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.

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

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…

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…

Two experiments were designed to investigate the developmental trajectory of children's probability approximation abilities. In Experiment 1, results revealed 6- and 7-year-old children's (N = 48) probability judgments improve with age and become more accurate as the distance between two ratios increases. Experiment 2 replicated these findings…

Knowing what kinds of patterns are easy for children to recognize early in their kindergarten year, and what kinds are difficult, can be a useful guide for patterning instruction. Hence, the ability of children to recognize complex patterns early in their kindergarten year was assessed in two experiments. One experiment showed that the children…

Family physicians can communicate to patients the risk of adverse drug reactions using words or numbers, and this format has important implications for patients' ability to make informed decisions. The present study (a) assessed which formats family physicians preferred to communicate the risk of a given side effect, (b) tested whether the…

This review covers the core concepts and design decisions of TensorFlow. TensorFlow, originally created by researchers at Google, is the most popular one among the plethora of deep learning libraries. In the field of deep learning, neural networks have achieved tremendous success and gained wide popularity in various areas. This family of models…

In the present study, we evaluated the number of attempts required to master specific subskills for working with whole and rational numbers among students at risk for math difficulties. Participants included a subset of students in grades four through eight receiving supplemental math support. Mastery--defined as 85% correct on short tests--was…

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…

Most literature related to Benford's Law discusses what the law can be used for and how it works but fails to address effective methods and procedures for teaching the law to students. This article examines existing information resources to determine the most effective methods and procedures used to explain this Law to those who have no experience…

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…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

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…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…