There are a variety of technologies that are increasingly being integrated into mathematics classrooms for their potential to increase student engagement, motivation, understanding, and achievement. YouTube can be an especially useful technology for students to create, share and interact with others, and learn more about mathematics. However, the…

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…

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

Recent studies have argued a shift of thinking about engineering practice from a linear conception to a system understanding. The complexity of engineering practice has been thought of as the root of challenges for engineers. Moreover, creativity has been emphasised as one key capability that engineering students should master. This paper aims to…

"Sustainability" is a very general term and the question arises how to specify it within daily laboratory work. In this regard, appropriate metrics could support a socially acceptable, ecological and economic product development. The application of metrics for sustainability should be strengthened in education, because they do not belong…

This article addresses two unsolved measurement issues in dynamic problem solving (DPS) research: (a) unsystematic construction of DPS tests making a comparison of results obtained in different studies difficult and (b) use of time-intensive single tasks leading to severe reliability problems. To solve these issues, the MicroDYN approach is…

Cooperating teachers can help student teachers make the most of their student teaching experience. The author has served as an on-site supervisor for many practicum students and interns. She has also worked on the university side, supervising pre-student teachers and school psychology practicum students. Having served in all three of these…

There is a wonderful community of art educators connecting a once-isolated profession through blogging. Art educators around the world are sharing ideas and communicating with their peers through this amazing resource. In this article, the author describes the bottle cap mural at Tulip Grove Elementary School which was inspired by this exchange of…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…

This article is the story of a very non-standard, absolutely student-centered multivariable calculus course. The course advocates the so-called problem method in which the problems used are a bridge between what the learners know and what they are about to know. The main feature of the course is a unique conceptual story that runs through the…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

This article introduces an optimization task with a ready-made motivating question that may be paraphrased as follows: "Are you smarter than a Welsh corgi?" The authors present the task along with descriptions of the ways in which two groups of students approached it. These group vignettes reveal as much about the nature of calculus students'…

The vision for science education set forth in "A Framework for K-12 Science Education" (NRC 2012) makes it clear that for today's students to become the scientifically literate citizens of tomorrow their educational experiences must help them become mathematically proficient. "The focus here is on important practices, such as modeling, developing…