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

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

Teaching science and technology at primary school level: theoretical and practical considerations for primary school teachers' professional training.

This paper focuses on the importance of starting science and technology education at a young age and at the consequential importance of providing primary school teachers with enough professional background to be able to effectively incorporate science and technology into their teaching. We will discuss a large-scale program in The Netherlands that is aimed at the professionalization of elementary school teachers in the field of science and technology. Theoretical and practical considerations will be provided for the three pillars that ideally should be included in teacher training programs in this domain: (1) Primary school teachers’ knowledge of and competency in scientific concepts and scientific reasoning; (2) Primary school teachers’ attitude towards science (in terms of cognitive, affective, and behavioural dimensions of attitude); and (3) Primary school teachers’ pedagogical competency to enhance inquiry-based learning

A framework to analyze argumentative knowledge construction in computer-supported collaborative learning

Computer-supported collaborative learning (CSCL) is often based on written argumentative discourse of learners, who discuss their perspectives on a problem with the goal to acquire knowledge. Lately, CSCL research focuses on the facilitation of specific processes of argumentative knowledge construction, e.g., with computer-supported collaboration scripts. In order to refine process-oriented instructional support, such as scripts, we need to measure the influence of scripts on specific processes of argumentative knowledge construction. In this article, we propose a multi-dimensional approach to analyze argumentative knowledge construction in CSCL from sampling and segmentation of the discourse corpora to the analysis of four process dimensions (participation, epistemic, argumentative, social mode)

Construction of embedded fMRI resting state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling (MDS), Isometric Feature Mapping (ISOMAP) and Diffusion Maps. Furthermore, based on key global graph-theoretical properties of the embedded FCN, we compare their classification potential using machine learning techniques. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the lagged cross-correlation metric. We show that the FCN constructed with Diffusion Maps and the lagged cross-correlation metric outperform the other combinations

Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule