Development of relational thinking of fifth grade students: A teaching experiment

The aim of this study is to investigate the development process of relational thinking skills of fifth grade students. Since the study aims to reveal how the students' relational thinking skills develop, teaching experiment design among qualitative research methods was used in the study. The study was held with a total number of six fifth grade students in a middle school in Eskisehir in 2012- 2013 teaching year. Within the teaching experiment design, initially pre-interviews were conducted with students. Then a teaching process, which consist of 8 teaching episodes supporting relational thinking, realized. Afterwards, post interviews were conducted with intend to observe the development. The data were collected with "video recordings", "clinical interviews", "students' work sheets", "researcher's diary" and "students' diaries". The analysis of data was held by considering the three phases consisting of "data reduction", "data display" and "conclusion drawing and verification". The teaching episodes within the teaching process of the study include the activities associated with addition, subtraction, multiplication and division which could improve students' relational thinking skills. As a result of these activities it is determined that students conceptualized the properties of the operations by using relational thinking skills, focused on the additional relationships among addends, minuends and subtrahends in the context of addition and subtraction, and focused on multiplicative relationships among multipliers, dividends and divisors in the context of multiplication and division instead of the result oriented approach. As a result of the analysis of the study's pre and post-interviews, it is observed that all of the students' relational thinking skills have developed. It is determined that there was a mutual interaction among the development of basic arithmetical concepts and development of the relational thinking skills in this development process. It was seen that students conceptualized the concepts associated with operations such as addend, sum, minuend, subtrahend, difference, multiplier, product, dividend, divisor and quotient, and also even if they can't express the relationships among them formally they can use these relationships effectively. It was determined that properties of operations which take part in the sixth grade mathematics curriculum can be learned in the context of relational thinking in the fifth grade. It was also seen that students understood the equal sign not only an announcement of the result of an operation but also a symbol of a mathematical equivalence which provides to relate among numbers, shapes and expressions. In the study it is inferred that emphasizing the basic properties of numbers and operations which is in the center of the relational thinking be determinative to find out the unknowns while developing the procedural skills.