Abstract
In preparing an address that fits well within the themes of the Frontiers in Mathematics and Science Education Research Conference 2014, I have chosen geometry. Evidently, geometric applications in Calculus, Algebra and other fields are essential for these disciplines’ development. In addition, the widespread use of geometry by pre-service and in-service teachers in elementary, middle, and secondary schools and universities makes it an indispensable discipline for a large population in education. In what follows I will try to highlight and present the main trends in recent research activities in teaching and learning undergraduate geometry that were carried out throughout the second half of the twentieth century up to the present. In particular, research on studying children and young adults’ processes of how they construct geometric and spatial ideas of objects will be discussed. Additionally, research in mathematics on proofs and proving with selected examples of proving the Pythagorean Theorem visually and through geometric construction including my own proof will be introduced.
Highlights
Introduction and backgroundThroughout the last half of the twentieth century, there have been critical didactic events in the area of thoughts development in geometry
In the late 1950s, the van Hieles Model of Levels of Geometric Thoughts Development was introduced by Pierre van Hiele and Dina-Geldof van Hiele (Pierre van Hiele, 1984a, 1984b & Dina van Hiele-Geldof, 1984a, 1984b)
The van Hieles model appeared within the writings of Dina van Hiele-Geldof (1984a) and Pierre van Hiele (1984b)
Summary
Throughout the last half of the twentieth century, there have been critical didactic events in the area of thoughts development in geometry. In the late 1950s, the van Hieles Model of Levels of Geometric Thoughts Development was introduced by Pierre van Hiele and Dina-Geldof van Hiele (Pierre van Hiele, 1984a, 1984b & Dina van Hiele-Geldof, 1984a, 1984b). The van Hieles model would seem to be one of the significant events in mathematics education. The work and research of scholars in geometry education from the 1950s to the present have been energized worldwide with specific interest into the levels of students’ geometric thinking processes and the methods of school teaching of geometry in the classrooms. The new studentcentered work and research activities in geometry may be classified into two main categories: Research in Thought Development in Geometry, and Research in Methods of Teaching Geometry. The following is an attempt to introduce major events in each of these categories and the influences of the two trends on each other as the allocated space allows
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