This paper considers year eleven students' solutions of a specific task, which includes both a numerical part and a generalization of the task context that needs a transition from arithmetic to algebra. We investigate if students can solve the given problem, explain a solution and justify why the generalized problem always can be solved. Students prefer to explain in rhetoric rather than in symbolic algebra. Seven different ways of explaining are traced among the written answers. Few students are able to give an acceptable justification for the solution of the generalized problem, even after a course including work with this kind of problem. There are signs of students being unfamiliar with meta-cognitive activity.

The article discusses concept maps and thinking maps as cognitive and metacognitive tools. It is a goal to create an overview and coherence of actual knowlegde on different areas of mathematics, and use these as tools to enhance learning. The concept of equation is treated as an example, the article also outlines practical use of conceptual maps at student level and for teachers.

In a longitudinal study I follow the first group of students aiming to become teachers in mathematics and science for compulsory school, grades 4-9. The research focus is the students' development of concepts in mathematics and mathematics education.

Teacher education is meant to be research based and many teacher educators try in different ways to achieve this aim also for the school practice during education. We report on an experiment to design a new form for inclusion of research during practice. A group of student teachers have during their fifth semester carried out interviews with pupils. The classroom observations and interviews take their starting point in data that have been collected in other parts of a larger ongoing research project. The students transcribe, analyse and report their results in written essays. We will describe the design, its results and evaluation. The theoretical framework used is the model for teacher competencies by Niss [1]. The research questions in the paper are (1) ‘In what ways is it meaningful to involve student teachers during practice in a research project?' and (2) ‘What kind of elements of learning do the students perceive in such a situation?'

In the department of mathematics of the Luleå University of Technology in Sweden, a dynamic model for the education of doctoral students and guidance of supervisors in research groups has been developed and applied for several years now. Presently groups in mathematics as well as a group in mathematics education are working according to this model and treated in the same way. Moreover, both the students and the supervisors get some education and experience also in elements, which usually are not included in more traditional models for supervision in the mathematical sciences in Sweden. In this paper, we describe our model as well as some experiences of it. Moreover, the results of a questionnaire addressed to and answered by all doctoral students (both finished and still in the program) are presented, evaluated and compared with some related investigations in Sweden. We claim that the students in general are very satisfied to be supervised and guided in this way. In principle, there have been no cases of dropping out of the Ph.D. programs, students obtained their degrees within the stipulated time and the careers after the studies have been successful. We hope that this positive experience will stimulate other universities to test and evaluate our model (or relevant parts of it) under different conditions.

The teachers in this study are participants in the LCM1- (Learning Communities in Mathematics) project run at Agder University College. The project emphasises the development of communities of teachers and researchers focused on inquiry in mathematics and teaching. This paper deals with a well-planned lesson in an eleventh grade class in a Norwegian upper secondary school. We will present data that illustrate how the teachers intervened to reach certain goals that had been identified through the planning process. These interventions identified discourses, which showed that there was a discrepancy between how the teachers interpreted and used a certain word for a mathematical concept and how the students interpreted the same word. Our findings illuminate common challenges faced when trying to build a community of inquiry in the classroom.

Students' beliefs and attitudes towards mathematics teaching and learning is the focus of the study described in this paper. Some preliminary results from research carried out in Norway in 2005 are given, which focus on first year students in upper secondary school. The answers from the ninth grade students in 2005 are briefly compared with students' responses from 1995 when corresponding data was collected within the KIM project in Norway. Both of these studies use a questionnaire elaborated in 1995. Some of the aspects related to a similar study amongst Estonian students, that will take place in spring 2006, are also discussed.

The article focuses on describing a theoretical framework, which can be applied to analyse the teaching and learning processes that occur in the classrooms as seen from the student's and the teacher's point of view. This theoretical framework can be used to analyse teaching and learning processes in general, but the authors apply it to teaching and learning processes in algebra. More specifically, they use it to analyse the quadratic functions and equations as an object of learning and the way in which the forming of this object of learning during classroom lessons influences the students' learning.