Discusses the probability of seeing a tire explode or disintegrate while traveling down the highway. Suggests that a person observing 10 hours a day would see a failure on the average of once every 300 years. (MVL)

Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)

Compared children's performance on initial-unknown and final-unknown problems involving the addition or subtraction of a single item. Found that although 4-year olds responded in a directionally appropriate way to the final-unknown problems but not to the corresponding initial-unknown ones, 5-year olds were able to respond appropriately to both.…

Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…

Discussed is the difficulty that students encounter when attempting to distinguish between independent and dependent variables, not only in the mathematics classroom, but also when devising and labeling graphs resulting from chemistry or physics experiments. (JJK)

Why children under 10 years do not use their mathematics knowledge to build a shortcut strategy to solve inversion problems was studied with 88 elementary school students in Munich (Germany). Most could use the shortcut but did so only when it did not compete with a more familiar strategy. (SLD)

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

The discrete mathematics topics of trees and computational complexity are implemented in a simple reliability program which illustrates the process advantages of the PASCAL programing language. The discussion focuses on the impact that reliability research can provide in assessment of the risks found in complex technological ventures. (Author/JJK)

Discusses, through quotes about mathematical understanding from mathematicians, the experience of understanding, a nonobjectivist theory of meaning, the origins of mathematical objects, and reification as the birth of metaphor.(Contains 35 references.) (MKR)

Describes classroom activities that integrate math concepts with environmental science, demography, and language arts. The lesson helps students understand the competition between natural resources and the law of supply and demand. (HTH)

The Spirograph, a device used for artwork and designs, is utilized to explore the mathematical topics of symmetry, ratio, divisibility, and modular arithmetic. A worksheet for each topic is included along with pedagogic information and extensions and also the answer key. (JJK)

Described are ways that specific concepts from abstract algebra can be programed using the software package features of the Ada Programming Language, which is the primary language of the Department of Defense. Included are typical programs with their respective outputs. (JJK)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

Outlines an epistemological conception that relates formal aspects of mathematical proof to its pragmatic dimensions. In addition to applications, makes use of several concepts from analytical philosophy to present a view of proof best categorized as dialectical. Implications for teaching are discussed. (Contains 30 references.) (Author/MDH)

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)