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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 the RME is influenced by:careful selection of the concepts to be presented; a team of experts to research, test and develop the learning activities; opportunities for student interaction and resources.

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Rita Kizito has spent the last thirty-two years in different educational sectors , beginning as a highschool teacher, branching into teacher training and NGO work, then finally into curriculum design.She is now working as a Teaching and Learning Specialist at the Faculty of Natural Sciences , theUniversity of the Western Cape, South Africa.

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