# The Strategies of Using the Generalizing Patterns of the Primary School 5th Grade Students

## Article excerpt

Abstract

The main purpose of this study is to determine the strategies of using the generalizing patterns of the primary fifth grade students. The practice of this research is conducted on twelve students, which have high, middle and low success levels. Task-based interviews and students journals are used as the tools for data collection. For the analysis of the data, a classification method including "data reduction", "data display" and "drawing conclusion and verification" are used. At the end of the research, it is seen that the visual and numerical approaches are adopted in the generalization of patterns and the visual approach is made easy for generalization, as well. In generally, the present strategies in the generalizing of patterns are also taken into account of near or far generalizing. The recursive strategies are used in the near generalizing. However, the explicit strategies are determined in using far generalizing.

Key Words

Elementary, Mathematics Education, Pattern, Generalization.

A systematic combination of geometric shapes, sounds, symbols, or actions is defined as a pattern (Souviney, 1994). According to Guerrero and Rivera (2002), a pattern is the rule between the elements of a series of mathematical objects which are constructed. It is defined by Olkun and Toluk-Uçar (2006) as a system of repetitious and orderly arranged objects or shapes. Also, Papic and Mulligan (2005) defined a pattern as a spatial or numerical regularity. According to structures and presentation styles, patterns can be combined in two groups as repeating and changing (Olkun &Yesildere, 2007). A pattern is a key concept for understanding of mathematical knowledge and concepts. Pattern studies are the basis for understanding of the system and logic of mathematics and the observing of mathematical relationships (Burns, 2000). Mathematical expedition and number sense for children have been developed by patterns (Reys, Suydam, Lindquist, & Smith, 1998). Especially, a pattern is an essential element of mathematical development for young children and also a central construction of mathematical inquiry (Waters, 2004). The mathematical knowledge and skills of young children develop with the process as counting, comparing, classifying, measuring, representing, estimating, and symbolizing. But patterns form a basis to build these mathematical efficiencies (Fox, 2005). Pattern activities performed at kindergarten level have important roles for forming of the basis of algebra. In other words, the studies with patterns and the relationships between patterns are a prerequisite and a basis for developing. In the beginning, the introduction to algebra with patterns enables the difficulties for formal algebra (Resnick, Cauzinille-Marmeche ve Mathieu, 1987 cited in Threlfall, 1999; Orton & Orton, 1999; Zazkis & Liljedahl, 2002; Orton & Orton, 1994; Herbert & Brown, 1997). So, it is necessary to have previous experiences with patterns for developing algebraic thinking and concepts. Generalization, which is the means of communication and the tool of thinking, is the basic for the development of mathematical knowledge and the center of mathematical activities. National Council of Teacher of Mathematics (NCTM; 2000) standards call for generalization as one of the main goals of mathematical instruction. A pattern is an essential step for the formation of generalization. It can be seen that the generalization is a basic structure of algebra and patterns are the basic structure of generalization. Jones (1993 cited in Hangreaves, Shorrocks & Threlfall, 1998) implies that the generalization is the principle of algebra and the search of pattern is the first step for generalization. Also, Kaput (1999) defines algebra as "formation of patterns and constraints and the generalization." According to Kieran (1989 cited in Radford, 2006), the generalization of a pattern as a route to algebra rests on the idea of a natural correspondence between algebraic thinking and generalizing. …

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