Functional thinking ways in relation to linear function tables of elementary school students

One of the basic components of algebraic thinking is functional thinking. Functional thinking involves focusing on the relationship between two (or more) varying quantities and such thinking facilitates the studies on both algebra and the notion of function. The development of functional thinking of students should start in the early grades and it should be improved gradually and extended over a long period of time. Also, patterns represented by function tables are the tools which support the early development of functional thinking. In this regard, the aim of this study was to investigate the functional thinking ways in the early grades, particularly those of elementary school fifth grade students through linear function tables. The study data were collected via task-based interviews conducted with a total of four elementary school fifth graders. Consequently, it was found that the four fifth grade students thought on covariation while working with the linear function tables. It was further obtained that the students were able to discover the correspondence relationship and generalize this relationship. The results of the study also revealed information about the reasoning abilities of the students, in other words about their alternative ways of thinking in generalizing the correspondence relationship.