Räkna med bokstäver! : en longitudinell studie av vägar till en förbättrad algebraundervisning på gymnasienivå

Sammanfattning: The main aim of the study is to create insight into students' algebraic knowledge and the conditions for their algebra learning at upper secondary level. An additional goal is to suggest ways to improve algebra teaching and learning within the Swedish edu­cational system, based on the results from the study. The study builds on an extended research and development project, which are presented in four phases. In the empirical study two cohorts of students were followed during their time of study at one upper secondary school in southern Sweden, and some main factors for success in algebra learn­ing were identified. This part of the study was presented more in detail in my licentiate thesis. The following three phases are described in the three articles, on which this thesis rests. In the second part of the study I reflect upon my development from being a teacher into being a teacher-researcher and what this has meant for my understanding of what happens in the classroom, and in what ways this has changed, especially enhanced, my way of teaching. In the third part, a deepened analysis is made of stu­dents' answers to how a functional relation can be explained. The fourth part is a literature review of recent research of the influence of calculators and other tech­nological tools on algebraic knowledge and skills. All parts of the project are put into one overarching frame, based on the didactical triangle with its main parts: the learning/the student, the teaching/the teacher, and the learning matter/the result of the education. As a background for the study a theoretical framework is used with five main components: mathe­matics and philosophy of mathematics, theories of knowledge and learning, the meaning of symbols, representational forms, and tools for learning. A thorough overview of earlier research in the field of algebra education is given, with a multi-dimensional perspective and with special focus on areas of importance for the study. A range of findings from the different parts of the study are presented and compiled, both on the basis of the theoretical framework and the didactical tri­angle. These results then form the starting point for consideration of significant implications for educational practice in mathematics within the areas: knowl­edge and development, symbols and representational forms, algebra as a strand in mathematics education, technology in mathematics education, and the importance of affective factors. Moreover, some suggestions is given to teachers about different methods and ways for local development projects in schools, and also suggestions for further research.