International studies on the knowledge of mathematics at the generalist-class teaching level have indicated that Slovene students are quite skilled at computations, but have difficulties solving mathematical problems. This finding stimulated us to create a problem-based instruction model. We wanted to find out whether the students in the experimental group, who received problem-based instruction, would display greater ability in solving difficult mathematical problems compared to the group receiving conventional instruction. We were also interested in the students' attitude towards mathematics. We formulated the experimental factor -problem posing and solving as the key math-teaching activity -broadened the conventional mathematical problem by introducing into it several other types of problems and strategies of their solving. The efficiency of the model created was tested on a sample of 179 nine-year-old students. The results of the study are useful for the preparation of mathematics curriculum reform and important for the authors of maths materials for teachers and students. The research findings are of great value in the undergraduate education of teachers, as well as for qualified and practicing teachers and their further and regular professional training.
IntroductionThe deep economic, social, technological and cultural changes in Europe represent a real challenge for teacher education. The teacher's role is becoming more complex and demanding, while the expectations of society are rising. Teachers are expected not only to enable optimal development of increasingly heterogeneous groups of pupils, but also to mitigate the effects of social inequality. All this requires qualitative changes in pre-service and in-service teacher education. In this regard, the transition from school/university to professional life -the induction period and early career years -requires special attention. In this phase, a fruitful synthesis of theory and practice can occur if novices are systematically introduced and supported by good mentoring in the transition from study to school life and culture, but a 'practice shock' is also possible during which many positive effects of pre-service education are lost. Buchberger et al. (2001) mentioned a certain 'blind spot' in this area and stressed the need to pay more attention to this issue by researching and building good models of induction. In this article, we present and compare different existing concepts and models of induction in various European countries and elsewhere, together with their critical analysis. Our aim is to identify some principles and optimal solutions that would foster teacher's professional development in this important phase of their career.
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