Design, including instructional design, is one of most complex and ill-structured kinds of problem solving. Historically, instructional design has been conceptualized as a linear set of phases (e.g., analysis, design, development, implementation, evaluation) that a designer progresses through. Silber (2007) has provided an alternative perspective…

Given the centrality of leadership for school success, leader morale and effectiveness in tough times can't be overemphasized. The authors' work examined how principals and superintendents deal with and are affected by a significant economic downturn. They surveyed 93 principals from one large upper-Midwest metropolitan area and 100…

In the natural world, learning emerges from the joy of play, experimentation, and inquiry as part of everyday life. However, this kind of informal learning is often difficult to integrate within structured educational curricula. This report describes an educational program that embeds naturalistic learning into formal high school, college, and…

The key questions are: is it true that persons with Down's syndrome can study mathematics only at a very elementary level? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? Is the use of a calculator recommended? Is…

Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…

An exact solution is found for the electrostatic potential of a family of conducting charged toroids. The toroids are characterized by two lengths "a" and "b", with "a" greater than or equal to "2b". They are closed, with no hole in the "doughnut". The results are obtained by considering the potential of two equal charges, displaced from the…

This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…

Many exercises in mathematical induction require the student to prove a divisibility property of a function of the integers. Such problems are generally presented as being independent of each other. However, many of these problems can be presented in terms of difference equations, and the theory of difference equations can be used to provide a…

In 1992, Klamkin and Liu proved a very general result in the Extended Euclidean Plane that contains the theorems of Ceva and Menelaus as special cases. In this article, we extend the Klamkin and Liu result to projective planes "PG"(2, F) where F is a field. (Contains 2 figures.)

In these days of financial turmoil, there is greater interest in depositing one's money in the bank--at least one might hope for greater interest. Banks and various trusts pay compound interest at regular intervals: this means that interest is paid not only on the original sum deposited, but also on previous interest payments. This article…

The didactic function of business games is often seen only in the development of sociocommunicative competences and general problem-solving strategies. An equally important aspect of business games lies in the acquirement of technical and problem-oriented knowledge, which is the focus of this article. Moreover, this knowledge dimension is further…

After years at the periphery of the social sciences, simulation is now emerging as an important and widely used tool for understanding social phenomena. Through simulation, researchers can identify causal effects, specify critical parameter estimates, and clarify the state of the art with respect to what is understood about how processes evolve…

This article describes how to multiply binomials so that middle school students produce the equivalence (a + b)[superscript 2] = a[superscript 2] + 2ab + b[superscript 2] after reasoning about and representing problems. First, a two-dimensional array representation is used so that students can become comfortable with multiplication embedded in…

This article describes an instructional model that science teachers can use to promote and support student engagement in scientific argumentation. This model is called the evaluate-alternatives instructional model and it is grounded in current research on argumentation in science education (e.g., Berland and Reiser 2009; McNeill and Krajcik 2006;…

Parent volunteers can be an important asset to a well-run school library. Parent volunteers are that extra pair of hands and extra eyes. Monotonous and even tedious tasks can be accomplished quickly by people searching for ways to spend a little time with adult conversation while providing a benefit to their children. And eventually they can…