Using Google SketchUp to Develop Students' Experiences of Dimension in Geometry

Dimension is a powerful mathematical construct that is rarely taught or researched explicitly. The study reported on here explored how the software Google SketchUp can facilitate students’ experiences of dimension. Clinical interviews based on carefully designed tasks were conducted with 10-year-old students. This article offers evidence from the data on how the task setting, including SketchUp’s dimensional tools identified in the software, prompted the construction of ideas about dimension. More specifically, children expressed intuitive ideas about an object/space’s freedom to move within a space/object of higher dimension and its capacity to house other objects/spaces of lower dimension

Research on the teaching and learning of geometry

The chapter provides a comprehensive review of recent research in geometry education, covering geometric and spatial thinking, geometric measurement, and visualization related to geometry, as well as encompassing theoretical developments and research into teaching and teacher development. Studies examining the uses of forms of digital technology are addressed in every section. The content of the chapter reflects the main emphases of research in geometry education as presented at PME conferences over the period 2005–2015. The synthesis is presented in the form of the following sections: spatial reasoning, geometric visualization, geometric measurement, geometric reasoning and proving, students’ knowledge, teachers’ knowledge and development, and teaching geometry and the design and use of geometric tasks. While some topics of research are under-represented (including the topics of congruency and similarity, transformation geometry, analytic/ coordinate geometry, vector geometry), research in geometry education is embracing the use of more recent discursive, embodied and eco-cultural perspectives, and is also employing new methods such as eye-tracking. As research develops further, the affordance of digital technologies is enriching approaches to geometric and spatial teaching and learning by providing new ways of apprehension and representation, new manipulation and processes, wider and deeper conceptual understanding and linking of different meanings and treatments