Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model

The aim of the research is to support students in constructing an array model as a bridge from their informal knowledge to the formal one in understanding the part-whole relation concept. The part-whole relation concept is important for students to reason about multiplication of fractions. Realistic Mathematics Education which is in Indonesia adapted as Pendidikan Matematika Realistik Indonesia (PMRI) is used as an approach in designing a series of lessons. For this purpose, hypothetical learning trajectory (HLT) became the base for conducting a teaching experiment and designing its learning materials. The research was conducted in the fifth grade of SD Al Hikmah Surabaya, an elementary school in Indonesia, with five students as the participants. The collected data were qualitative data in the form of students’ written works and the transcript of video recording during the lesson. The data were analyzed retrospectively by confronting the conjecture of students’ thinking in the HLT with the fact in the teaching experiment. The result of the research shows that most students could use the contextual problem in promoting their ability on constructing their own array model to reason about part-whole relation