Laskutaitoharjoittelusta ongelmanratkaisuun : matematiikan opettajien matematiikkauskomukset opetuksen muovaajina - Kupari, Pekka (1999)
The study examines the beliefs that Finnish comprehensive school mathematics teachers hold about mathematics and about learning and teaching it, and the important role that these beliefs play in the teaching of mathematics. The study is linked with a subject field that has been discussed animatedly on an international level for more than ten years. However, the present study looks for answers to the questions it addresses specifically from the perspective of Finnish teaching culture. In this way the study attempts to describe and understand the instructional practices of mathematics teachers and the preconditions under which these practices develop and change. The theoretical foundations of the study consist of a conceptual analysis of beliefs and belief systems and a theory of teachers' thinking and decision-making that describes the way in which a teacher's beliefs are transmitted. Beliefs are here considered to be connected with a teacher's teaching practices and, through the studying process, also with pupils' activities and learning. The social context of the school community is an important factor in the construction of beliefs. Within a school community teachers are constantly interacting with one another and with pupils, which not only creates opportunities for but also acts as a restraint on both the preservation of prevailing beliefs and the emergence of new ones. The empirical data of the study were collected in connection with the National Assessment Studies carried out in Finland in the 1990s and comprise three parts. In 1990 the subjects were class teachers of Grades 4 and 6 of the Finnish comprehensive school (N=108) and subject teachers teaching Grade 9 (N=65). The second stage of the study in 1995 covered only subject teachers teaching Grade 9 (N=68), of which 15 had taken part also in the 1990 study. In these first two stages of the study the data were gathered by using belief questionnaires. Further, in spring 1996 the subject was explored in greater depth through thematic interviews with four teachers. The questionnaire data were analysed using not only the usual statistical procedures but also more recent methods of statistical analysis. The findings of the study showed that mathematics teachers hold relatively strong beliefs about mathematics. These beliefs emphasise particularly the importance of thinking and of setting pupils tasks involving problems that give them scope for independent reflection and encourage them to look for a number of potential solutions. Both the class teachers and the subject teachers had multidimensional belief structures: their beliefs were based on several different factors rather than on one single type of belief. All belief structures featured an emphasis on practical exercises, something that may be considered an aspect of the traditional idea of mathematics and of traditional teaching methods. On the other hand, another prominent ingredient of the teachers' beliefs was learner orientation, a special focus of the constructivist conception of learning. The simultaneous prevalence and vigour of such different or even conflicting beliefs is made possible by the fact that belief systems allow for the existence of competing beliefs. Despite being multidimensional and in part contradictory, the teachers' mathematical beliefs were quite stable and changed little over the course of five years. A very obvious factor underpinning this constancy are such core beliefs as faith in a mastery of basic computational skills, in a great deal of practical exercises and in an exact use of mathematical language, which are deeply rooted and seem tenacious. No very strong links were found between beliefs and teaching practices. The teachers' beliefs were transmitted to their pupils' learning outcomes in the sense that strong beliefs concerning the centrality of practical exercises led to a deterioration in the pupils' learning outcomes. The findings of the study suggest that it is fruitless to simply demand that teachers must bring their teaching of mathematics into line with new conceptions of learning and curricula. Teaching methods and beliefs cannot be changed by compulsion or instantly. Only teachers' own active participation makes changing beliefs and also practices possible. Accordingly, the essential thing is creating opportunities for and situations conducive to changing one's beliefs. Here teacher education and more long-term development projects are a central factor. Helping trainees become aware of their own beliefs and present arguments for their reasonableness and validity should be seen as one of the most important challenges facing teachers' pre-service and in-service training. Without such an awareness, at their worst training events and development projects merely perpetuate prevailing teaching practices. Because changes in teaching involve a demanding and long-term process, it is crucial from the perspective of teachers' professional development to create within schools environments for teachers' active interaction. If teachers are able discuss their experiences from using different teaching methods with each other, even profound changes in attitudes and beliefs are possible. Such changes are yet more permanent if teachers are able to observe the effects of an approach or method also in their pupils' learning outcomes. Another important factor is enhancing teachers' content and pedagogical knowledge and developing assessment practices.