How Can Digital Technology Enhance Mathematics Teaching and Learning?

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.