In recent years, there has been a growing interest in spatial reasoning as a component of mathematics education, with many countries incorporating it into their mathematics curriculum. The study of spatial reasoning in the learning areas of geometry presents an essential opportunity for improvement of students within the realm of mathematics…

The purpose of the study was to determine the association between van Hiele geometric thinking levels and circular achievement exam results for middle school students in 7th grade. The design of the study was a survey method. 157 middle school students were participated into study from three different schools in Kayseri in the spring semester of…

Given the important role played by students' spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes…

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the…

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…

While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In this paper, we report findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging.…

This dissertation reports the results of a qualitative research project on area measurement. The study utilized structured, task-based interviews with students to (a) investigate the ways students enumerate and structure two-dimensional space with a variety of area units; (b) identify conceptual, procedural, and intuitive aspects of area…

Within the study of geometry in the middle school curriculum is the natural development of students' spatial visualization, the ability to visualize two- and three-dimensional objects. The national mathematics standards call specifically for the development of such skills through hands-on experiences. A commonly accepted method is through the…

The author describes a pilot study to investigate the extent to which learners use imagery in a variety of spatial problems. In order to discover how to encourage pupils to use imagery and thus to become better problem solvers, this study set out firstly to explore how pupils are able to use imagery in a variety of tasks. The tasks involved mental…