Senin, 30 September 2013

Investigating The Progress of Indonesian Fifth Grade Students Learning on Multiplication of Fraction with Natural Numbers




Reflection Paper

Design Research on Mathematics Education

Investigating The Progress of Indonesian Fifth Grade Students Learning on

Multiplication of Fraction with Natural Numbers

By : Nenden Octavarulia S., Yusuf Hartono, Ratu Ilma Indra Putri, Dede de Haan



This research have aimed at investigating the progress of students learning on multiplication fraction with natural number through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. The object for this research were students fifth grade in SDN 179 Palembang.

In the first level, students started to produce their own fraction and recalled back their knowledge about the meaning of fractions as part of a whole. Related to the first tenet of RME, the researcher used the measurement (length) activity as contextual problems. The researcher thought that was a good context that has allowed students to structure and to mathematize following the five activity levels. 


In the second and third levels, students were generating equivalencies and operating through mediating quantity. Problem situation in which the students drew the number line as a representation of string of yarn had strongly generative nature.  Connected to the second tenet of RME, namely the use of models, the use string of yarn here was a bridge to the number line model which was in more abstract level. Through using the material, the students are given the opportunity to actively contribute to their own mathematics.


The fourth and fifth level gave opportunity to students to use their strategies that can be used to developed the next learning process. Connected to the third tenet of RME, namely the use of students own creation and contribution, the use of number line as a model of measuring situation transformed into a model for more formal reasoning.

Connect to the fourth tenet of RME, namely interactivity, the classroom setting was elabotared where the students could share their thinking in the class discussion. And for the last tenet of RME, namely intertwinement, the researcher found that fraction have close relation with fraction.  


To sum up, from the explanation above about this research, it was obvious that this study has taken an important initiative to improve education in Indonesia. Realistic Mathematics Education (RME) can be used as an approach to teach mathematics because students can feel welcome, since they have a right to experience mathematics on a level they can understand and use in daily life.  


By : Wuli Oktiningrum








Rabu, 18 September 2013

Understanding RME


Reflection Paper
Understanding RME
Researcher : Prof. Zulkardi

1.     Philosophy and characteristics of RME
The combination of Van Hiele’s three levels, Freudenthal’s didactical phenomenology and Treffer’s progressive mathematization (Treffers, 1991) result in the five characteristics (tenets) of RME (de Lange, 1987; Gravemeijer, 1994) :
a.    The use of contexts in phenomenological exploration
The process of extrating the appropriate mathematical concepts from concrete situation ii called conceptual mathematization. And the process of apply mathematical concepts to other aspects of their daily life, and by so doing, reinforce and strengthen the concepts is called applied mathematization.   This figure show the conceptual and applied mathematization by de Lange, 1987.

Selasa, 10 September 2013

PMRI’s journey in Surabaya



Reflection Paper
PMRI’s journey in Surabaya
Researcher : Siti M.Amin, Gatot Sulanjono
Translation and adaptation by Annelies Gijse

Introduction
In July 2001, the staff meeting in the Department of Mathematics of University of Surabaya (UNESA), Professor R. Soedjadi announced an important project that we were going to involved with. He explained that a group of mathematicians including him, had committed themselves to innovating the quality of the existing mathematics educational system of Indonesia especially in primary school. They introduced Realistic Mathematics Education (RME) principle, they believed that this mathematics approach was suitable to the situation in Indonesia mainly to students in primary school. To realize the noble cause, Mrs. Siti Khabibah was invited to join the team. The team start with three primary school in Surabaya, that is Jambangan Islamic School, Unesa Lab School, and Al Hikmah Primary School. They choose Islamic primary school because they want to change their style in mathematics instruction, because they thought that public Islamic primary school have different learning methods, specifically in mathematics,
For the purpose of the experiment, the team was ask to decide upon particular topic for each school level (grade 1, 2 and 3)which would be experiment within limited measures. They choose topics : non- standard measurement (inch, feet, etc)for grade 1, non-standard measurement (stick, beads) for grade 2, and fraction for grade 3. The topics for grade 1 and 2 were composed by Siti M.Amin and for Grade 3 by Siti Khabibah, and Mr.Ilham assisted in the development of the experimental material. 
The first pilot
Between October until November, after an agreement had been reached between the team from Unesa and the representatives of affiliated schools, a pilot was conducted at the three schools to implement the material that already had been developed. The pilot was supervised by observers from Unesa in each class. They were observing the learning process in the classrooms.
They observed some interesting facts during the learning process. For example, usually the students of grade 3 always wanted to check whether they had found the right solution or approach to open-end equations after they had solved the problem, whereas his behaviour was not found among students of grade 1 and 2. During the lesson, they found that most of students enthusiastic and happy during lesson. The students performed excellently in stating their own opinion or presented their ways when solving the problems. But  on the other hands, teacher impatient to wait the students initiative or answers and also in posing question to guide students with.
After learning process in the class, they made the reflection session for every lesson. The teachers generally admitted that they were impatient to wait the students to come up with initiatives to solve the problems using their own method. The teachers of grade 3 classes presumed that their students kept on asking which method or answer was right because they have been conditioned to solve problems with the one single method or solution that was provided by teacher. But now the teachers had started to tell the students to use other method to solve their problems, however the students  were still confused.
In the reflection session discussed about issues such as the presentation of probing questions, class management matters, and comprehensive study of materials, also teacher shared their experience in the lesson process. In general, teachers appeared to rather good at class management but they needed improvement on respecting the different opinions of the students an their different ways of thinking and they certainly needed some more patience too.
Further experimentation and implementation
At the First National Wokshop in August 2001 in Bandung , the RME team decided that the program being experimented required a name. The team agreed on the name “ Pendidikan Matematika Realistik Indonesia (PMRI)”. The core team conclude that each Teacher Education College was subject to implement the experiment in comprehensive manner and decided that the experiment was to be performed in phases, beginning from grade 1 classes.
The comprehensive experiment for grade 1 started in 2002-2003, it was conducted one single class at each affiliated school of the teacher education college, and the experiment performed on the grade 1classes was subsequently followed by implementation of the program into grade 1 classes in following school year 0f 2003 – 2004. While grade 1 conducted PMRI in implementation phase, students of grade 2 began their experimental phase. This cycle continued, in which experimentation and implementation were applied continuously.
Unesa had already composed instruction material for Semester 1 of grade 1 in 2001, grade 3 in 2003 and in 2007 we received the task to composed instruction material for grade 5. In 2007 was when the team begun to understand how to write proper PMRI material, because was not easy to make context and the team needed to focus not only on mathematical progress but on developing the students thinking too. So, 2007 was momentous in that the team were finally able to make proper materials.
Result
The team found that the teachers experienced the unexpected outcome from their students during the lesson they were happy to teach according to the PMRI approach. Most of students were able to state how they had discovered methods to solve problems appropriately, and they were able to communicate their ideas clearly. The teachers expressed that PMRI has made teaching more enjoyable because found unexpected abilities in their students which they had never seen before.
By : Wuli Oktiningrum

Selasa, 03 September 2013

REFLECTION PAPER " Design Research on Fraction "

Author : Wuli Oktiningrum
REFLECTION PAPER
Design Research on Fraction
Researcher : Rooselyne Ekawati
Matematika FMIPA Universitas Negeri Surabaya
This research presented by Rooselyne Ekawati from Matematika FMIPA Universitas Surabaya. The researcher found that most of students in the elementary school felt that fraction is one of difficult materials in mathematics. Most of them probably have to skill to do operation with fraction, but on the other hand, some of them just mastering the procedure without understanding. Even, mastering the procedure without understanding it is worthless. 

Based on that problem, the researcher made design research to students in the fourth grade in elementary school. The researcher used fraction as material and used Realistic Mathematics approach with measurement as the context and the paper strip folding and rubber band as the model for fraction. The paper folding used in the first sequence activity and the rubber band used as generalize model of paper folding. The researcher given context situation : a long bar cake, it called “ Lapis” that must devide into several number part can be illustrated as a paper strip that must be folded, and the size of the paper strip must be equal as the size of the cake. With the paper folding, student can support their reason about the equal fraction, for example to find the equal fraction of 1/2 , the students can fold the paper into two part and have one part is ½ and they can also do that by fold the paper into 4 and have two parts of or in fraction notation is 2/4 as ½ of 4 parts. Because the students difficult to fold the paper into odd number, the researcher used the string rubber band models but with different context. The researcher used the context of cone cap game because to support this game, the students need the string rubber band. The rubber band can be stretched, the students can stretch the string rubber band into the number that the student want. For example, student will be difficult to divide a thing into seven part, so they used seven rubbers and stretch those rubber as long as the size of the thing that they want to divide. After that activity, the students symbolized which they notate the paper folding with the fraction notation and used the model for reasoning with the number relation in fraction. 

To conclude, to introduce the materials of mathematics especially fraction is better not to be introduced abstractly first, but used model of mathematics such as paper strip folding and rubber band. So that the students get more understanding of operation with fraction and they are trained to reason. I personaly believe that the researcher did was very great. The researcher used model of mathematics and realistics mathematics approach to made students understanding about fraction. Model of mathematics is important to students, because it make students interesting to study and can develop their knowledge.