Working With Patterns Through Chess-Based Problems. Strategies and Reasoning Levels of Primary School Students.

The study of patterns has been recognised for many years as setting up the very essence of mathematics. Patterns are connected to all topics in mathematics, so this theme is present throughout the school mathematics curriculum. Among the large number of interesting examples for working on pattern search in elementary school using situations familiar to students, we chose chess because of the relationships shown between this game and different aspects of mathematics. The objectives were to determine the strategies and classify the students' levels of reasoning when working with patterns to solve chess-based problems. A sequence of activities was designed to carry out this task. The sequence presents visual and numerical patterns ordered progressively from a greater presence of visual aspects to a predominance of numerical aspects. The results of this work suggest that chess favours the use of a variety of strategies, some of them even different from those found in previous literature. Students rely on the geometry of the board when working with these particular types of patterns. However, the results show that the level of reasoning is higher in the case of solving numerical patterns.