A major challenge in the field of spatial reasoning is the translation of decades of accumulated research findings from the domain of psychology and mathematics education into the school mathematics curriculum. This study aimed to operationalise a heuristic termed visualise-predict-check (VPC) for the teaching of spatial visualisation and explore…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

A value-centered approach to science, technology and society (STS) education illuminates the need of reflexive and relational learning through communication and public engagement. Visualization is a key to represent and compare mental models such as assumptions, background theories and value systems that tacitly shape our own understanding,…

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

This article explores the influence of personal and professional experiences on the development of teacher identity. The holistic perspective in this article refers to the language teachers' exploration of their personal and professional experiences with the use of both conscious/rational and intuitive/tacit thought processes. Three language…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to "think aloud" so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are…

This article presents 3 studies that examine how students and experts employ mental rotation and a learned heuristic to solve chemistry tasks that involve spatial information. Results from Study 1 indicate that despite instruction in analytical strategies, students choose to employ mental rotation on canonical assessment tasks. In Study 2, experts…

This article details a heuristic history teachers can use in assigning and evaluating multimedia projects in history. To use this heuristic successfully, requires more than simply following the steps in the list or stages in a recipe: in many ways, it requires a reorientation in what it means to think like an historian. This article, as much as…

Contends that students must learn to adopt a lateral way of thinking, which generates multiple solutions, to resolve their problems. Offers examples of heuristics (plans of attack) that students can use to better approach their problems, such as: visualizing the situation, exploring ideas, choosing a strategy, finding a solution, and checking to…

Explores the role of proof in mathematics education and provides justification for its importance in the curriculum. Discusses three applications of dynamic geometry software--heuristics, exploration, and visualization--as tools in the teaching of proof and as potential challenges to the importance of proof. (Author/MM)

Reports on a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school as part of a larger research project. Aims to clarify the role of a particular software, Cabri Geometry, in the teaching/learning process. Focuses on the social construction of knowledge. (Author/MM)