Progression of algebraic discourse in school years 2 to 8
Sammanfattning: In contemporary educational settings algebra is considered to be of vital importance for student’s continuation to more advanced studies in mathematics, thereby affecting their chances for future education and employment. However, a substantial number of students do not benefit from the algebra presently taught in schools and fail to use algebraic reasoning. The purpose of this study was to enhance the understanding of how classroom discourse supports the students' learning of algebra. The study rests on two basic assumptions, firstly mathematics is regarded a discourse, secondly teachers’ instruction during lessons and the textbooks used in school are envisioned as potential means for supporting students’ algebraic development. The issue of learning was examined through a focus on progression of algebraic discourse in mathematics textbooks, for grade levels 2, 5 and 8. Furthermore, in order to study classroom discourse more broadly, the algebraic discourse of teachers’ lesson introduction talks in grade 8, were examined in relation to the algebraic discourse of textbooks. The foundation for the analyses was a discursive perspective and a communicational theory depicting algebraic development as a hierarchical structure of consecutive discursive levels. The mathematics textbooks’ and teachers’ discourses were analysed regarding the presence of signifiers of algebraic objects, more informally unknowns, and concerning four measures of discursive complexity. Mean value of the number of words constituting the signifier of algebraic object, signifier length equal to or exceeding two words, signifier length equal to or exceeding six words, and as amount of signifiers of algebraic objects of a higher discursive level.The results show that there were signifiers of algebraic objects present in all three mathematics textbooks and in teachers’ lesson talks. The number of these signifiers of algebraic objects in the mathematics textbooks grew substantially between grade 2 and 5 with a moderate increase between grade 5 and 8. Also the mean value of the number of words constituting these signifiers of algebraic objects grew between grade 2 and 8, as well as the amount of signifiers of algebraic objects consisting of six or more words. Complexity measured as amount of signifiers of algebraic objects of a higher discursive level grew from grad 2, were there were no such signifiers of algebraic objects, to grade 8 were there were 17 % of the total amount. Thus, the analyses of the textbooks exhibit a progression of increasing complexity in terms of the measures focused in this study. In comparison, the complexity of teachers’ discourse is lower than the discourse of any of the mathematics textbooks concerning mean value of signifier length. The amount of signifiers of algebraic objects of a signifier length equal to or exceeding two words were comparable with the amount in the grade 2 mathematics textbook. Concerning signifier length equal to or exceeding six words the amount in the teachers’ lesson talks were in the same order of size as the corresponding measure in the mathematics textbook of grade 5.
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