• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.