Academic journal article Educational Technology & Society

Technologies to Enhance and Extend Children's Understanding of Geometry: A Configurative Thematic Synthesis of the Literature

Academic journal article Educational Technology & Society

Technologies to Enhance and Extend Children's Understanding of Geometry: A Configurative Thematic Synthesis of the Literature

Article excerpt

Introduction

Geometry is the study of properties, relationships, and transformations of spatial objects, within an interconnected network of concepts and representational systems. Spatial reasoning undergirds geometry, enabling students to cognitively construct and manipulate mental representations of those spatial objects (Clements & Battista, 1994). Therefore, concomitant study of geometry and spatial reasoning should take place (Battista, 2007). The study of geometry provides students with opportunities to better understand the physical environments in which they live. Unfortunately, mathematics is often taught through lecture, which affords surface understanding, merely requiring students to memorize mathematical facts. The epistemological nature of geometry is called into question, as the findings of copious studies (e.g., Ubuz & Ustun, 2004) indicate that students are not learning geometry with relational understanding of the concepts (Skemp, 1976).

For students to develop a full understanding of the geometry, they must take an active role in the learning process (Piaget & Inhelder, 1967; Vygotsky, 1978). The learner-centered philosophy, stemmed from Bruner's (1966) discovery learning and since then has included constructivist learning, constructionist learning, and socio-constructivist learning. In a dual progression, throughout the learner-centered pedagogical epoch, technology was becoming affordable and accessible for use in schools, and educators witnessed the explosive growth of technologies available for the teaching and learning of geometry (Fey et al., 1984). These technologies provided a way for students to take that active role in learning geometry.

The purpose of this study is to find out what types of digital technologies can be used to support the learning of geometry and what affordances the digital technologies can provide to geometry students. To that end, the two questions guiding this study are:

* What types of digital technologies support the learning of geometry?

* How can the use of digital technologies enhance and extend children's understanding of geometry?

Literature review Configurative thematic synthesis

A systematic review is the art and science of identifying, selecting, and synthesizing studies to provide a comprehensive and trustworthy picture of the topic being studied (Oakley, 2012). There are two broad modes of synthesis: aggregation and configuration (Sandelowski, Voils, Leeman, & Crandlee, 2011). Aggregation syntheses are conducted by counting the numbers of studies and particular components of those studies. Configuration studies as those that generate new theories with the studies similar to pieces in a mosaic slotted together to form a gestalt image (Sandelowski et al., 2011). In this study, a configuration approach is used to determine what technologies are available for learning about geometry and how they support the learner.

A thematic synthesis is intertwined with a configurative approach. It is a systematic approach to bringing a variety of findings together to provide a perspective on a particular theme that emerges. Those findings can be empirical studies and theoretical papers (Thomas & Harden, 2008). This study employs the configurative, thematic synthesis approach to answer the two research questions guiding this study.

Past reviews

Laborde, Kynigos, Hollebrands, and Strasser (2006) conducted a review of teaching and learning geometry with technology over three decades. This synthesis of research was organized studies using four categories; (a) the nature of geometry mediated by technology, (b) technology and the learning of geometry, (c) the design of tasks, and (d) the use of geometry by teachers. Zbiek, Heid, Blume, and Dick (2007), published a study about technology in mathematics education. This study was not focused on geometry in particular, but specifically referenced technological tools and technology-based mathematical activities, students' behavior in the context of technology, teaching issues related to technology in mathematics education, and effects of technology on mathematics curriculum content. …

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