The field of fractions as a sine-qua-non in upper secondary mathematics

Specialeforsvar ved Mikkel Bülow Tofteng

Vejleder: Carl Winsløw, IND

Censor: Claus Michelsen, IMADA, SDU

Abstract:

The rational numbers and the didactic challenges in relation to rational numbers where considered in order to present the rational numbers in the Danish school system. For the latter the exercises and the curriculum where thoroughly examined. It showed that division of fractions were not present at the exams in the years 2010 and 2015 - 2019 in spite it is a part of the curriculum. In contrast to the curriculum of Lower Secondary School, the curriculum of Upper Secondary Schools showed several usages of the rational numbers and the understanding of the Arithmetics in this regard in relation to the topics of Upper Secondary School. The lack of the pupils’ knowledge will affect their further education.

The thesis examines new Upper Secondary students' knowledge of the rational numbers. The Anthropological Theory of Didactics is used to construct a Praxeological Reference Model to identify the techniques the students possess. Using the reference model, a test was constructed to determine the students' abilities. The test was given to one class in five different Upper Secondary Schools (n = 137) in the beginning of the students’ first school year. It was evident that the students lacked several techniques both practical and theoretical. Especially division of fractions, multiplication of percentages, the denseness of rational numbers and ratios, may be mentioned as extremely problematic. In these categories the students answered at most 30% of the questions correctly.