Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. We determine Fay's optimal path minimizing segment length, and thus maximizing the number of times they meet…

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

This article focuses on the role of history in shaping learning interactions in a high school mathematics class, in which we argue that students participate in two key activity systems: Learning mathematics and doing school. Within the context of these two activity systems, we highlight the nature of "sociogenesis," the patterns of shift…

This study tested a model that links stress, social support, problem-focused coping, and well-being. First, it looks at how high support significantly moderated the association between stress and well-being. Next, the students' problem-focused coping was seen as mediating this moderated association. Finally, a 3-way interaction of stress, social…

This article provides an account of self-managed action learning (SMAL), where it came from and how it has been implemented in practice. Self-managed action learning offers a way of realising action learning without the continuing presence of a set advisor in set meetings to facilitate the process. It enables participants to manage and facilitate…

This study investigates the common difficulties that students in introductory physics experience when solving problems involving integration in the context of electricity. We conducted teaching-learning interviews with 15 students in a second-semester calculus-based introductory physics course on several problems involving integration. We found…

This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

Conceptual models are useful for facing the challenges of environmental sciences curriculum and course developers and students. These challenges are inherent to the interdisciplinary and problem-oriented character of environmental sciences curricula. In this article, we review the merits of conceptual models in facing these challenges. These…

Previous research has consistently shown that the left parietal cortex is critical for numerical processing, but the role of the right parietal lobe has been much less clear. This study used the intraoperative cortical electrical stimulation approach to investigate neural dissociation in the right parietal cortex for subtraction and…

A review of the literature reveals that although the teaching of critical thinking skills is a significant aim of post-secondary pedagogy, much ambiguity exists regarding the topic. In fact, due to the lack of faculty familiarity with the concept compounded by student resistance to put forth the intellectual labor to take charge of their own…

Solving real-world problems is an effective learning activity that promotes meaningful learning in formal educational settings. Problems can be classified as being either well structured or ill structured. Internet information search approaches have an influential role to play in the successful performance of problem solving. A better…

This study investigates what pupils aged 10-12 can learn from working with robots, assuming that understanding robotics is a sign of technological literacy. We conducted cognitive and conceptual analysis to develop a frame of reference for determining pupils' understanding of robotics. Four perspectives were distinguished with increasing…

Children are naturally curious and want to make sense of their world. To implement mathematical tasks that nurture children's desire to reason, it is valuable for teachers to have experienced for themselves comparable tasks and learning environments (Ball and Bass 2000). In this article, the author describes three strategies to facilitate…

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between…

The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…