This research investigates the paradox of creativity in autism. That is, whether people with subclinical autistic traits have cognitive styles conducive to creativity or whether they are disadvantaged by the implied cognitive and behavioural rigidity of the autism phenotype. The relationship between divergent thinking (a cognitive component of…

This article reviews the history of thought on how intelligence and creativity, two individual differences important to teaching and learning, are connected. For decades, intelligence and creativity have been seen as essentially unrelated abilities. Recently, however, new theories, assessment methods, and statistical tools have caused a shift in…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Fermi problems are problems which, due to their difficulty, can be satisfactorily solved by being broken down into smaller pieces that are solved separately. In this article, we present different sequences of activities involving Fermi problems that can be carried out in Secondary School classes. The aim of these activities is to discuss…

In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

This article is part of a larger project focusing upon explanatory illustrations that children encounter in pre- and primary school education. The research questions concerned (a) how preschool children make sense of iconic symbols when placing items of refuse on illustrations of refuse bins in a sorting task and (b) what stumbling blocks they…

Encouraging engineering students to handle advanced technology with multimedia, as well as motivate them to have the skills of solving the problem, are the missions of the teacher in preparing students for a modern professional career. This research proposes a scenario of problem solving in basic electrical circuits based on an e-learning system…

Our high school optics course finishes with an assignment that students usually appreciate. They must take pictures of everyday situations representing optical phenomena such as reflection, refraction, or dispersion, and post them on Instagram. When the photos were presented to the class, one student revealed an intriguing photo, similar to Fig.…

The aim of this study was to develop a novel cognitive procedure for operationalizing how the re-encoding and constraint relaxation, suggested by representational change theory (RCT) (Ohlsson, 1992, 2011), can effect representational change in verbal insight problem solving, thus circumventing the constraints imposed by past experience. Some…

Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5-6 years) in a block puzzle…

Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…

The topic of inhibition in mathematics education is both well timed and important. In this commentary, we reflect on the role of inhibition in mathematics learning through four themes that relate to how inhibition is defined, measured, developed, and applied. First, we consider different characterizations of inhibition and how they may shape the…

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

We analyze the mathematical solutions of 7- to 8-year-old pupils while individually solving an arithmetic problem. The analysis was based on the "configuration of objects," an instrument derived from the onto-semiotic approach to mathematical knowledge. Results are illustrated through a number of cases. From the analysis of mathematical…