Toward a Semiotic Framework for Using Technology in Mathematics Education: The Case of Learning 3D Geometry

This paper proposes and examines a semiotic framework to inform the use of technology in mathematics education. Semiotics asserts that all cognition is irreducibly triadic, of the nature of a sign, fallible, and thoroughly immersed in a continuing process of interpretation (Halton, 1992). Mathematical meaning-making or meaningful knowledge construction is a continuing process of interpretation within multiple semiotic resources including typological, topological, and social-actional resources. Based on this semiotic framework, an application named VRMath has been developed to facilitate the learning of 3D geometry. VRMath utilises innovative virtual reality (VR) technology and integrates many semiotic resources to form a virtual reality learning environment (VRLE) as well as a mathematical microworld (Edwards, 1995) for learning 3D geometry. The semiotic framework and VRMath are both now being evaluated and will be re-examined continuously

Visualising Music with Impromptu

This paper discusses our experiments with a method of creating visual representations of music using a graphical library for Impromptu that emulates and builds on Logo’s turtle graphics. We explore the potential and limitations of this library for visualising music, and describe some ways in which this simple system can be utilised to assist the musician by revealing musical structure are demonstrated

Two Turns Must Take Turns: Primary School Students' Cognition about 3D Rotation in a Virtual Reality Learning Environment

This paper reports on five primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements

Knowledge Construction of 3D Geometry Concepts and Processes Within a Virtual Reality Learning Environment

A consensus has emerged within the mathematics education community about the limitations of traditional approaches for teaching and learning 3D geometry. Therefore, it has been suggested that new approaches based on the use of computers need to be adopted. One such new approach that has been proposed utilises Virtual Reality Learning Environment (VRLE). This paper reports on the initial phases of a research study whose major aim is to design and evaluate a VRLE to facilitate the construction of knowledge about 3D geometry concepts and processes. This research study investigates two primary school students’ construction of 3D geometry knowledge whilst engaged within a VRLE developed by the researcher. A design experiments research methodology was employed in this study. This is research that iterates through cycles of design and research with the objective of arriving at theoretical and design principles that will have application both within and beyond the immediate research study. Therefore, the results being reported in this paper will be used to inform the modification not only of the VRLE but also of theoretical frameworks underlying the design and implementation of VRLEs

Designing digital technologies and learning activities for different geometries

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and co-ordinate geometries in two and three dimensions, and non-Euclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry

The importance of being accessible: The graphics calculator in mathematics education

The first decade of the availability of graphics calculators in secondary schools has just concluded, although evidence for this is easier to find in some countries and schools than in others, since there are gross socio-economic differences in both cases. It is now almost the end of the second decade since the invention of microcomputers and their appearance in mathematics educational settings. Most of the interest in technology for mathematics education has been concerned with microcomputers. But there has been a steady increase in interest in graphics calculators by students, teachers, curriculum developers and examination authorities, in growing recognition that accessibility of technology at the level of the individual student is the key factor in responding appropriately to technological change; the experience of the last decade suggests very strongly that mathematics teachers are well advised to pay more attention to graphics calculators than to microcomputers. There are clear signs that the commercial marketplace, especially in the United States, is acutely aware of this trend. It was recently reported that current US sales of graphics calculators are around six million units per year, and rising. There are now four major corporations developing products aimed directly at the high school market, with all four producing graphics calculators of high quality and beginning to understand the educational needs of students and their teachers. To get some evidence of this interest, I scanned a recent issue (April 1995) of The Mathematics Teacher, the NCTM journal focussed on high school mathematics. The evidence was very strong: of almost 20 full pages devoted to paid advertising, nine featured graphics calculators, while only two featured computer products, with two more featuring both computers and graphics calculators. The main purposes of this paper are to explain and justify this heightened level of interest in graphics calculators at the secondary school level, and to identify some of the resulting implications for mathematics education, both generally, and in the South-East Asian region

Importing Vector Graphics: The grImport Package for R

This article describes an approach to importing vector-based graphical images into statistical software as implemented in a package called grImport for the R statistical computing environment. This approach assumes that an original image can be transformed into a PostScript format (i.e., the original image is in a standard vector graphics format such as PostScript, PDF, or SVG). The grImport package consists of three components: a function for converting PostScript files to an R-specific XML format; a function for reading the XML format into special Picture objects in R; and functions for manipulating and drawing Picture objects. Several examples and applications are presented, including annotating a statistical plot with an imported logo and using imported images as plotting symbols.

Logo in mainstream schools: the struggle over the soul of an educational innovation

Technologies do not follow some predetermined and inevitable course from their context of production to their context of use, and technologies used in schools are no exception. Rather, technologies and their use in the classroom are socially contextualised. They are often appropriated in ways unanticipated by their developers, locking into institutional arrangements and reflecting elements of the prevailing social relations in and around the particular context(s) of application. Through the discussion of a particular technology (the Logo programming language) as a case study in educational innovation, this article demonstrates how the use of technologies in schools is socially shaped. The paper looks into the place that Logo occupied within the institutional and organisational cultures of US and UK mainstream schools after its introduction in the early 1980s. It discusses the ways in which Logo was received in the educational arena and was implicated in the politics of educational innovation at a time of conservative restoration