Initial diagnosis of pupils' knowledge of natural number division on entry to the secondary school

This thesis aims to conduct a conceptual analysis of the knowledge and skills that pupils are expected to have at the end of primary school in order to understand the topic of divisibility of natural numbers. The first part focuses on the propaedeutics of divisibility and on divisibility itself within the primary school curriculum. I examined commonly used primary school textbooks to identify suitable tasks that could serve as a basis for developing a diagnostic test designed to determine whether sixth-grade pupils possess the expected knowledge and skills. The second part of the thesis is practical. It describes the conditions under which pupils took the diagnostic test, the correct solutions to the tasks, the approaches pupils chose, and what these solutions may reveal about their understanding of the topic. The final section discusses the diagnostic test in relation to pupils' work and proposes possible modifications of the tasks based on insights gained from the pupils' solutions. An important component of this work is the qualitative analysis of pupils' approaches to individual tasks. The findings indicate that pupils entering lower secondary school demonstrate a solid understanding of multiples of natural numbers and can apply this concept in concrete contexts. They are less consistent in...