This study explored changes in relative achievement over time. It also investigated differences in how two groups of students activate mathematical competencies. The aim of the study was to investigate students’ relative achievement in mathematics over time, and how mathematical competencies can be used to explore differences between groups of students on a non-curriculum based test in mathematics. The study was divided in two parts. Study 1 compared students’ (n=568) relative achievement in two national tests in mathematics (years 3 and 6). Study 1 explored changes in relative achievement between the two national tests as well as differences in relative achievement between the national test in year 6 and the mathematical kangaroo in year 7 (age 13). The study identified, from a sample (n=264) of study 1, two groups of students with high achievements in only one of the tests, the national test in year 6 or the mathematical kangaroo. Study 2 explored how differences between those students relative achievement on the mathematical kangaroo could be explained through activation of mathematical competencies. The results in study 1 show that students undergo large changes, both increases and decreases, in relative achievement between the national tests in years 3 and 6. Study 2 shows how the two identified groups activate the mathematical competencies differently on the mathematical kangaroo. 9% of the students achieve highly in the mathematical kangaroo although they do not in the national test. The study implicates the importance of using non-curriculum bounded tests to identify strength in mathematical competencies among students that not are able to show them through the national test.

This diploma thesis presents the perspective of a future teacher on mathematical contests and their impact on the development of crucial competencies, with special focus on the contest Mathematical kangaroo. The thesis deals with test questions from categories Benjamin and Kadet from 2015. Furthermore, a set of worksheets expounding similar examples that can be found in this contest, is included in the thesis. These exercises are established to serve pupils with inferior results as a preparation for the contest, or for the enlivening of math classes. Solution is illustrated via pictures, sketches, geometrical constructions, tables and verbal comments that should help pupils to better understand the topics.