This paper reports on the interaction between upper intermediate German as a Foreign Language (GFL) learners in Tokyo and prospective GFL teachers in Berlin in an online videoconferencing environment. It focuses on the way problems in comprehension and production are brought up and solved in the subsequent interaction. Our findings illustrate that…

This book explores the concepts of innovation and entrepreneurship through multiple lenses in the context of education. Mixing equal parts of theory and practice, this volume takes a closer look on how innovation and entrepreneurship are approached around the globe as disciplines, methods, and mindsets. Focusing on ubiquitous learning and…

I found the need to explore the difficulties faced by Arabic-speaking English language learners studying mathematics as soon as I moved to the United Arab Emirates. Thus, I began a line of research that aimed to explain and understand these issues and find effective teaching strategies for the students. This case study describes the first research…

What makes a person able to solve problems creatively? One interesting factor that may contribute is experience with multiple languages from an early age. Bilingual individuals who acquire two languages by the age of 6 have been shown to demonstrate superior performance on a number of thinking tasks that require flexibility. However, bilingual…

A complete, non-trivial, traveling sales tour problem contains at least one "indentation", where nodes in the interior of the point set are connected between two adjacent nodes on the boundary. Early research reported that human tours exhibited fewer such indentations than expected. A subsequent explanation proposed that this was because…

This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular…

As with so many aspects of mathematical enquiry, there is little that is "original", or "brand new", but that does not diminish the outcome of work that borrows from "those who have gone before". In this piece the author "borrows" from the work of Desargues, Monge, Ceva, Menelaus, van Aubel, and Gergonne. This novel approach to providing a proof…

We are frequently told that Hong Kong has a model system for learning mathematics. In this article Daniela Vasile notes one short-coming in that the pupils are not taught to problem-solve. She begins with a new class by asking them to write down the craziest equation they can come up with and bases her whole lesson, and the following homework,…

Establishing and maintaining key mathematical practices in whole-class discussions, such as justifying claims, representing mathematical objects and making connections between the representations, is crucial to the development of students' mathematical competencies. The aim of this article is to investigate how and why the establishment of key…

Sources of individual differences in scientific problem solving were investigated. Participants representing a wide range of experience in geology completed tests of visuospatial ability and geological knowledge, and performed a geological bedrock mapping task, in which they attempted to infer the geological structure of an area in the Tobacco…

The opportunities for meaningful classroom learning activities are everywhere. In this article, we explain some of the little known, widespread, horrific issues associated with one aspect of the pet trade. By the time they reach high school age, many students have personally experienced the end result of the deplorable business practices on which…

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

The revelation effect is a change in response behavior induced by a preceding problem-solving task. Previous studies have shown a revelation effect for faces when the problem-solving task includes attractiveness ratings of the faces. Immediately after this problem-solving task participants judged faces as more familiar than without the…

A mixed-method exploratory approach was employed to examine the relationship between epistemological beliefs and quality of thinking when participants first thought about an ill-structured problem alone, and then with another person in a dyad. The results showed that there was not a systematic connection between epistemological beliefs and…

This paper reports on a study that introduces and applies the "K[subscript 5]Connected Cognition Diagram" as a lens to explore video data showing teachers' interactions related to the partitioning of regions by axes in a three-dimensional geometric space. The study considers "semiotic bundles" (Arzarello, 2006), introduces "semiotic connections,"…