ONE POSSIBLE WAY OF TRAINING TEACHERS FOR INQUIRY BASED EDUCATION Alena Hošpesová, Marie Tichá University of South Bohemia České Budějovice, Institute of Mathematics of the Academy of Sciences of the Czech Republic The paper describes the results of a research study aimed at preparation of pre- service primary school teachers for inquiry based mathematics education (IBME). The teaching experiment involved pre-service teachers’ work using a variety of techniques (with strictly formulated questions and open problems) in various environments suitable for this approach. We concentrated on pre-service teacher content knowledge and ability to apply the gained knowledge in problem solving. Keywords: inquiry based mathematics education, pre-service teacher training, subject matter knowledge, knowledge base for teaching INTRODUCTION We have been focusing on various issues connected to the process of professionalization of teachers for many years. Contemporary we tried to find the ways of improvement of teachers’ knowledge base for teaching (Scherer, Steinbring, 2004) through introducing substantial learning environments (Tichá & Hošpesová, 2011). The issue is closely connected to the question of how to introduce these environments into reality of teaching at schools. This lead us to inquiry based mathematics education (IBME), to the role of the teacher as understood in thus conceived education, and to the requirements on pre-service teacher training. This contribution is concerned mainly with the quality of pre-service teachers’ content knowledge, and their ability to apply the gained knowledge in solving process of problems leading to IMBE (requiring discovery, exploratory approach). INQUIRY BASED MATHEMATICS EDUCATION IBME in contemporary education raises great interest (for example Canavarro, 2011). It transmits procedures known from real scientific research to everyday school work with pupils. It puts emphasis on independent discovery (a self-discovery), on proper justifying, and on links with everyday reality (i.e. on a practical desirability). “Inquiry based mathematics education refers to an education which does not present mathematics to pupils and students as a ready-built structure to appropriate. Rather it offers them the opportunity to experience how mathematical knowledge is developed through personal and collective attempts at answering questions emerging in a diversity of fields, from observation of nature as well as the mathematics field itself, ...“ (Artique, Baptist, Dillon, Harlen and Léna 2011, p. 10). The concept of this approach is far from new. Let us recollect here for example the concept of guided rediscovery, anchored in the concept of genetic style of teaching