Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…

This paper focuses on an inferential view on introducing new concepts in mathematics classrooms. A theoretical framework is presented which helps to analyse and reflect on the processes of teaching and learning mathematical concepts. The framework is based on the philosophies by Ludwig Wittgenstein and Robert Brandom. Wittgenstein's language-game…

Although problem-based learning (PBL) has many advantages, it often fails to connect to the real world outside the classroom. The integration with the laboratory setting and the use of information and communication technologies (ICTs) have been proposed to address this deficiency. Multi-user virtual environments (MUVEs) like Second Life (SL) are…

There is no doubt that a lesson plan is a necessary product of Lesson Study. However, the collaborative work among teachers that goes into creating that lesson plan is largely under-appreciated by non-Japanese adopters of Lesson Study, possibly because the effort involved is invisible to outsiders, with our attention going to its most visible…

As education has turned towards technology to provide academic support, the incidence of e-tutoring has grown due to decreasing educational budgets and as a potential remedy for the generational digital divide. However, many service-learning e-tutoring studies have focused on tutees' academic achievement and tutors' cognitive development rather…

To help students master challenging, threshold concepts in physiology, I used the flipped learning model in a human anatomy and physiology course with very encouraging results in terms of student motivation, preparedness, engagement, and performance. The flipped learning model was enhanced by pre-training and formative assessments that provided…

In this article, the authors describe an inexpensive and simple way to make students intuitively experience the probabilistic nature and nonorientated motion of diffusing particles. This understanding allows students to realize why diffusion works so well over short distances and becomes increasingly and rapidly less effective as the distances…

Students who otherwise seem unreachable through traditional approaches to algebra require some alternative teaching methods. So do teachers who seek to add elements of freshness and innovation to their classrooms or who simply appreciate variety. This article offers some unconventional techniques for teaching a few conventional algebra topics.…

This paper discusses some difficulties in teaching introductory courses to programming, paying particular attention to their mathematical nature. We consider some aspects, which have not been commented in detail in textbooks and often neglected by course outlines and schedules. Some of these are constructing complex conditions, exceeding array…

Problem-solving skills are imperative to a child's growth and success across multiple environments, including general and special education. Problem solving is comprised of: (a) attention to the critical aspects of a problem, (b) generation of solution(s) to solve the problem, (c) application of a solution(s) to the identified problem, and…

Gestures are profoundly integrated into our communication. This study focuses on the impact that gestures have in a mathematical setting, specifically in an undergraduate calculus workshop. There was strong correlation between diagramming and the two types of gestures identified in this study (i.e., dynamic and static gestures). Dynamic and static…

This article discusses an instructional strategy which explores eventual similarities and/or analogies between familiar problems and more sophisticated systems. In this context, the Atwood's machine problem is used to introduce students to more complex problems involving ropes and chains. The methodology proposed helps students to develop the…

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…

The Solution Circle (SC) approach is a flexible tool which encourages participants to maintain a positive, creative approach to problem-solving. This project focussed on the introduction of this approach to staff in a primary and a secondary school. The rationale was to implement a problem-solving/discussion tool that would allow staff to utilise…