THE HYPOTHETICAL LEARNING TRAJECTORY OF ENUMERATION RULES WITH ISLAMIC VALUES

Abstract

A context with Islamic values lies in can be used as a starting point in learning mathematics. The challenge is how teachers can deliver, formulate, and connect the mathematical content and the Islamic values in the learning activities. One of the learning approaches that can solve that challenge is Realistic Mathematics Education (RME) by implementing context as one of the activities. This study aims to design hypothetical learning trajectories (HLT) for supporting students in learning the rules of enumeration with the RME approach based on Islamic values. This study uses the first phase of design research (DR) methods. The first phase, namely preliminary design. The HLT is developed in this phase and will then be tested on students in experimental design, and the implemented results are analyzed in the retrospective analysis. Researchers began the study with a literature review, then obtained data about students' difficulties in the enumeration (counting) rule. Based on the review, researchers formulated activities into learning procedures and expected students and teachers’ responses, called HLT. The HLT of enumeration rules on data content with RME based on Islamic seen from the perspective of the four emerging modeling levels. At the first level – the 'situational level' – students explore the realistic context of determining the possible route to the mosque. The second level is the 'referential level' where the selection rules are used as a starting point for learning the concept of probability. At the third level – the 'general level' – students use diagrams to generalize the possible outcomes of an experiment and develop an understanding of multiplication rules. Finally, students develop their informal knowledge at the 'formal level' into formal concepts of multiplication rules.