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…

The topics of decimals and polygons were taught to two classes by using challenging tasks, rather than the more conventional textbook approach. Students were given a pre-test and a post-test. A comparison between the two classes on the pre- and post-test was made. Prior to teaching through challenging tasks, students were surveyed about their…

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)

PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

In this study we attempted to highlight the pedagogical role of activities to familiarize pre-schoolers with the measurement processes of container capacity. The sample of the study consisted of 20 subjects aged five-six, all coming from two Greek state kindergartens of the same area, bearing the same middle socioeconomic background. The research…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

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…