The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

We provide tools for identification and exploration of data with very large variability having power law tails. Such data describe extreme features of processes such as fire losses, flood, drought, financial gain/loss, hurricanes, population of cities, among others. Prediction and quantification of extreme events are at the forefront of the…

The goal of the paper is to pay attention to some important techniques and approaches including adequate designations as a tool for unambiguous understanding and a key to success in solving problems, vivid visual images as a mnemonic techniques, and special formulas as a universal tool for solving typical problems, when teaching medical students…

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this…

Frequent forced switching between tasks has been shown to reduce switch costs and increase voluntary switch rates. So far, however, the boundary conditions of the influence of forced task switching on voluntary task switching are unknown. Thus, the present study was aimed to test different aspects of generalizability (across items, tasks, and…

The current study was conducted with the goal of helping to address the research gap of improving preservice teachers' pedagogical knowledge about probability by investigating how preservice teachers explored concepts of probability during aleatoric music composition, as well as their contemplation process during follow-up reflections focused on…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Preparing for the future during ongoing activities is an essential skill. Yet it is currently unclear to what extent we can prepare for the future in parallel with another task. In two experiments, we investigated how characteristics of a present task influenced whether and when participants prepared for the future, as well as its usefulness. We…

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs' level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex,…