Maurice J. Burke

On Simulation and the Teaching of Statistics

The use of simulation as an instructional tool can promote a deep conceptual understanding of statistics and lead to misunderstandings. Teachers need to be aware of the misconceptions that can arise as a result of simulation and carefully structure classroom activities so as to derive the benefits of this powerful instructional tool.

By Definition: An Examination of the Process of Defining in Mathematics

Our work as mathematics education researchers in a department of mathematical sciences rests upon a foundation of reflections on our own teaching practices and on the mathematical practices that our preservice mathematics teachers are expected to learn. In the nexus of these reflections sit issues relevant to the learning and teaching of mathematics, and the understanding of these issues requires sustained and systematic research that includes and goes beyond reflecting on practices. We present an example of a teaching episode focused on preparing secondary mathematics teachers to better understand mathematical definitions and the process of creating mathematical definitions. We then examine some historical developments in mathematical practice related to definitions and the defining process and relate these developments to challenges entailed in teaching practice. We conclude with examples of researchable areas embedded in these issues and comment on the impact of our work.

Twists on the Tower of Hanoi

The author considers the effects of two or more different colored disks on the number of necessary moves in this well-known puzzle. Counting and combinatorics as well as the binary number system are some of the mathematics involved.