Examination of seven grade students pattern generalization processes and prefe

Abstract

Generalization is a very important element of mathematics. It is the basic building block of mathematical thinking, starting from counting to functional thinking. It is important for the development of mathematical thinking that the students understand why and how the task is performed instead of mechanically performing the generalization process. In this study, the generalization processes of patterns and the strategies preferred by seventh-grade middle school students in the process of generalizing patterns were examined. The qualitative research design was taken as a basis for collecting, analyzing, and interpreting the data. The study group consisted of 152 seventh-grade students selected by a simple random sampling method. The Pattern Test developed by the researchers was used as a data collection tool. According to the results of the study, it was observed that most of the students could not make algebraic generalizations and remained at the level of arithmetic generalization or immature induction. Students have been determined to prefer iterative and modelling for finding terms close to the pattern, iterative multiplication with a difference as the most favoured strategy in the middle step, and iterative multiplication with a difference and functional strategies for determining terms far from the pattern. The study showed that the participants were successful in identifying the components of the pattern, one of the steps of pattern generalization process, but the number of students who recognized the common feature. The results showed that students generally used different strategies in solving the same problem and did not stick to a single strategy.