From Middle to High school: Teachers reflecting on the role of definitions with the aid of van Hiele’s Theory

This paper concerns a work carried out during 2002 with a group of 6 expert teachers who were to change from middle school (11-14 year-olds) to high school (14-19 year olds) teaching at the beginning of the successive school year. Disciplinary theoretical aspects involve questions on van Hiele's theory of levels and teachers' conceptions on the role of definitions. The work was a continuation and an adaptation of an experience that has been going on for some years with a group of teachers from high schools. Attempting to help teachers in facing their new scholastic level, it emerged that knowledge and beliefs concerning, for instance, the hierarchical classification of geometric figures, may have relevant effects when we move from one world of experience to another (Ponte, 1994). In addition to this, the character of the group may be affected by less willingness to re-discuss the previous experience. This leads the authors to interpret the results in comparison with other researches in which theoretical knowledge is shared among teachers and researchers, and thus to investigate the characterization of a group of collaborative intervention research (Krainer, 2003)