Preliminary Design of Learning the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) Using the RADEC Learning Model

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Learning obstacles were found in students who studied LCM and GCF. This research aims to develop an initial design in the form of a hypothetical learning trajectory for LCM and GCF using the RADEC (Read, Answer, Discuss, Explanation, and Create) learning model which is based on obstacles learning findings. This research is part of the design research method. The design research method consists of preliminary design, teaching experiment, and retrospective analysis. The focus of this research is the preliminary design stage. Based on the results, it is known that students have difficulties in solving questions on LCM and GCF material, namely that students cannot use the concepts of LCM and GCF to solve problems, students tend to think that the concepts of LCM and GCF are only factor trees or procedural factorization, and students do not understand the concepts of LCM and GCF. To overcome these learning obstacles, a hypothetical learning trajectory for the LCM and GCF was prepared using the RADEC learning model which was divided into three meetings. The first meeting was about multiples, common multiple, and LCM. The second meeting was about factors, common factors, and GCF. The third meeting was regarding determining the LCM and GCF using prime factorization. Each learning flow from each meeting is described in the form of HLT which consists of learning objectives, learning activities, and student thinking estimates. The theoretical implications in this research are the new findings of HLT LCM and GCF with the RADEC learning model and practical implications in this research are that HLT can be used as a consideration for teachers in designing LCM and GCF learning by paying attention to students' learning trajectories.