This study examined preservice teachers' reactions to and reflections on a set of five animations as representations of algebra instruction. The results showed that most comments in the preservice teachers' reflections were related to: (a) student learning and motivation, or (b) the classroom and instructional environment. Few comments in the…

The importance of student understanding of the concept of place value cannot be underestimated. Place value is a "gate keeper" in developing mathematical understanding. The purpose of this study was to examine and develop a teacher-made test of place value knowledge. The questions were developed using the progressions from the Number…

A small-group, web-interactive approach to teaching precalculus concepts was investigated. Following an online pretest, 3 participants were given a brief (15 min) presentation on the details of reciprocal math relations and how they operate on the coordinate axes. During baseline, participants were tested regarding their ability to construct…

Although there has been some attention in the literature to such issues as students' attitudes toward statistics, instructors are still constantly faced with the challenge to engage students; understand their perceptions, motivations, and interests; and deal with their reluctance and negative attitudes toward the field of statistics. The purpose…

It is argued that the discourse currently regulating early years mathematical development in the UK and elsewhere is "producing its own truths" in an unhelpfully narrowing way, restricting the objects, imagery, and symbols involved to those arising within "everyday" or "realistic" situations, and producing an…

The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…

The Freundlich adsorption isotherm is a useful description of adsorption phenomena. It is frequently presented as an empirical equation with little theoretical basis. In fact, a variety of derivations exist. Here a new derivation is presented using the concepts of fractal reaction kinetics. This derivation provides an alternative basis for…

The traveler's dilemma is a generalization of the prisoner's dilemma which shows clearly a paradox of game theory. In the traveler's dilemma, the strategy chosen by analysis and theory seems obviously wrong intuitively. Here we develop a measure of evolutionary stability and show that the evolutionarily stable equilibrium is in some sense not very…

The boundary between convergent and divergent series is systematically explored through sums of iterated logarithms.

Several jeeps are poised at base camp on the edge of a desert aiming to escort one of them as far as possible into the desert, while the others return to camp. They all have full tanks of gas and share their fuel to maximize penetration. In a friendly desert it is best to leave caches of fuel along the way to help returning jeeps. We solve the…

The "N" queens problem is a classic puzzle. It asks for an arrangement of "N" mutually non-attacking queens on an "N" x "N" chessboard. We discuss a recent variation called the "N" + "k" queens problem, where pawns are added to the chessboard to allow a greater number of non-attacking queens to be placed on it. We describe some of what is known…

In this article, the author proves two conjectures of Thomas Dence.

Numeracy--that is, how facile people are with mathematical concepts and their applications--is gaining importance in medical decision making and risk communication. This article proposes six critical functions of health numeracy. These functions are integrated into a theoretical framework on health numeracy that has implications for risk…

The author has worked for three days on a range of mathematical tasks in order to gain a deeper understanding of the role of notation in mathematics education. The general conclusions were that while mathematical notation can be powerful it can also be obstructive. In this article, the author explores the importance on notation in supporting…

We describe a simple photographic assignment appropriate for an abstract algebra (or other) course. Students take digital pictures around campus of various examples of symmetry. They then classify these pictures according to which of the 17 plane symmetry groups they belong. (Contains 2 figures.)