# 7TH AND 8TH GRADE STUDENTS` GENERALIZATION STRATEGIES OF PATTERNS

## Abstract

Pattern is a combination of shapes, sounds, actions or symbols in a specific order (Souviney, 1994). The definition of mathematics which is stated as pattern and system science (Goldenberg, Cuoco and Mark, 1998) and the universal language which is used to understand the relationships among these (Olkun and Toluk-Uçar, 2006) shows the importance of pattern in mathematics. Pattern is one of the main concepts that contribute to comprehend mathematical concepts, recognize mathematical relationships and interpret them correctly (Burns, 2000). Therefore, it is important to know the strategies that students used to reach generalization in patterns and how they think in this process in terms of teaching mathematics. The purpose of this study is to describe 7^{th} and 8^{th} grades students` ways of thinking related to pattern and investigate the generalization strategies. This research was carried out total 8 students attending the teaching program at 7^{th} and 8^{th} grades in a primary school in İstanbul in the term of 2012-2013. Of these participants, 4 were at 7^{th} grade and 4 were 8^{th} grade. Open ended 4 problems related to patterns were used as data collection tool. Besides, semi-structured interviews were made with the aim of exposing how students think while solving these problems. The collected data was classified through the generalization strategies in the related literature. As a result of the study it is seen that most of the students use guess and check or explicit strategies whereas few of them apply contextual and only one use addictive strategy. In addition, addictive strategies are usually used in near generalization whereas explicit strategies are used in far generalization.

**Keywords: **Pattern, generalization strategies, 7^{th} and 8^{th} grade students

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