Realistic Mathematics Education (RME) as an instruction design perspective for introducing the relationship between the derivative and integral via distance education

[摘要] ENGLISH ABSTRACT: 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. This was particularly important in a distance education environment where learners depend on instructional texts to make sense of what is being presented, often without support from tutors.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. Curve sketching was prominent in this exercise. Applying RME required developing a hypothetical learning trajectory (HLT) while attempting to adhere to methodological guidelines of design research. In this project, the instructional designer's conceptualization and interpretation of the derivative-integral construct has had the most immediate implications for the study. The line of inquiry has been largely didactic, in that it was framed by a need to establish ways of introducing the teaching of a mathematical concept following instructional design principles. Throughout the project, the instructional design space has been contested, broken down, rebuilt and, ultimately, enriched by the contributions of the expert teachers and the engagement of participating students. The series of design experiments have revealed knowledge about student reasoning in this learning domain in relation to four main areas of quantifying change, curve sketching, general mathematical reasoning and symbol use. The primary contribution of this research has been a deeper understanding of the extent to which RME can be used as an instruction design theory for planning and introducing a distance teaching Calculus unit. From the study, it is clear that successful adoption of the RME theory is influenced and facilitated by a number of factors, including: careful selection of the concepts and mathematical structures to be presented; a team of experts (mathematicians and mathematics subject didacticians) to research, test and develop the learning activities; opportunities for student interactions; and time and resources for effective RME adoption. More involved research is required to get to the stage of the evolution of a local instructional theory around introducing the derivative-integral relationship as expressed in the Fundamental Theorem of Calculus.

[发布机构] Stellenbosch University