This article uses parts of qualitative data from the first author's study that focused on exploring Pirie and Kieren's process of "folding back," revisiting previously held understandings of a concept for its extended understanding in order to solve the problem of enhancing Grade 10 learners' reasoning in geometry. In South Africa,…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

Research has demonstrated that instruction that relies heavily on studying worked examples is more effective for less experienced learners compared to instruction emphasizing problem solving. However, the guidance associated with studying some worked examples may reduce the performance of more experienced learners. This study investigated…

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

Needs assessments in substance abuse prevention often rely on secondary data measures of consumption and consequences to determine what population subgroup and geographic areas should receive a portion of limited resources. Although these secondary data measures have some benefits (e.g. large sample sizes, lack of survey response biases and cost),…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

Researchers who make tutoring systems would like to know which sequences of educational content lead to the most effective learning by their students. The majority of data collected in many ITS systems consist of answers to a group of questions of a given skill often presented in a random sequence. Following work that identifies which items…

In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…