Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

The concept of symmetry is vital for the study of science and developing spatial and geometric relationships. Yet few studies have been conducted to examine how students learn this concept. This study investigates 757 Year 4 to 10 students' ability to reason about symmetrical relationships. By analysing the semiotic processes through the lens of…

Creativity is a dynamic process which generates ideas that are both novel and of value. However there is little understanding in what drives creativity in students and how to help teachers or education experts to detect creative thinking. This paper begins to address this gap by providing a platform and experiments for studying how creative…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

This study is part of a larger project exploring students' thinking of Dynamic Measurement (DYME), an approach to area measurement that engages students in dynamic digital experiences of measuring rectangular surfaces through sweeping lengths. The goal of this study was to evaluate the extent to which students could bridge the mathematical…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

This paper attempted to make explicit some of the underlying characteristics of spatial visualisation using the concept of area of composite shapes. By engaging students with metric-free tasks, we identify the type of perceptual and visual/spatial manoeuvres that they deploy in such situations. Interview data collected from three students in Grade…

Amongst important and under-researched questions are how introductory lessons can be designed for teaching initial proofs to junior high school students, and how such lessons enrich students' understanding of proofs. With a view to improving the learning situation in the classroom, in this paper we report on the various functions of introductory…

Spatial visualisation is a subset of spatial ability and is exemplified in predicting whether or not a net will fold to form a target solid. The researchers examined video of interviews to explore the schemes of Year 5 students for determining the validity of nets for a cube and pyramid. Findings suggest the significance of imaged actions, shown…

This investigation is part of a combined research/curriculum development project in which children's learning is being examined in the context of developing and testing instructional units on 3-D geometry in grades 3, 4, and 5. There are two components to the article. First, the strategies and cognitive constructions that students utilize to…

This paper examines the differences between student performance on two separate measures, the Spatial Visualization portion of the "Differential Aptitude Test" and the "Geometry Content Knowledge Test." Results from the hybrid quantitative/qualitative study indicate that although there were no differences in performance on spatial visualization…

The effects of an experimental geometry course on gender differences in standardized test performance were studied. The experimental approach involved: (1) reading new concepts and materials followed by class discussion; (2) relating applications to real-life situations; and (3) conducting a spiraling review of concepts throughout the year.…