Relational thinking: The bridge between arithmetic and algebra

Ayhan Kızıltoprak; Nilüfer Yavuzsoy Köse

Vol. 10 No. 1 (2017) IEJEE

Relational thinking: The bridge between arithmetic and algebra

Ayhan Kızıltoprak
Nilüfer Yavuzsoy Köse

Published October 2, 2017 | Pages: 131-145 | Views: 1995

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Abstract

The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students by means of clinical interviews and teaching episodes. For observing the development of relational thinking, pre and post clinical interviews were also conducted before and after the eight-session teaching experiment. Qualitative analysis of the research data revealed that the relational thinking skills of all the students developed. It was also found that there was an interaction between the development of fundamental arithmetic concepts and relational thinking; that the students developed concepts related to arithmetical operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividend, divisor and quotient. Moreover, students were able to use these concepts effectively although they failed to provide formal explanations about the relations between them. In addition, the students perceived the equal sign not only finding a result but also as a symbol used to establish a relation between operations and expressions.

<p>The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students by means of clinical interviews and teaching episodes. For observing the development of relational thinking, pre and post clinical interviews were also conducted before and after the eight-session teaching experiment. Qualitative analysis of the research data revealed that the relational thinking skills of all the students developed. It was also found that there was an interaction between the development of fundamental arithmetic concepts and relational thinking; that the students developed concepts related to arithmetical operations such as addend and sum; minuend, subtrahend and difference; multiplicator and product; and dividend, divisor and quotient. Moreover, students were able to use these concepts effectively although they failed to provide formal explanations about the relations between them. In addition, the students perceived the equal sign not only finding a result but also as a symbol used to establish a relation between operations and expressions.</p>

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Keywords

Mathematics teaching, Secondary school students, Relational thinking, Equal sign, Teaching experiment

Affiliations

Ayhan Kızıltoprak

Turkey

Nilüfer Yavuzsoy Köse

Anadolu University, Eskisehir, Turkey

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How to Cite

Kızıltoprak, A., & Yavuzsoy Köse, N. (2017). Relational thinking: The bridge between arithmetic and algebra. International Electronic Journal of Elementary Education, 10(1), 131–145. Retrieved from https://iejee.com/index.php/IEJEE/article/view/305