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.

External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which…

Reform movements in mathematics education advocate that mathematical argumentation play a central role in all classrooms. However, research shows that mathematics teachers at all grade level find it challenging to support argumentation in mathematics classrooms. This study examines the role of teachers' mathematical knowledge in teachers' support…

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…

Research shows that teachers influence students' attitudes towards; performance in; and perceptions of a subject. Hence, the need to improve the teaching and learning of many curricular subjects has been well documented for many years. This paper focusses on efforts made to develop competence among out-of-field teachers of mathematics and…

In the study reported on here I evaluated the alignment between the Annual National Assessment (ANA) and Trends in International Mathematics and Science Study (TIMSS). Theoretical perspectives were drawn from the Survey Enacted Curriculum (SEC), while quantitative correlational methods were used to determine the alignment between ANA and TIMSS…

In this paper, we derive the result of the classical gambler's ruin problem using elementary linear algebra. Moreover, the pedagogical advantage of the derivation is briefly discussed.

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community's social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic,…

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,…

This study measures the mathematical abilities high school graduates' in Bahrain. Mathematical abilities encompass conceptual understanding, procedural knowledge and problem-solving skills in the five content domains which are Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. While procedural understanding…

Data science has maintained its popularity for about 20 years. This study adopts a bottom-up approach to understand what data science is by analyzing the descriptions of courses offered by the data science programs in the United States. Through topic modeling, 14 topics are identified from the current curricula of 56 data science programs. These…