| Abstract [eng] |
Mathematics learning is one of the most complex areas, requiring not only procedural skills but also conceptual thinking, logical reasoning, and abstract understanding. A particularly challenging stage is the learning of rational numbers in the sixth grade, when students move from natural numbers to broader sets of numbers. This transition creates difficulties related to understanding new concepts of magnitude, direction, signs, and different numerical representations; therefore, teaching the addition and subtraction of rational numbers remains a relevant issue in mathematics didactics. Students’ learning difficulties in this area may affect the further development of algebraic thinking as well as later achievement in mathematics. The learning difficulties of sixth-grade students in the addition and subtraction of rational numbers are analysed by applying a mixed research strategy that combines quantitative and qualitative data, while the effects of different teaching methods are evaluated within the same group of students. The study is not limited to measuring achievement alone, but also seeks to reveal students’ experiences, the strategies they applied, their reflections, and the difficulties that remained. Research object: students’ learning difficulties and the strategies used to overcome them when teaching the addition and subtraction of rational numbers in the sixth grade. Research aim: to investigate strategies for overcoming sixth-grade students’ difficulties in learning mathematics while teaching the addition and subtraction of positive and negative rational numbers. Research objectives: 1. To analyse scientific literature on sixth-grade students’ learning difficulties in learning the addition and subtraction of rational numbers and the strategies for overcoming these difficulties. 2. To develop a research methodology enabling the identification of students’ learning difficulties. 3. To reveal the effects of different teaching methods on sixth-grade students’ understanding of the addition and subtraction of rational numbers and on overcoming their learning difficulties. Data collection methods: analysis of scientific literature, classroom observation, mathematics achievement tests, student reflection, teacher reflection, and semi-structured interviews with students. A quasi-experimental method was applied in this study in order to evaluate the effects of new teaching methods on students’ achievement. The study examined the effects of traditional teaching, the number line method, and the gamification method on students’ achievement and on overcoming learning difficulties. The empirical study was carried out in one educational institution, in one sixth-grade class of 19 students, without random sampling. Data on students’ achievement were collected before and after the intervention using mathematics achievement tests created by the author of the study. Data analysis was conducted using paired t-tests in order to evaluate changes between measurements. The study was carried out in accordance with ethical requirements, and participants’ consent was obtained. Data analysis methods: descriptive statistics and correlational analysis. Based on the obtained results, it was found that traditional teaching is useful as an initial stage for consolidating rules and procedures; however, it is not sufficient for developing a deeper understanding of rational numbers. When the number line method was applied, students’ results improved significantly, and qualitative data revealed a better understanding of number magnitude, direction, and the logic of operations. The highest achievement was reached after the application of the gamification method, which not only increased the overall mean score but also promoted students’ engagement, motivation, and collaboration. This shows that active and game-based forms of teaching effectively contribute to students’ deeper understanding and the success of the learning process. The study I conducted presents an analysis of students’ learning difficulties and effective teaching methods related to the topic of fractions and mixed numbers. Based on quantitative and qualitative data, it was found that the greatest challenges arise precisely in this area. Students often had difficulty finding common denominators, confused mixed numbers with improper fractions, solved tasks more slowly, avoided operations with fractions, and frequently made mistakes when choosing the sign of the answer. The study also revealed that the most effective teaching approach is not a single method, but rather a combination of methods. This effective set of methods includes structured presentation of rules, the use of visual supports, answer checking, error analysis, and gamified elements. These methods help students better understand complex concepts and encourage them to participate more actively in the learning process, reducing the number of errors and improving the quality of results. The research results may be highly useful in the practice of mathematics teachers, especially when planning the teaching of the addition and subtraction of rational numbers in the sixth grade. They make it possible to select more effective teaching strategies and to combine traditional and innovative teaching methods more efficiently. In addition, the findings may help improve educational practice, develop appropriate teaching materials, and plan differentiated support for students who experience difficulties in learning mathematics. This contributes to strengthening students’ achievement and motivation by creating a favourable learning environment. The thesis consists of an introduction, theoretical and empirical parts, conclusions, a list of references, and appendices. The theoretical part analyses the importance of mathematics learning, the characteristics of learning rational numbers, students’ learning difficulties, and the traditional and innovative teaching methods important for overcoming these difficulties. The empirical part presents the research methodology, the organisation of the study, and the methods of data collection and analysis. The third chapter presents the research results and their analysis. |
