A simple mathematical formulation of Mach's principle is given based on a century of investigation into inertia, and used to check the results of Newton's famous bucket experiment.

In this paper we consider the main properties of cylindrical lenses and propose several demonstrational experiments that can be performed with them. Specifically we use simple glasses full of water to demonstrate some basic geometrical optics principles and phenomena. We also present some less standard experiments that can be performed with such…

Two practical activities are described, which aim to support critical thinking about statistics as they concern multiple outcomes testing. Formulae are presented in Microsoft Excel spreadsheets, which are used to calculate the inflation of error associated with the quantity of tests performed. This is followed by a decision-making exercise, where…

The article discusses three empirical examples of Computer Algebra System (CAS) use in a Danish upper secondary school mathematics class that had experienced a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students' mathematical…

This study investigated 11 pre-service middle school teachers' solution strategies for exploring their knowledge of fraction division interpretations. Each participant solved six fraction division problems. The problems were organized into two sets: symbolic problems (involving numbers only) and contextual problems (involving measurement…

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the case "g"?=?2) of the general term of the sequence factorial of "g"-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of any…

The purpose of this paper is to investigate a novice primary teacher's mathematical knowledge in teaching on area measurement. Data were collected from a novice primary teacher of fourteen students in a primary school located in Ankara, Turkey using field notes, video recordings of lessons, and audio recordings of interviews before and after her…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

Calibration of new items online has been an important topic in item replenishment for multidimensional computerized adaptive testing (MCAT). Several online calibration methods have been proposed for MCAT, such as multidimensional "one expectation-maximization (EM) cycle" (M-OEM) and multidimensional "multiple EM cycles"…

Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…

The general public consumes financial products such as loans that are administered in the realm of nominal and effective interest rates. It is debatable if most consumers really understand how these rates function. This article explores the conceptions that student teachers have about nominal and effective interest rates. The APOS theory…

Measurement in geometry is one of the key areas of school mathematics, however, pupils make serious mistakes when solving problems involving measurement and hold misconceptions. This article focuses on the possible links between lower secondary pupils' (n = 870) success in solving non-measurement tasks and calculations tasks on area and volume and…

This quasi-treatment study, using a non-equivalent group design, explored how a set of animations related to various concepts in algebra impacted students' ability to learn as measured by changes in quiz and test scores. The concepts that were investigated were addition and subtraction of rational expressions, solving equations involving rational…