The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed,…

Several myths have grown up around problem solving as a result of the manner in which problem solving has traditionally been taught in schools. These myths are harmful to children, they affect curriculum decision of teachers, distort discussions about problem solving and undermine the mathematics reform movement in general.

A committee composed of students, parents, teachers, administrators, college/university persons, and representatives from business and industry carefully studied the mathematics curriculum in North Carolina public schools and formulated the recommendations contained in this report. It contains ideas, suggestions, and information resulting from…

Based on the premise that psychology can be an invaluable tool to mathematics educators, this book highlights how informal mathematics develops, how children construct their view of school arithmetic, and how mathematical thinking operates. The ideas offered are intended to assist teachers in making informed decisions concerning mathematics…

Reports a case study to evaluate whether basic concepts of fractal geometry are teachable to elementary school children and to determine the effectiveness of having an elementary school student present a lesson to inservice and preservice teachers. Concludes that simple concepts of fractal geometry appear appropriate for the elementary school…

The purpose of this study was to describe students' attempts to solve nonroutine math problems and to explore possible correlates of their performance. The focus of this study was on inattended (i.e., intentionally avoided) dimensions that have been underrepresented in the literature, including attitudes, interests, values, aesthetics,…

Research examining instruction in geometry and standardized tests suggests that students have difficulty grasping geometry concepts and developing problem solving skills. The purpose of this study was to examine the relationship between the use of inquiry-based strategies in a geometry class and achievement on the end of course test (EOCT) and to…

In recent times, science education researchers have identified a lot of instruments for evaluating conceptual understanding as well as students' attitudes and beliefs about physics; unfortunately however, there are no broad based evaluation instruments in the field of problem-solving in physics. This missing tool is an indication of the complexity…

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12-13 years old. In this study we identified different types of approaches to…

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we…

Recent research has provided evidence that students' computer use at home is positively associated with their performance at school. However, most of the previous studies have failed to take into account the multiple determination of school performance and, in addition, to explain why using computers at home should benefit students' academic…

Reversing is the notion of thinking or working in reverse. Computer science textbooks and tutors recognize it primarily in the form of recursion. However, recursion is only one form of reversing. Reversing appears in the computer science curriculum in many other forms, at various intellectual levels, in a variety of fundamental courses. As such,…

Despite its importance in mathematical problem solving, verification receives rather little attention by the students in classrooms, especially at the primary school level. Under the hypotheses that (a) non-standard tasks create a feeling of uncertainty that stimulates the students to proceed to verification processes and (b) computational…

We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…

This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event-locked procedure is described for dealing…