Möjligheter till lärande i matematik: Lärares problemformuleringar och dynamisk programvara

This thesis presents the first Swedish empirical evidence on how teachers employ a dynamic mathematical software when teaching mathematics in upper secondary school. The study examines: a) How teachers formulate mathematical problems? b) How they use the experience the students have gained? and c) What use they make of the software s potential? These questions are examined through classroom observations followed up by discussions with the teachers.

The study comprises three teachers and shows that they have very different mathematical experiences and teaching skills. A questionnaire was sent to the teachers prior to the classroom visits to collect relevant background information; e.g., the teachers were asked to describe their teacher training, their view of mathematics and of how a dynamic software could contribute to their teaching.

The results show that the teachers ability to pose thought-provoking openended problems is the most important factor as it significantly influences what the students learn. The way a mathematical problem is formulated could, in conjunction with a dynamic software, actually limit the students achievement.

However, this study confirms that it could also provide an opportunity for students to discover new mathematical relations, draw conclusions, generalise and formulate hypotheses. This could in turn lead to an in formally proving a mathematical relation. A conclusion of the study is that to be successful, teachers need a good mathematical background with a firm knowledge base and an understanding of the software s potential, but they also need the skill to formulate open-ended problems that will enable their students to work successfully with a dynamic mathematical software.