Patterns as learning environment for learning mathematics

The thesis is about patterns in mathematics and their role in learning mathematics in lower secondary school. The thesis consists of two parts, a theoretical and an empirical one. In the theoretical part we describe what patterns in everyday life are. Then we consider in greater detail the patterns as a means in school mathematics. We define patterns as a sequence of objects together with perceived regularity among them. We classify patterns according to two criteria: the type of objects and the type of regularity. The typical objects in patterns are numbers, geometric shapes, arithmetic expressions. These objects give rise to arithmetic, geometric, and operational patterns. Regarding the regularities we consider repetitive, linear, quadratic, and recursive patterns. We consider also patterns based on geometric transformations and tilling of the plane. The main topic of the theoretical part is the role of patterns in school mathematics. We describe several levels of understanding patterns, ranging from the perception of regularity, continuation, prediction, and expressing generality. Using these classifications we reviewed the Slovenian mathematics curriculum and textbooks for grade 8. Finally, we considered some interesting learning environment, in which patterns can be developed. In the empirical part we study whether and how mathematics teachers use patterns in teaching mathematics. To find out their point of view we devised a questionnaire in which they compared pattern based tasks with other introductory tasks into various topics