Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

Managers are often faulted for not managing performance; when performance issues surface, they first look to training as a possible solution. But without correctly identifying the cause of a performance problem, they can choose the wrong solution. The behavior engineering model (BEM) helps diagnose performance problems as well as engineer a…

A colleague was moving, and someone on the professional moving crew, upon hearing she was a mathematician, asked what happens when you repeatedly transfer water back and forth between two classes using a straw. The question is simple to solve if you alternate which glass you transfer from and to, but if more general patters are allowed, some…

The purpose of this article is to suggest an expansion of the conceptualizations and measurement of applied problem solving and, relatedly, coping. The author discusses the evolution of his programmatic line of research over the last 30 years to illustrate the changing landscape in applied problem solving and, to a lesser extent, in the coping…

Industry has indicated the desire for academic programs to produce graduates that are well-versed in collaborative problem solving and general project management concepts in addition to technical skills. The primary focus of a curriculum is typically centered on the technical training with minimal attention given to coalescing team and project…

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

Visualizing spatial material is a cornerstone of human problem solving, but human visualization capacity is sharply limited. To investigate the sources of this limit, we developed a new task to measure visualization accuracy for verbally-described spatial paths (similar to street directions), and implemented a computational process model to…

In responding to the research on conceptual change, this article attempts to make two points. First, scientific concepts are not possessed by individuals; rather, they are part of a culture's resources, which individuals learn to use for their own or for group purposes. Second, particular concepts are most effectively mastered when the learner is…

An elementary proof by contradiction of the Collatz Conjecture (CC) (also known as the "3X + 1" Conjecture), is presented. A modified form of the Collatz transformation is formulated, leading to the concept of a modified Collatz chain. A smallest counterexample N[subscript 0] is hypothesized; the existence of N[subscript 0] implies that…

Six tree shrews and 8 rats were tested for their ability to infer transitively in a spatial discrimination task. The apparatus was a semicircular radial-arm maze with 8 arms labeled A through H. In Experiment 1, the animals were first trained in sequence on 4 discriminations to enter 1 of the paired adjacent arms, AB, BC, CD, and DE, with right…

This paper presents research findings related to the "Dynamic Enhanced Evaluation of Problem Solving (DEEP)" (Spector & Koszalka, 2004) methodology for assessing how participants conceptualize ill-defined problems in biology using annotated concept maps. The methodology engages highly experienced (expert) and less experienced…

This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…

The purpose of this study was to examine how prevalent classroom cheating and plagiarizing has become and to inform educators on how to reduce these practices. Student cheating and plagiarism will be examined and analyzed to determine how severe the problem is, as well as finding potential reasons, methods, and solutions to the unethical practice.…

Research on human and animal behavior has long emphasized its hierarchical structure--the divisibility of ongoing behavior into discrete tasks, which are comprised of subtask sequences, which in turn are built of simple actions. The hierarchical structure of behavior has also been of enduring interest within neuroscience, where it has been widely…

The concept of critical thinking was featured in taxonomies a few decades ago. Critical thinking is a complex process that requires higher levels of cognitive skills in the processing of information. The teachers' perceptions of critical thinking among students influence their behaviors in the classroom. It has been found that teachers perceive…