How Can Digital Technology Enhance Mathematics Teaching and Learning?

How Can Digital Technology Enhance Mathematics Teaching and Learning?

Monika Dockendorff (Pontificia Universidad Católica de Chile, Chile)
DOI: 10.4018/978-1-7998-0249-5.ch011

Abstract

As digital technology becomes more ubiquitous in society and education, mathematics teachers are expected to design and integrate technology-enriched learning environments effectively. This task encompasses many challenges, but primarily, it entails the identification of how technology may produce insights. This study examines several categories of core mathematical processes that can be enhanced by the integration of dynamic interactive software such as identifying properties, connecting multiple representations, and solving problems, among others. The process of visualization appears at the center of dynamic and interactive mathematics learning environments. Evidence of its functionality and the benefits it reports to the teaching and learning process for each category is presented. Further discussion on the challenges that mathematics teacher education programs and teachers face—not only in their digital competences but also in the role they play—are outlined.
Chapter Preview
Top

Introduction

Since the rise of digital technologies in society, schools have been attempting to integrate them for learning and communicating purposes, but according to Cuban (2001) the process of embedding technology in classrooms has been slow and complex. For several decades now, games and simulations have been introduced in schools as tools used for science learning. But there are many cases reported in which digital technology has ultimately made little impact in meaningful learning. These tools should serve a purpose, otherwise their integration would lack real relevance: “tools are just tools until they are applied to some end” (Clark, Nelson, Sengupta, & D´Angelo, 2009, p. 52).

In the mathematics curricula, where major benefits can be obtained, ICT has been integrated to a diverse extent, unequally throughout the world. ICT integration in mathematics teaching and learning serves many purposes and goals. There are several perspectives that justify the use of digital technology in mathematics education such as practical reasons (easy-fast-exact), student motivation and interest, and the cognitive benefits it entails for better understanding abstract mathematical entities (Hoyles, 2018). Creating a conceptual image of a mathematical object is a complex process given its abstract nature. Therefore, visualizing and manipulating virtual entities that represent these objects facilitates a deeper understanding, both procedural and conceptual. “Visual forms of representation can be important, not only as a heuristic and pedagogical tools, but as legitimate elements of mathematical proof”(Barwise & Etchemendy, 1991, p. 9). Technology offers multiple representations of mathematical objects that are related dynamically, elucidating the interplay between different registers of representations. These features elevate the dynamic-graphic register to a new status, supporting reasoning and proof (Novembre, Nicodemo, & Coll, 2015). Because these dynamic visual environments became so important for the representation of complex concepts and communication of ideas, design principles that assure their educational effectiveness have been validated. These principles encompass two dimensions: visual and interactive (Plass, Homer, & Hayward, 2009).

Many teachers are not fully prepared to integrate ICT into the mathematics curriculum, and many teacher training approaches tend to focus on the available digital resources and their use rather than focusing on their pedagogical purposes (Hamilton, Rosenberg, & Akcaoglu, 2016). Therefore, the framework used for integrating digital technology and the prominence of the pedagogical dimension, is key to create effective digital learning environments.

Several models offer ways to inform and guide K-12 teachers’ understanding and uses of technology in teaching. For example, Beaudin and Bowers (1997)Play, Use, Recommend, Incorporate and Assess (PURIA) model structures the process as consecutive stages, as Puentedura´s (2006) Substitution, Augmentation, Modification, and Redefinition (SAMR) model describes how technology may transform or enhance learning. But, the most commonly used theoretical framework that describes how technology is integrated into mathematics teaching and learning is TPACK: Mishra & Koehler´s (2006) Technological Pedagogical Content Knowledge includes the teacher´s understanding of how to represent concepts using technologies; pedagogically addressing the use of technological resources to teach, and constructively promoting student learning on the curricular concepts – in this case, mathematics concepts. History and experience, however, have taught us that this integration should have an emphasis: pedagogy. We should not forget that the whole purpose is learning, this is, learner’s knowledge construction.

Key Terms in this Chapter

Hard Construction: As opposed to soft construction or drawing. Geometric construction based on the object´s properties. If correctly drawn the shape of the figure will remain unchanged under dragging.

GeoGebra-Based Dynamic Applet: Is a digital tool generated by means of GeoGebra software with extension ggb . It is used to teach and learn mathematics in an exploratory way due to its interactive and dynamic features. Given the software opensource nature, shared applets can be modified and further used by other learners around the world.

Stages of Cognitive Representation: Three stages are usually described regarding levels of abstraction. Enactive, which is the representation of knowledge through actions. Iconic, which is the visual summarization of images. Symbolic representation, which is the use of words and other symbols to describe experiences.

Technology-Enriched Learning Environment: Classrooms, in which open-ended, rich information tasks and resources are available, most of which use a range of technologies or digital tools in interactive, multi-media and inter-disciplinary formats, constantly challenging students and teachers.

Simultaneous Dynamic Representations: Software capability to depict simultaneously the symbolic and graphic representation of a mathematical entity. Combined with the dynamic interactive feature -that enables the user to modify either the symbolic or the graphic representation and observe the corresponding modification in the other register of representation- allows deep access to mathematical objects.

Visualization: Visualization is the ability, the process and the product of creation, interpretation, use of and reflection upon pictures, images, diagrams, in our minds, on paper, or with technological tools, with the purpose of depicting and communicating information, thinking about and developing previously unknown ideas and advancing understandings.

Dragging Test: Changing a geometrical object without changing the significant properties of the object. Normally the dragging test is performed by dragging one or more vertices of geometric figures.

Complete Chapter List

Search this Book:
Reset