Ortaokul öğrencilerinin doğrusal örüntüleri genellemelerinin incelenmesi

The purpose of the present study was to explore sixth, seventh, and eighth grade students' generalizations of patterns using arithmetical generalization, algebraic generalization, and naïve induction. In addition to studying their generalization process, the study also focuses on how this process of generalization differs according to their grade level. The study employed a qualitative case study design. The data were collected from five sixth grade, four seventh grade, and five eighth grade students during the spring semester of the 2015-2016 academic year. Data were collected through the Pattern Test and individual interviews. The findings revealed the use of four generalization approaches: (i) algebraic generalization strategies only, (ii) a combination of arithmetical generalization and algebraic generalization strategies, (iii) a combination of arithmetical generalization and naïve induction strategies, and (iv) a combination of arithmetical generalization, algebraic generalization, and naïve induction strategies. It was found that the combination of arithmetical generalization and algebraic generalization was the most frequent generalization approach, while the combination of arithmetical generalization, algebraic generalization, and naïve induction was the least frequent ones used by the students in all grade levels in this study. Moreover, the use of algebraic generalization strategies only was observed by the sixth graders only. It was also seen that sixth, seventh, and eighth-grade students used arithmetical generalization strategies in order to find near terms of the pattern. In order to find the far terms or the general term, they either used algebraic generalization strategies or naïve induction strategy.