Design Research on Mathematics Education: Investigating the Progress of Indonesian Fifth Grade Students' Learning on Multiplication of Fractions with Natural Numbers

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory (HLT) plays important role as a design and research instrument. This HLT tested to thirty-seven students of grade five primary school (i.e.SDN 179 Palembang). The result of the classroom practices showed that measurement (length) activity could stimulate students' to produce fractions as the first level in learning multiplication of fractions with natural numbers. Furthermore, strategies and tools used by the students in partitioning gradually be developed into a more formal mathematics in which number line be used as the model of measuring situation and the model for more formal reasoning. The number line then could bring the students to the last activity level, namely on the way to rules for multiplying fractions with natural numbers. Based on this findings, it is suggested that Streefland's five activity levels can be used as a guideline in learning multiplication of fractions with natural numbers in which the learning process become a more progressive learning

Eliciting Mathematical Thinking of Students Through Realistic Mathematics Eucation

This paper focuses on an implementation a sequence of instructional activities about addition of fractions that has been developed and implemented in grade four of primary school in Surabaya, Indonesia. The theory of Realistic Mathematics Education (RME) has been applied in the sequence, which aims to assist low attaining learners in supporting students' thinking in the addition of fractions. Based on the premise that eliciting and addressing learners' alternative conceptions in mathematics is beneficial in assisting them to improve their understanding, the paper seeks to explore the role that RME plays pertaining to this particular supposition. The paper presents and discusses examples of learners' responses to contextual problems given to them during the course of the instructional activities