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Abstract
A learning trajectory (LT) for teaching the least common multiple (LCM) and the greatest common factor (GCF) using realistic mathematics education (RME) approach was developed to improve the students’ mathematical reasoning abilities. The cycle of design research namely preparing for the experiment, conducting the experiment, and retrospective analysis were applied in the development processes. The subjects of the research were 26 fifth grade students at a primary school in Padang, Indonesia. The method of data collection were videotaping, interviews, observations, and analysing the students’ worksheets. The validity and practicality of the LT were evaluated trough expert judgements, one-to-one and small group try out, and field test. The results show that the LT reached the criteria of validity as it fulfilled the state of the art and characteristics of RME. The LT also worked as intended in which the students could reinvent the concepts of the LCM and the GCF by themselves after solving a series of the contextual problems provided in the LT. It indicated that the LT satisfied the criteria of practicality. Finally, we discovered that the LT effective in improving the reasoning abilities of the students.
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