tailieunhanh - Didactic Reform: Organising Learning Projects on Distance and Applications in Taxicab Geometry for Students Specialising in Mathematics

In the early 20th century, Hermann Minkowski (1864-1909) proposed an idea about a new metric, one of many metrics of non-Euclidean geometry that he developed called Taxicab geometry. The purpose of this paper is to design activities so that students can construct the concept of distance and realise practical applications of Taxicab geometry. | VNU Journal of Science: Education Research, Vol. 33, No. 4 (2017) 1-9 Didactic Reform: Organising Learning Projects on Distance and Applications in Taxicab Geometry for Students Specialising in Mathematics Chu Cam Tho1,*, Tran Thi Ha Phuong2 1 Vietnam Institute of Educational Sciences Bac Giang Specialized Upper Secondary School, Hoang Van Thu Street, Bac Giang City, Bac Giang, Vietnam 2 Received 12 January 2016 Revised 15 March 2016; Accepted 22 June 2017 Abstract: In the early 20th century, Hermann Minkowski (1864-1909) proposed an idea about a new metric, one of many metrics of non-Euclidean geometry that he developed called Taxicab geometry. The purpose of this paper is to design activities so that students can construct the concept of distance and realise practical applications of Taxicab geometry. Keywords: Didactic reform, taxicab geometry, project-based learning. 1. Introduction * postulates of metric space. Taxicab geometry is one of his works which is different from Euclidean geometry in terms of distance structure. Thus, if Euclidean geometry is a good model of the “natural world”, Taxicab geometry is a better model of the artificial urban world that man has built, applied widely in real space [2, p110]. Our purpose of this paper is to design activities so that students can construct the concept of distance and realise practical applications of Taxicab geometry. At the same time, we propose research topics in line with students’ capacity regarding several content areas of this geometry through project-based learning. Moreover, similarly to Euclide geometry, form the concept of the three types of conic section, through project-based learning, students can construct “conic section” in Taxicab distance and compare with three respective types of conic section in Euclidean geometry. One of the ways to gain a deeper understanding of Euclidean geometry is to examine its relation to other non-Euclidean geometries. The selected non-Euclidean geometry which