A survey of 7th grade students' development of functional thinking with a hypothetical learning trajectory on the theme of growing figure patterns

The aim of the research is to examine the functional thinking development of seventh grade students through a hypothetical learning trajectory based on growing figure patterns. In accordance with this aim, the model of the research was determined to be design-based research. The research was conducted with 21 seventh-grade students from a secondary school located in the center of Adana's Seyhan district in the spring semester of the 2021–2022 academic year. The literature search on functional thinking shed light on the formation of assumptions and the selection of tasks and activities for the assumptions. In the literature review made, it was seen that analyzing the physical growth of growing figure patterns is an effective and significant way of improvement in students' functional thinking development. In this context, a hypothetical learning trajectory was designed on the basis of growing figure patterns, and a series of activities were planned to determine how seventh grade students' comprehension of functional relationships could be improved. A teaching experiment consisting of 8 lesson hours over 4 weeks was carried out with 21 seventh grade students in a classroom-based environment using the designed activities. Before and after the teaching experiment, the functional thinking test developed by the researcher, consisting of 19 open-ended questions, was administered among the students participating in the teaching experiment. The difference between the development of functional thinking of the seventh grade students participating in the research before and after the teaching experiment was examined by analyzing the functional thinking test quantitatively and qualitatively. After the analysis during the teaching experiment and the retrospective analysis, the hypothetical learning trajectory was compared to the actual learning of the students and it was revised.The analysis of the data revealed the development of students' functional thinking, and a useful structure of teaching activities was designed for the development of functional thinking in the context of growing figure patterns by formulating how the students' functional thinking improved with the growing figure pattern tasks. As a result of the research, following the teaching experiment, it was determined that the functional thinking of the students improved, and it was seen that growing figure patterns are an effective context in the functional thinking development of students. A beneficial structure for the development of functional thinking in seventh grade students was presented as a result of an analysis of the congruence between the hypothetical learning trajectory and the student's actual learning. Keywords: Functional thinking, hypothetical learning trajectory, growing figure patterns