An exploration of combinatorics and combinatorial geometry from a pedagogical perspective

Abstract

This thesis explores combinatorics and combinatorial geometry and how it can be used in the classroom, with a particular focus on using these sorts of tasks with younger students. There are 4 different types of combinations and 4 formulas for them, which will be presented in the thesis, along with explanations, examples and suggestions for similar tasks. In addition, one of the formulas will be found and proven using generating functions. For the part on combinatorial geometry there will be an introduction to polyominoes, and the polyomino-based game Quadrillion. The gameboard in Quadrillion is made up of 4 squares that essentially can be shaped as half-tetrominoes, and we are interested in finding the different configurations the gameboard can have, in addition to a description on how this can be utilised in the classroom.