# Generalization of patterns: the tension between algebraic thinking and algebraic notation

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## Abstract

This study explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. We discuss students' emergent algebraic thinking and the variety of ways in which they generalize and symbolize their generalizations. Our results indicate that students' ability to express generality verbally was not accompanied by, and did not depend on, algebraic notation. However, participants often perceived their complete and accurate solutions that did not involve algebraic symbolism as inadequate.

## Keywords

Elementary School School Teacher Accurate Solution Elementary School Teacher Algebraic Thinking
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