The rationale for this study emerged from a realization that conventional instructional design approaches for introducing Calculus concepts, based on the logical sequencing and structuring of the concepts, did not adequately attend to or address students’ ways of thinking. The instructional design theory of Realistic Mathematics Education (RME) offered a promising approach for designing learning sequences based on actual investigations of the ways in which students think. This study’s focus was on trialling the process of RME theory-based design using the Fundamental Theorem of Calculus as an example.Applying RME required developing a hypothetical learning trajectory (HLT) while attempting to adhere to methodological guidelines of design research. The series of design experiments have revealed knowledge about student reasoning four main areas of quantifying change, curve sketching, general mathematical reasoning and symbol use. From the study, it is clear that successful adoption of...
