RETA Model for Teaching Mathematics: From the United Kingdom to Turkey

Introduction

This chapter provides an international perspective on a reform-based practice in mathematics teaching and learning by describing a novel mathematics teaching model, and presenting sample lesson practices on how to use the model in the Turkish context. Specifically, this chapter introduces a model to teach geometry lessons with realistic, exploratory, technology-enhanced and active (RETA) principles, and its practical applications in middle schools in Turkey. First, both the alternative models of teaching geometry and the typical geometry teaching approach in Turkey are discussed. Then, how these existing models led to the RETA model is described, followed by a discussion of the principles of the RETA model along with pros and cons. For the pros and cons of each principle of the model, practical applications of the principles are presented through sample lesson plans. These sample RETA-based lesson plans are on orthogonal and isometric drawings of polycubes which were developed, implemented, and evaluated as a part of a design-based research project with four cycles. The lessons were intended to help middle school students learn about three-dimensional (3D) shapes and in particular orthogonal and isometric drawings of polycubes. Last, the chapter ends with a discussion of the solutions, recommendations, and future research directions.

The 3D geometry thinking is “the conception of thoughts and ideas about 3D geometry concepts by amalgamating various types of reasoning;” and reasoning in this concept refers to “a set of processes and abilities that act as a feasible tool in problem-solving and enable us to go beyond the information given” (Pittalis & Christou, 2010, p.192). Orthogonal and isometric drawings have a variety of names in the literature; for example, orthogonal drawings can be referred to as orthogonal projections (Jones et al., 2012), orthographic projections/drawings (Moyer-Packenham & Bolyard, 2002), plan/top view, and elevations/side views (Yeo et al., 2005), and isometric drawings are also known as isometric projections (Gambari et al., 2015) and perspective drawings (Oldknow & Tetlow, 2008), as well as sometimes very vaguely as a building or a representation/picture of a building (Ben-Haim et al., 1985). The differing titles for these 2D representations were deemed synonyms in this chapter, and it is opted to use orthogonal and isometric drawings, which are both among the earliest names for these sorts of representations in the literature (Cooper & Sweller, 1989). In a similar vein, polycubes are three-dimensional shapes that are constructed from unit cubes. Polycubes are also referred to as polycubical shapes/objects (Cooper & Sweller, 1989), (solid) cube constructions (Ben-Haim et al., 1985) and a solid or an object constructed from unit-sized cubes (Pittalis & Christou, 2010).