# The understanding of infinity in primary school

Irena Gole (2013) The understanding of infinity in primary school. MSc thesis.

## Abstract

Infinity is a concept that occurs in a variety of discussions, not only in mathematical, but also in the philosophical, physical and religious ones. The concept is often referred to an infinite set with such a large number of items that that it is impossible to count them. A number of paradoxes occur in connection with infinity (Hotel Infinity, the Barber, Achilles and the tortoise, dichotomy, Galileo's paradox, etc), showing a contradiction, since it is difficult to understand something which opposes our intuition. This thesis deals with the understanding of infinity with primary school pupils. The pupils find infinity interesting, they think about it intuitively, linking it to various contexts, especially with everyday life. In mathematics they come across the concept of infinity in arithmetic (numbers, number of solutions to inequalities, etc.), geometry (line, plane, etc.), but their perception of this concept depends to a large extent on the type and content of tasks. The understanding of infinity cannot be explored in one, but in various contexts. Since the concept is so complex, the understanding is developed over time in students’ mental structures. Students' understanding and interpretation of the concept of infinity depends on the context in which the term is expressed (numeric, geometric), the type of an infinite set (infinitely many, infinitely close) and the way of presenting the problem. The empirical part presents the understanding of the concepts of infinity with primary school pupils. A test was designed which verified students' understanding of the concept of infinity in different contexts. The aim was to explore how the fifth and ninth graders understand the different types of infinity, the differences between them, and which type of tasks about infinity presents the most problems and which infinity the students used in solving various infinity problems. Another interest was to learn the differences in the understanding of infinity between the ninth graders, according to the homogeneous group (level) they attend in mathematics. The results showed that the ninth graders are more successful in solving the tasks than the fifth graders. The fifth graders, as well as the ninth graders were the most successful in the tasks that were connected to concrete examples from everyday life, while they had the most difficulties with the tasks that checked the application and understanding of the potential and actual infinity. It turns out that the understanding depends on the type of the task and the context in which it is introduced. Taking into account the results of research, knowledge of the different types of infinity and the stage of students’ development, some recommendations have been created for teachers to provide guidance for teaching selected topics on infinity in primary school.

Item Type: Thesis (MSc thesis)
Keywords: infinity, understanding of infinity, types of infinity, mathematics lessons, learning about infinity
Number of Pages: 121
Language of Content: Slovenian
Mentor / Comentors:
Mentor / ComentorsIDFunction
izr. prof. dr. Tatjana Hodnik ČadežMentor
Institution: University of Ljubljana
Department: Faculty of Education
Item ID: 1963
Date Deposited: 19 Dec 2013 07:22