Hypothetical Learning Trajectory of Limit and Derivative Based on Realistic Mathematics Education

Abstract

Purpose: The learning trajectory of limits and derivatives found in Calculus textbooks is still conventional and complicated for students. Moreover, it does not involve students to discover the concept. This study developed a Hypothetical Learning Trajectory (HLT) based on Realistic Mathematics Education (RME) for Limit and Derivative with a valid and practical GeoGebra.

Methods: This research used design research that combined the Plomp model and the Gravemeijer& Cobb model. There were three phases, the first was preliminary research of analyzing the needs, curriculum, concept analysis, and finding the literature review. In the second phase, the development or prototyping design was conducted through formative evaluations of self-evaluation, expert validation, and one-to-one evaluation. The last phase was assessment or retrospective analysis where evaluating the learning trajectory implementation was performed.

Results: The research results indicate that the HLT has been fulfilled for being a valid learning method to learn limits and derivatives based on the expert judgments and the evaluation result after it has been implemented instructional either in a one-to-one test or in a small group.

Conclusions: The availability of RME-based LIT on Limit and Derivative materials that meet valid criteria with characteristics, namely student-centered learning activities, and the time provided is sufficient to achieve learning goals.