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STUDENTS’ COGNITIVE PROCESSES IN SOLVING PROBLEM RELATED TO THE CONCEPT OF AREA CONSERVATION Ekawati, Rooselyna; Kohar, Ahmad Wachidul; Imah, Elly Matul; Amin, Siti Maghfirotun; Fiangga, Shofan
Journal on Mathematics Education Vol 10, No 1 (2019)
Publisher : Department of Doctoral Program on Mathematics Education, Sriwijaya University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (998.766 KB) | DOI: 10.22342/jme.10.1.6339.21-36

Abstract

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area conservation test. Results indicate that both samples performed more cyclic processes on formulating solution planning, regulating solution part and detecting and correcting error during the problem-solving. However, it was found that the high achiever student performed some processes than those of low achiever. Also, while the high achiever student did not predict any outcomes of his formulated strategies, the low achiever did not carry out the thought process after detecting errors of the initial solution gained. About the concept of area conservation, the finding also reveals that within the samples? cognitive processes, the use of area formula come first before students decided to look for another strategy such as doing ?cut-rotate-paste? for the curved planes, which do not have any direct formula. The possible causes of the results were discussed to derive some recommendation for future studies.
DESIGNING LESSON PLAN OF INTEGER NUMBER OPERATION BASED ON FUN AND EASY MATH (FEM) APPROACH Fouryza, Darin; Amin, Siti Maghfirotun; Ekawati, Rooselyna
International Journal of Evaluation and Research in Education (IJERE) Vol 8, No 1: March 2019
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (542.321 KB) | DOI: 10.11591/ijere.v8i1.15514

Abstract

This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the patterns and rules, making it easier for students to understand mathematical concepts and driving them to actively participate in learning activity. Furthermore, the number line model based on the rules aimed to provide the real idea of mathematical concept and avoid the mathematical manipulation. The design of RPP development was intended to create a new RPP which was divided into three activities, namely introduction, core, and closing. The method of lesson plan development used a Plomp?s development model which was consisted of three phases, namely preliminary research, prototype, and evaluation. The results of this development were expected to help students in understanding the mathematical concepts, namely integer calculation operations especially addition and subtraction, increasing student activeness in learning process, and avoiding the existence of mathematical manipulation.
PELATIHAN PEMBELAJARAN MATEMATIKA REALISTIK (PMR) DENGAN MEDIA BERBAHAN BEKAS DI SEKOLAH DASAR Palupi, Evangelista Lus Windyana; Lukito, Agung; Khabibah, Siti; Amin, Siti Maghfirotun
Jurnal ABDI: Media Pengabdian Kepada Masyarakat Vol 5, No 2 (2020)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/ja.v5n2.p97-105

Abstract

Pembelajaran Matematika Realistik (PMR) merupakan salah satu alternatif pendekatan pembelajaran yang memberikan kesempatan kepada siswa untuk belajar matematika secara bermakna dan realistik bagi siswa. Prinsip emergent modeling dalam PMR menuntut ketersediaan media pembelajaran agar siswa dapat membayangkan situasi masalah yang diberikan. Namun permasalahan yang muncul adalah keterbatasan media murah yang dapat digunakan guru dan keterbatasan pengetahuan guru dalam merancang pembelajaran matematika realistik berbantuan media. Di lain pihak, sejumlah besar barang bekas dibiarkan menumpuk, kurang dimanfaatkan. Padahal barang bekas dapat didaur ulang menjadi barang dengan nilai guna, salah satunya dengan memanfaatkannya untuk kepentingan belajar dan mengajar matematika. Pelatihan pembelajaran matematika realistik dengan bantuan media berbahan bekas di sekolah dasar dapat menjadi solusi praktis untuk membantu guru menyelenggarakan proses pembelajaran matematika yang bermakna, menarik, interaktif, mudah diikuti dan murah. Meskipun rancangan pembelajaran yang dihasilkan belum memenuhi prinsip dan karakteristik pembelajaran matematika realistik, kegiatan ini dinilai bermanfaat dan berhasil dalam membantu guru untuk memilih bahan bekas sebagai media dan merancang pembelajaran matematika dengan media tersebut. Dari kegiatan ini, dihasilkan 27 desain pembelajaran matematika dengan media berbahan bekas yang berbeda dari 36 desain yang dibuat. Rancangan pembelajaran yang dibuat meliputi beberapa topik matematika untuk kelas 3 dan 4 sekolah dasar.
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
Learning The Concept of Area and Perimeter by Exploring Their Relation Winarti, Destina Wahyu; Amin, Siti Maghfirotun; Lukito, Agung; Gallen, Frans Van
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.3.1.616.41 - 44

Abstract

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a  given area, there are many possibilities of perimeter and vice versa. When student are not aware of this relation they might confuse about the concept in their continuation of learning process. This research was conducted to study if it would support students’ understanding of the concept of perimeter and area if we let them explore the relation between perimeter and area in the very first phase of the learning process. Design research was chosen as the method to study this issue and the three basic principles in The Realistic Mathematics approach were applied in this study to support the learning process of perimeter and area. Real life context such as picture frames was choosen in developing a sequence of learning line to reach the learning goal of perimeter and area. The partipants of this research were students and mathematics teacher of grade 3 in one of the elementary school in Surabaya. Two classes were taken to involve in the first cycle and second cycle respectively.  The teaching experiment shows that the class activities such as making photo frame, measuring photo paper with sticky paper and arranging shapes with wooden matches are activities which can be used to reveal the relation of perimeter and area. From those activities students build their own understanding that in fact area and perimeter are not in one to one correspondence, they found that for the given area they might find different perimeter or vice versa. They also found the reason why they multiply length and width to count the area of rectangular or square shape from sticky paper activity. Somehow some students were found still struggle with their understanding of area and perimeter. They often simply count the area and perimeter but when it comes into comparing the area or perimeter  they still struggle to differentiate between area and perimeter. Keywords: Perimeter, Area, Relation between perimeter and area, Understanding DOI: http://dx.doi.org/10.22342/jme.3.1.616.41-54
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
Learning The Concept of Area and Perimeter by Exploring Their Relation Winarti, Destina Wahyu; Amin, Siti Maghfirotun; Lukito, Agung; Gallen, Frans Van
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

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a  given area, there are many possibilities of perimeter and vice versa. When student are not aware of this relation they might confuse about the concept in their continuation of learning process. This research was conducted to study if it would support students’ understanding of the concept of perimeter and area if we let them explore the relation between perimeter and area in the very first phase of the learning process.  Design research was chosen as the method to study this issue and the three basic principles in The Realistic Mathematics approach were applied in this study to support the learning process of perimeter and area. Real life context such as picture frames was choosen in developing a sequence of learning line to reach the learning goal of perimeter and area. The partipants of this research were students and mathematics teacher of grade 3 in one of the elementary school in Surabaya. Two classes were taken to involve in the first cycle and second cycle respectively.  The teaching experiment shows that the class activities such as making photo frame, measuring photo paper with sticky paper and arranging shapes with wooden matches are activities which can be used to reveal the relation of perimeter and area. From those activities students build their own understanding that in fact area and perimeter are not in one to one correspondence, they found that for the given area they might find different perimeter or vice versa. They also found the reason why they multiply length and width to count the area of rectangular or square shape from sticky paper activity. Somehow some students were found still struggle with their understanding of area and perimeter. They often simply count the area and perimeter but when it comes into comparing the area or perimeter  they still struggle to differentiate between area and perimeter.  Keywords: Perimeter, Area, Relation between perimeter and area, Understanding
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
Motivation Cards to Support Students’ Understanding on Fraction Division Wahyu, Kamirsyah; Amin, Siti Maghfirotun; Lukito, Agung
International Journal on Emerging Mathematics Education IJEME, Vol. 1 No. 1, March 2017
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (642.751 KB) | DOI: 10.12928/ijeme.v1i1.5760

Abstract

This design research aims to develop a learning activity which supports the fifth-grade students to understand measurement fraction division problems (A whole number divided by a fraction that result in a whole number answer) conceptually. Furthermore, how students solve the fraction division problem using models is also analyzed.  Data for the retrospective analysis is collected through two teaching experiments in the form of students’ work, field notes, and some part of classroom discussions. The important findings in this research are: 1) the developed learning activity namely Motivation Cards support students understand that  3 divided by one-half means how many one-half are in 3 through models. However, when the divisor is not a unit fraction they could not directly relate the unshaded part in area model for example. 2) area model is proper model to be firstly introduced when the students work on fraction division. 3) understanding this kind of fraction division help students understand other measurement fraction division where both divisor and dividend are fractions. 4) the learning activity supports the development of character values for students.