In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and…

Most often radio dials of analogue radios are not uniformly graded; the frequencies are cramped on the left side or on the right side. This makes tuning more difficult. Why are dials made this way? We shall see here that simple calculus can help understand this problem and solve it. (Contains 7 figures.)

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

How can statistics clearly be mathematical and yet distinct from mathematics? The answer lies in the reality that statistics is both an art and a science, and both aspects are important for teaching and learning statistics. Statistics is a mathematical science in that it applies mathematical theories and techniques. Mathematics provides the…

The properties of a function such as limit, continuity, derivative, growth, or concavity can be determined more easily from its graph than by doing any algebraic operation. For this reason, it is important for students of mathematics to interpret some of the properties of a function from its graph. In this study, we investigated the competence of…

How does classroom interaction support students' apprenticeship into the ways of speaking, writing, and diagramming that constitute the practice of mathematics? We address this problem through an interpretative analysis of a whole-group conversation about alternative ways of solving a problem involving percent discounts that occurred in a sixth…

In the world of teaching with technology, there are constant challenges. Often that leads to tension between the teachers who are using technology in the classroom and the IT techs who are charged with installing and setting up new computers, ordering new equipment, making sure software programs are up to date, and securing the system. IT techs…

Genetics is a unifying theme of biology that poses a major challenge for students across a wide range of post-secondary institutions, because it entails complex problem solving. This article reports a new intelligent learning environment called the Genetics Cognitive Tutor, which supports genetics problem solving. The tutor presents complex,…

Radiation pressure is an important topic within a standard physics course (see, in particular, Refs. 1 and 2). The physics of radiation pressure is described, the magnitude of it is derived, both for the case of a perfectly absorbing surface and of a perfect reflector, and various applications of this interesting effect are discussed, such as…

Linear planning and decision-making models assume a level of predictability that is uncommon today. Such models inadequately address the complex variables found in higher education. When academic organizations adopt paired-down business strategies, they restrict their own vision. They fail to harness emerging opportunities or learn from their own…

The article provides a review of recent research on insight problem-solving performance. We discuss what insight problems are, the different types of classic and newer insight problems, and how we can classify them. We also explain some of the other aspects that affect insight performance, such as hints, analogs, training, thinking aloud, and…

Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

This article presents an English for Specific Purposes (ESP) task developed for teaching aeronautical engineering students. The task Design-Build-Write rests on the assumption that engineering students are skilled at mathematical reasoning, problem solving, drawing and constructing. In Gardner's 1983 Multiple Intelligences (MI) theory, these…

The present study, located in the socio-cultural tradition of research in developmental psychology, uses experimental tasks, adapted from the groundbreaking Lurian study (Luria, 1979, 1976) to investigate South African children's acquisition and development of thinking and concepts -- involving classification and generalisation, and how these…

This dissertation is a case study focused on the question, "What are students' attitudes toward school mathematics and toward nonroutine math problems and mathematical games?" It addresses the definitions of some of those terms and then moves on to a literature review that suggests that some change in the curriculum may be needed. In an attempt to…