25. august 2014

Gymnasiealgebra i et historisk perspektiv - Matematiske organisationer i gymnasiealgebra

Gymnasiealgebra i et historisk perspektiv - Matematiske organisationer i gymnasiealgebra [2,41 MB]

IND's studenterserie nr. 36. Kandidatspeciale. Matematik.

Mariam Babrakzai Zadran, Marts 2014

Vejleder: Carl Winsløw


High school algebra appears in the form of algebraic expressions and manipulations thereof in order to solve equations. The principles associated with these expressions and their manipulation are explained using implicit and explicit conventions (calculation rules) presented without explanation. This is partly due to the fact that mathematical textbooks primarily emphasize an algebra in which algebraic rules are presented solely on a practical level, and theory is omitted. This gives rise to a number of problems for students, when they need to explain and justify their mathematical practice with respect to algebraic expressions. Based on investigations of various perspectives on algebra, an epistemological reference model for high school algebra with special attention to the justication of the manipulation of algebraic expressions is proposed. The anthropological theory of didactics forms the theoretical basis for the proposed model. This theory is used to analyze algebra as a scientic discipline from a historical perspective and as an academic subject as it manifests itself in curricula, textbooks and high school exam questions. The analysis is performed with the intention of, firstly determining which mathematical organizations the students are expected to be capable of performing with regard to algebraic exercises and, secondly identifying possible and actual correlations between these organisations. The historical perspective of algebra as a scientific discipline will in particular be used to analyze the mathematical knowledge to be taught, as formulated in curricula and textbooks. This thesis also contains a small empirical investigation (diagnostic test) of students' command of techniques and technologies used for solving algebraic exercises.