Awareness of one's own strengths and weaknesses during visualisation is often initiated by the imagination -- the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West…

Adolescent learning is a complex process, distinctive from learning prior to and after this stage because of the connection between learning and the physical, intellectual, emotional, and social development of students in this age group. Indeed, questions about middle school learning examine both "what" and "how" they learn (Gross, 2002). This…

This article describes phases of post-lesson reflective dialogues that were enacted by secondary school mathematics student teachers with their peers. Five pairs of student teachers on 12 weeks of teaching practice provided data through lesson assessments, post-lesson reflective dialogues, and end-of-teaching-practice reflective interviews. A…

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

This research aims to determine whether the use of specific types of visualization (3D illustration, 3D animation, and interactive 3D animation) combined with narration and text, contributes to the learning process of 13- and 14- years-old students in science courses. The study was carried out with 212 8th grade students in Greece. This…

Spontaneity has been linked to high quality learning experiences in mathematics (Csikszentmihalyi & Csikszentmihalyi, 1992; Williams, 2002).This paper shows how spontaneity can be identified by attending to the nature of social elements in the process of abstracting (Dreyfus, Hershkowitz, & Schwarz, 2001). This process is elaborated…