At the heart of the recent focus on mathematics has been an increased emphasis on developing students' "number sense." Ironically, although growing as a force in the education literature, number sense has not been clearly defined for teachers. Teachers need specific support in understanding how to develop number sense in students, to…

Describes a theoretical development to explain the shadow patterns of an object exposed to an extended light source while held at varying distances from a screen. The theoretical model is found to be accurate in comparison with experimental results. (MDH)

Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

Discusses the rate of fall of a wooden beam or a chimney by examining the fall of a highway lamp pole when it is sheered off at its base upon impact by a vehicle. Provides the mathematical formulas to explain and an experiment to illustrate the phenomenon. (MDH)

Presents an activity in which students construct model hot air balloons to introduce the concepts of convection current, the principles of Charles' gas law, and three-dimensional geometric shapes. Provides construction and launching instructions. (MDH)

Discusses the early recognition of chaos as seen in Poincar's work solving dynamical problems. Proposes five examples from which an inventory of the manifestation of chaos can be inferred. Discusses some instructional consequences of the development of ideas of chaos. (MDH)