This note presents geometric and physical interpretations of the sufficient condition for a critical point to be a strict relative extremum: f[subscript xx]f[subscript yy] - f[superscript 2][subscript xy] greater than 0. The role of the double derivative f[subscript xy] in this inequality will be highlighted in these interpretations. (Contains 14…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

Everyone knows what makes a 3-4-5 triangle special, but how many know what makes a 4-5-6 triangle special? It is an integer-sided triangle in which one angle is twice another. It is enjoyable to search for these things, but for those who are impatient, this article derives explicit polynomial formulas that generate all of the basic examples of…

Reality--real life--is complex, more complex than can be imagined. The majority of our most pressing issues confronted in the management of organizations are overwhelmingly complex. I make the case for a systems design approach as a remedy. Examples introduced in this paper illuminate conceptual tools that advance how people transform their…

In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)

The aim of this paper is to present a simple way of establishing the general solution of the linear, second-order differential equation without using complex numbers.

A technique is presented, which is different from the well-known Ferrari's method, to solve a general quartic equation. Formulae for the four roots of quartic are derived. A numerical example verifies the formulae obtained.

Introduction: Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences. Method: We developed a teaching experiment with a group of…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Water chemistry is central to aquarium design, and it provides many potential applications for discussion in undergraduate chemistry and engineering courses. Marine aquaria and their life support systems feature many chemical processes. A life support system consists of the entire recirculation system, as well as the habitat tank and all ancillary…

This article discusses a classroom activity in which students in a small-sized (n = 4) Abstract Algebra class were able to discover some properties related to permutations and transpositions by physically moving from chair to chair according to suggested guidelines. During the lesson students were able to determine ways to write a permutation as a…

This article describes an activity for developing the notion of association between two quantitative variables. By exploring a collection of scatter plots, the authors propose a nonstandard "intuitive" measure of association; and by examining properties of this measure, they develop the more standard measure, Pearson's Correlation Coefficient. The…

In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justified. Also, in each of the three cases mentioned…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…