In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual…

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

Manipulatives have been used in many mathematics classrooms across many age groups with the aim of helping students to understand abstract concepts through concrete, kinesthetic, and visual experiences. In this paper, after we provide a background for the use of physical and virtual manipulatives in teaching and learning of mathematics, we will…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…