An Instructional Sequence Triggering Students’ Quantitative Reasoning during Learning of Quadratic Functions

Abstract

The purpose of this study is to design an instructional sequence triggering students’ quantitative reasoning in the process of learning quadratic functions. The study was conducted as a design-based research, following a cyclical process. The study consisted of three phases of the design, implementation, and analysis phases and the implementation phase consisted of two consecutive cycles. While the first cycle was carried out to evaluate the success of the instructional sequence in supporting student learning in a class with ten 10th students, the second cycle was carried out with two 10th grade students. The video recordings taken during the teaching experiments, the researchers’ observation notes, the clinical interviews, and the students’ reflective journals constituted the data sources of the study. In the data analysis process of the study, the constant comparison method simultaneously conducted with the data collection process was used and also a retrospective analysis of the teaching experiments data was conducted after completing the cycles. Because the tasks were grounded in real-life contexts involving dynamic situations, they contributed to the students’ understanding of functional relations and helped them construct the idea of covarying change in the functions. It is suggested that mathematics teachers revise and use the instructional sequence according to their own classroom context with the aim of supporting their students’ understanding of quadratic functions.