Dede de Haan
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Supporting Fifth Graders in Learning Multiplication of Fraction with Whole Number Khairunnisak, Cut; Amin, Siti Maghfirotun; Juniati, Dwi; Haan, Dede de
Journal on Mathematics Education Vol 3, No 1 (2012)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.3.1.615.71 - 86

Abstract

The meaning of fractions with integer multiplication is something that is difficult to  understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local instructional theory to support the students expand their understanding of the meaning of multiplication of fractions with integers. By applying the characteristics of realistic mathematics education (Realistic Mathematics Education), the researchers designed a  series of instructional activities related to daily life, such as Indonesia prepares dishes and equitable distribution. Participants of this study were Grade 5 students from an elementary school in Surabaya, along with a mathematics teacher of that class.  Some students of the class participated in the first cycle, in order to see how the design of the hypothetical learning trajectory (Hypothetical Learning Trajectory) is running. After going through several revisions, HLT is then implemented in all the other students in grade 5. The results showed that students prior knowledge affect their learning process. The fractions solve multiplication problems with whole numbers, some students convert the integers to fractions and then use a fraction by a fraction multiplication procedure. The learning process begins with students exploring the contextual situation of fair division, where students extend their understanding that the fraction associated with the division and multiplication. One indicator that the student has broadened his understanding is the more varied representation of the given problem. Keywords: multiplication of fraction with whole number, RME, daily life situations, extend the understanding, initial knowledge, design research DOI: http://dx.doi.org/10.22342/jme.3.1.615.71-86
Eliciting Mathematical Thinking of Students through Realistic Mathematics Eucation Anwar, Lathiful; Budayasa, I Ketut; Amin, Siti Maghfirotun; Haan, Dede de
Journal on Mathematics Education Vol 3, No 1 (2012)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.3.1.620.55 - 70

Abstract

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. Keywords: Realistic Mathematics Education, mathematical thinking, a sequence of instructional activities DOI: http://dx.doi.org/10.22342/jme.3.1.620.55-70
Supporting Fifth Graders in Learning Multiplication of Fraction with Whole Number Khairunnisak, Cut; Amin, Siti Maghfirotun; Juniati, Dwi; Haan, Dede de
Journal on Mathematics Education (JME) Vol 3, No 01 (2012): Journal on Mathematics Education (JME)
Publisher : IndoMS Pusat

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The meaning of fractions with integer multiplication is something that is difficult to  understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local instructional theory to support the students expand their understanding of the meaning of multiplication of fractions with integers. By applying the characteristics of realistic mathematics education (Realistic Mathematics Education), the researchers designed a  series of instructional activities related to daily life, such as Indonesia prepares dishes and equitable distribution. Participants of this study were Grade 5 students from an elementary school in Surabaya, along with a mathematics teacher of that class.  Some students of the class participated in the first cycle, in order to see how the design of the hypothetical learning trajectory (Hypothetical Learning Trajectory) is running. After going through several revisions, HLT is then implemented in all the other students in grade 5. The results showed that students prior knowledge affect their learning process. The fractions solve multiplication problems with whole numbers, some students convert the integers to fractions and then use a fraction by a fraction multiplication procedure. The learning process begins with students exploring the contextual situation of fair division, where students extend their understanding that the fraction associated with the division and multiplication. One indicator that the student has broadened his understanding is the more varied representation of the given problem.  Keywords: multiplication of fraction with whole number, RME, daily life situations, extend the understanding, initial knowledge, design research
Eliciting Mathematical Thinking of Students through Realistic Mathematics Eucation Anwar, Lathiful; Budayasa, I Ketut; Amin, Siti Maghfirotun; Haan, Dede de
Journal on Mathematics Education (JME) Vol 3, No 01 (2012): Journal on Mathematics Education (JME)
Publisher : IndoMS Pusat

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

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.  Keywords: Realistic Mathematics Education, mathematical thinking, a sequence of instructional activities
Design Research on Mathematics Education: Investigating The Progress of Indonesian Fifth Grade Students’ Learning on Multiplication of Fractions With Natural Numbers Shanty, Nenden Octavarulia; Hartono, Yusuf; Indra Putri, Ratu Ilma; Haan, Dede de
Journal on Mathematics Education (JME) Vol 2, No 02 (2011): Journal on Mathematics Education (JME)
Publisher : IndoMS Pusat

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

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. Keywords: multiplication fractions with natural numbers, measurement(length) activity, design research, Hypothetical Learning Trajectory, model of, model for.
Design Research on Mathematics Education: Investigating The Progress of Indonesian Fifth Grade Students Learning on Multiplication of Fractions With Natural Numbers Shanty, Nenden Octavarulia; Hartono, Yusuf; Ilma, Ratu; Haan, Dede de
Journal on Mathematics Education Vol 2, No 2 (2011)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (226.265 KB) | DOI: 10.22342/jme.2.2.749.147-162

Abstract

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 Streeflands 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.Keywords: multiplication fractions with natural numbers, measurement (length) activity, design research, Hypothetical Learning Trajectory, model of, model for