Combining the how and why of combinatorics

Master thesis defence by Charlotte Olsen

Abstract

In upper secondary school, combinatorics is treated as a sub-topic of probability theory, and the guidelines even state that combinatorics should only be taught in order to understand the binomial distribution, and combinatorial problems are a means to calculate possible outcomes in a probability space. However, the upper secondary school reform of 2017 introduced the topic of discrete mathematics, which allows for teaching combinatorics as an independent mathematical object, while still functioning as a stepping-stone towards probability theory. This thesis aims to create a teaching design that employs study and research activities in order to support the development of full praxeologies through autonomous student work. The findings in the a posteriori analysis revealed a minor success as two of the five specific answers were partially developed through types of tasks, applied techniques, and the justification of the technique. Based in the data it is possible to conclude that study and research activities promote autonomous development of praxeologies in combinatorics.