Hellenic Conference on Innovating STEM Education, 16-18/12/16, Athens, 16-18 December 2016 1 New perspectives for Geometry teaching: Mechanical linkages Technology Kalliopi Siopi 1 and Eugenia Koleza 2 1 , Model High School of Evangeliki School of Smyrna, Athens, kalsiopi@gmail.com 2 University of Patras, Department of Primary Education, Patra, ekoleza@upatras.gr Abstract: In this paper we try a brief presentation of mechanical linkages, and especially of the drawing machines. Our focus is on the pantograph, that incorporates mathematical properties and relationships in structure in such a way to allow the implementation one geometrical transformation, such as, symmetry, reflection, translation and homothety. In order to investigate subjects’ concepts/ theorems-in-action developed by investigating the structure of the pantograph, and especially the identification of the math concepts and laws incorporated in the machine , we selected a pantograph’s model and taught homothety to high school students for four hours (early 2016), in the framework of an attempt to incorporate artifacts with the characteristics geometrical machine’s in the instruction of Euclidean geometry. Keywords: ‘linkages’, ‘pantograph’, ‘geometry’, ‘teaching’, ‘homothety’ 1. Introduction Learning with the use of various technological tools attracts a lot of research interest and holds great promise; the use of the tools in the current learning environments allows the students to have increased chances of achieving mathematical concepts, exploring and experimenting with mathematical ideas and expressing such ideas and concepts via a variety of representations (Taimina, 2008). At the same time, integrating engineering-based problem solving within the learning objectives of the students is also very appealing in the progressive societies, making the teaching of Science, Technology, Engineering and Mathematics (STEM) a very important component of their education. Technology is often referred to as the tool and the application of math and science. Within the classroom, computer technology is often used to facilitate lesson planning, class activities or even to create resources. Studying the history of technology, during the mechanical age (between 1450 and 1840) a lot of new technologies were developed. These technologies embodied the knowledge of their time and were the first attempt of math and science modeling. Such technologies include the slide rule (an analog computer used for multiplying and dividing) and the Pascaline (a very popular mechanical computer) by Blaise Pascal that could be used even nowadays. Nevertheless, the use of mathematical machines as technological tools to promote learning seems to be under-researched, with limited existing knowledge regarding the experience of the students. A sound exception is the MMLab (Laboratory of Mathematical Machines, www.mmlab.unimore.it). where researchers (Bartolini Bussi, 2010; Martignone, 2011; Mariotti et al., 1997) have investigated from an epistemological and pedagogical aspect the use of mechanical machines -concerning geometry and arithmetic - as a way to generate mathematical ideas or concepts in the classroom. This Research Group has investigated the use of simple mathematical machines in different contexts and grade