The Thinking Process of Students Using Trial and Error Strategies in Generalizing Linear Patterns

Abstract

Patterns generalization learning at the junior high school is more emphasis on the generalization of linear patterns. One problem in generalizing linear patterns is that students do not know the process of using trial and error strategies to generalize linear patterns. For this reason, the purpose of this study was to analyze the thought processes of 2 junior high school students who succeeded in generalizing linear patterns using trial and error strategies. The results show that there are two trial and error strategies that can be used to generalize linear patterns, namely: (1) Trial and error strategy by looking at the relationship of quantity consists of three steps. The first step is called relating, namely, the subject connects between the first term, the term in question, and difference. The second step is called searching, where the subject finds similarities by using addition and subtraction operations to obtain the n^th term formula. The third step is called extending; the subject expands the pattern into more general structures by looking at the relationship between quantities. (2) Trial and error strategy by looking at patterns that consist of three steps. The first step is called relating, namely, the subject connects small positive integers by using arithmetic operations to obtain the first term and the second term. The second step is called searching, where the subject finds similarities by finding the formula for the first, second, and third terms. The third step is called extending, where the subject expands the pattern into more general structures by looking at the pattern that applies to the first, second, and third terms.