Algebra in upper secondary mathematics: a study of a selection of textbooks used in the years 1960-2000 in Sweden
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
The research interest in this licentiate thesis is the development of school algebra in the Swedish upper-secondary school. To be more precise, the notion of school algebra, in the period 1960-2000, is described and analyzed through the study of mathematics textbooks and their revisions as a consequence of curricular reforms. Thus a historical-epistemological perspective on the teaching of mathematics is taken. The methodological approach taken in this study is inspired by phenomenography and hermeneutics. The focus is on the treatment of algebra for Natural Science students in their first year of the upper-secondary school in Sweden. An analysis of two sets of textbooks is presented. The analysis is concentrated on the algebraic content as it was presented by the textbook authors, including definitions, descriptions, worked examples and exercises for students. The results constitute a characterization of algebra in school mathematics over time. Three periods were identified, called the ‘pre-New Math', ‘New Math' and ‘post-New Math' periods. In the pre-New Math period (until the early 60s), algebra was a separate school subject which focused on skills in the manipulation of algebraic expressions. The New Math reforms started a gradual integration of algebra with other mathematical subjects, science and everyday life. The New Math algebra can be characterized as ‘abstract algebra' where, for example, numbers were studied as ‘number structures' or sets closed under certain operations (groups, rings, fields). This ‘abstract-algebraic' approach was abandoned in the post-New Math period in favor of a stronger integration of the study of numbers with geometry and applications; especially, applications in everyday life, using algebraic tools such as literal expressions, equations and their formal manipulation, emerged. The significance of this research work is in its contribution to the existing knowledge on the teaching and learning of algebra. The study can serve as a profound background for teachers to plan their teaching of algebra. Moreover, since the study highlights the role of algebra in different mathematics curricula, it points to aspects of importance for reform work in the future. The research in this thesis is inspired and motivated by some preliminary studies on algebraic thinking by the same author (see the preface).
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2006. , 157 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2006:33
Research subject Mathematics Education
IdentifiersURN: urn:nbn:se:ltu:diva-18350Local ID: 8218f940-9fea-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-18350DiVA: diva2:991357
Godkänd; 2006; 20070109 (haneit)2016-09-292016-09-29Bibliographically approved