecondary education is made up of complex sets of constructs and role performances that differ markedly across the disciplines and professions. These often defy definition as learning outcomes because they are multidimensional and holistic.
On the classification of inverse limits of tent maps
Fundamenta Mathematicae2005 Let fs and ft be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of fs and ft are periodic and the inverse limit spaces (I,fs) and (I,ft) are homeomorphic, then s=t. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.
A classification of inverse limit spaces of tent maps with periodic critical points
Fundamenta Mathematicae2003 We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps fa, fb with periodic critical points, we show that the inverse limit spaces (
A partial classification of inverse limit spaces of tent maps with periodic critical points
Topology and its Applications2002 We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps fa, fb with periodic turning points of the same period, we use the finite kneading sequences of the maps to obtain a necessary condition for the inverse limit spaces and to be homeomorphic.
