International Center for Innovation in Education (ICIE) Conference Proceedings (2009-2010) 362 (A.6) Ioannis kougias; L. Seremeti; D. Kalogeras; G. Polyzos; V. Triantafillou: Teaching and Learning of Mathematics: An Autopoietic Approach. Teaching and Learning of Mathematics: An Autopoietic Approach I. Kougias; L. Seremeti; D. Kalogeras; G. Polyzos; V. Triantafillou Technological Educational Institute of Messolonghi, Department of Telecommunication Systems and Networks Nafpaktos - Greece Abstract In this article, the use of an educational web based application dealing with the various problems, which arise during the mathematics teaching/learning procedure at university level, is presented. The aim of the application is to help the instructor detect not only the learning needs, but also the difficulties of the whole group of learners, that is, the perceptive nature of the entire class. In doing so, he/she is able to adapt the lecture to the class’ cognitive needs, while, simultaneously, providing each and every student with personalized support and observation services concerning their progress. With this in mind, the constructive elements (i.e. instructor, students, cognitive subject) of the educational system are self-organized within the system that generates them, which in turn generate the system itself. From that point of view, one can consider the educational system as an autopoietic one, for it is defined as the system that organizes the production of its constructive elements in such a way that they are continuously reproduced and, therefore, the system is capable of maintaining the processes (i.e. , teaching, learning), which produce the elements in question. Within this conceptual aspect, the proposed web based application can be considered as a unified, autonomous and unique autopoietic machine, which consequently, through the actions of learning and teaching, continuously generates and specifies its own structure. Finally, the components of the educational environment (instructor, students and material) generate the whole system, out of which they have been previously generated. Keywords: Autopoiesis, autopoietic machine, web-based application, knowledge module. 1. Introduction In the teaching and learning processes a number of parameters are interacting with each other as students and instructors work together in order to incorporate new knowledge, behavior and skills to their range of learning/teaching experiences. Over the last century, various perspectives on the processes of learning/teaching have emerged. The most important amongst them are: behaviorism, i.e. response to external stimuli; perception, i.e. learning as a mental operation; and constructivism, i.e. knowledge as a constructed element resulting from the learning process. Rather than considering these theories separately, it is best to think of them holistically as a range of possibilities that can be integrated into the learning/teaching experience. During the integration process, it is also important to consider a number of other factors, such as cognitive style, learning style, the multiple natures of subjects to be taught, the technology used, as well as, the participants’ cognition level, which depends on diverse knowledge backgrounds. Considering these factors and the ways in which they interact, we are provided with an organic view of the teaching/learning process that leads us to the notion of autopoiesis, that is, a concept used to describe biological systems. Using this perspective of the autopoiesis, one can examine the processes within different educational environments and effectively design the processes of teaching and