IEPS2016University Technology of Malaysia, Johor Bahru, Malaysia. 18 & 19 December 2016

THE SWIMMING CONTEXT TO ASSIST STUDENT IN LEARNING ADDITION OF FRACTION

Meta Silvia Gunawan*1, Zulkardi2, & Ratu Ilma Indra Putri3

1,2,3 Fakultas Keguruan dan Ilmu pendidikan, Universitas Sriwijaya, Palembang, Indonesia(Email: metasilviagunawan@gmail.com, zulkardi@gmail.com, & ratu.ilma@yahoo.com)

*corresponding author

ABSTRACT

This study aims to produce a learning trajectory using the swimming context in helping students to understand the concept of addition of fractions. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning addition of fractions. Learning trajectory designed in the early phases and tested on 6 fourth-grade students in SD IBA Palembang. The results showed that the activity of swimming can stimulate informal knowledge of students in partitioned to generate fractions as part of a whole. Furthermore, the strategies and tools used by students in the partitioning gradually developed into mathematics more formal where the fraction bar is used as a model of measurement situations. Representation of the fraction bar can lead students toward the end of the activity level, ie the way to the fractional summation rule and more formal reasoning.

Keywords: Design research, Swimming context, Addition of fraction

INTRODUCTION

Fraction lessons in Indonesia is focusing only on its procedure. Students are given the formula directly, without understanding what the actual meaning of fractions. The problem is the meaning of fractions that varies is one of the causes difficulties in learning fractions [1]. The students should be given the widest possible opportunity to explore the meaning of fractions before students study the relationship between fractions and operations on fractions [2]. The other problems is the students' difficulties in adding fractions, especially with a different denominator. The difficulty in conventional teaching caused hazy understanding of fractions itself. Thus, when the teacher explains how to solve addition operations fractions by equating the denominator, the students followed mechanistically (without understanding).

Building fraction comprehension for elementary students is not an easy task to do. Teachers should also be rich in creativity in designing the education in the classroom. It needs a promising approach to apply using Realistic Mathematics Education or in Indonesia usually called Pendidikan Matematika Realistik Indonesia (PMRI). PMRI provide opportunities for teachers and students to communicated well in creating social interaction in the classroom. Social interaction can occur if students work together in solving mathematical problems given and able to explain born out of the social norms and socio-mathematical norms. The social norm is a common pattern of social interaction that is not tied to the topic or learning materials while the socio-mathematical norms specifically linked to the arguments in mathematics. Sociomathematical norms related to participation in joint activities for troubleshooting. Sociomathematical norms are for example

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shown by the student's agreement about the correct answer contains not only in correct mathematical calculation but also the correct understanding and interpretation of the teacher's questions [3,4].

PMRI is an approach that can be used to motivate students to learn mathematics in a way closer to the world of mathematics, to improve students discussion ability so that the end result of their findings can be used to solve the individual and group problems [5]. The situation of student life is not only what is real in view of students but also all imaginable students, reached by imagination [6,7]. Learning starts from reality so that students can get involved in the learning process significantly. In the teaching PMRI built on informal knowledge of students, it is important to give students the opportunity to explore the daily life situations where fractions play a role [1]. PMRI needs a context that is close to the students to help students understand the lesson. Swimming has been selected for the context of this study. It has been due to represent fractions using measurements. The shape of the pool is one of the models that allow representing part of the whole.

In addition to the need for context, it also takes a right way to teach fractions. The general approach to help students understands fractions is to get them to use the model to find the names of the different fractions. This activity is their first experienced that a certain quantity can have various names. To give a few examples of models that can be used that model of the area, length model with a bar or strip, and a model of the set. This study uses the model of a bar where students use a smaller field to find the names of fractions for a given section. Moreover, to make the names of fractions can be obtained by the folding paper. Half a tape obtained by folding into two folds the other will produce the names of the others.

Several previous studies have also been getting maximum results in learning fractions using PMRI approach, among the others research showed that through a series of activities that have been done to assist students in learning fractions [8]. And this is also shown by others research which shows the result of the use of the fractional card can support students' understanding of understanding fractions of informal phases to formal phases [9]. In the others development study on a material sum of fractions using PMRI approach also showed the maximum results, the learning process of students using the teaching materials sum of fractions based on the PMRI approach can really have the role of guiding students to develop ideas and foster creativity in solving problems [1]. From the results of previous studies that use PMRI approach, suggesting that the PMRI approach has a very good role to be applied in the material fractions or other materials.

To implement the study, researcher used design research method. It is consists of three phases: preliminary design, experiment (pilot experiment and teaching experiment), and retrospective analyze. But in this study was limited to the pilot phase of the experiment.

From the above discussion, researcher carry out research with the aim of developing a theory of learning to assist students to understand the concept of the adding fractions using the swimming context.

MAIN RESULT

This study was designed to produce a learning trajectory in the learning material fractions addition operation using the swimming context with PMRI approach. This research through two phases of the three phases of design research, namely: preliminary design and the design experiment were conducted in the pilot experiment.

Preliminary design

At the phase of preliminary design, researcher examined the literature on material fractions, PMRI approach, the relationship between content and context of the pool used, and design research that was used as research methods.

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Once the researcher have designed the initial learning, later obtained a learning device that will be used in the experiment phase. Before researcher conducted experimental phase, researcher discuss in advance with the mathematics teacher who became a model teacher. This is done because the teacher is more familiar with the characteristics of students who will be the subject of study. At this phase of these discussions, researcher and the teacher together to discuss learning device, if it is not in accordance with the research subjects, it will be revised. Among them is a learning device Hypothetical Learning Trajectory (HLT), student activity sheet, lesson plans, teacher guide, pre-test and post-test questions, as well as the observation sheet.

Pilot experiment

At this phase involving six students from fourth grade of IBA Palembang Primary School consisting of 2 high-ability students, two students of average, and 2 low-ability students.

To determine the initial ability of students, researcher provides preliminary tests (pre-test) to know their basic capabilities. Pre-test results showed that students' difficulties in add fractions because they still add fractions by adding the denominator. After learning the ability of students' initial results of the pre-test, the next phase performed in the form of a pilot experiment. At this phase, the students formed a group and researcher as a model teacher. The student working on an activity sheet in which includes three mathematical problems. The first issue is about the meaning of fractions, then the second issue is the sum of fractions with the same denominator using fraction bar and number line, the latter is the sum of fractions with the different denominators using fraction bar.

a. Student activity sheet 1 – The meaning of fraction

In the first problems are introduced in the context of activities such as swimming. There is a problem that refers students to better understand the meaning of the fractional part of a whole. Students are asked to share the experience related to swimming activities. There is an athlete who swims for over 25 meters out of 50 meters pool length. Then the students will find the part of the athlete swim. The results of the student’s answers can be seen in Figure 1.

Figure 1. The student's answers in student activity sheet 1

In Figure 1 the student makes fractions of a given problem. The length of the pool is expressed as the denominator, and the distance traveled by the athlete is the numerator. The following transcript of a conversation on student activity sheet 1.

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T: According to Annisa, how far the distance that has taken by the athlete?S: Half of the poolT: Why did you say half of the pool?S: let's see .. The end of the pool here, and here is the beginning of the poolT: What is the meaning of 25?S: 25 is the location where he arrivesT: Oh .. what about the 50's?S: It is the whole pool lengthT: Annisa did you know in the fractions, what is the meaning of the number 25?S: Numerator, and here is the denominator (pointing to the number 50)

Conversation Transcripts 1. The student’s answer in student activity sheet 1

b. Student activity sheet 2 – The sum of the same fraction denominator

In student activity sheet 2, students will add fractions with the same denominator. Student activity sheet 2 consists of two learning activities in the form of different problems. Students are required to resolve an issue where an athlete reach certain distances in seconds, and then the two distances added together. In this activity, students are asked to use the fraction bar in the process of finding the result of the sum of fractions. Activities of the students can be seen in Figure 2.

Figure 2. The student’s answer in student activity sheet 2 – fraction bar

In Figure 2 the student adds fractions with the same denominator using a fraction bar. Students are asked to follow the directions in which the first fraction is represented by a fraction bar A and bar B. The next second the students will cut bars B and stick it in bar A so they get the results of the two distances. Here's a transcript of the conversation.

T: So how can the results be obtained?

S: First she swam until 15 the distance

T: OkS: Well it's part of the bar A

T: Oh, so only 15shaded of total area

S: Then she swam again as far as 35 , bar B

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T: And then?

S: Then bar B is cut and connected here, the answer can be calculated from 45 shaded area

Conversations Transcripts 2. The student’s answer in student activity sheet 2 – fraction bar

On the second issue, students still need to add fractions with the same denominator. Students are required to resolve an issue where two athletes cover the distance at a certain time, then the distance is summed. In this activity, students are asked to use the number line in the process of finding the result of the sum of the fractions. The results of the student’s answer can be seen in Figure 3.

Figure 3. The student’s answer in student activity sheet 2 – number line

In Figure 3 the student adds fractions with the same denominator using the number line. Student is required to determine how the distance of each athlete and then add them together. Here's a transcript of the conversation.

T: Rafi, why is the answer obtained 2730?

S: Because this is a total, so Indah 12 meters plus Silvy 15 meters. It makes 27 meters, meaning that within 20 seconds it can cover the 27 meters when added. While the pool is 30 meters long

T: Oh .. 30-meters long is the pool size huh?

S: Yes. So the answer is 2730

T: So, what is the conclusion?S: If the denominator is the same number, it can be directly added to the numerator.Conversations Transcripts 3. The student’s answer in student activity sheet 2 –

number line

b. Student activity sheet 3 – The sum of the different fraction denominator

In student activity sheet 3, students will add fractions with different denominators. Students are required to resolve an issue where athletes from Japan and Korea a distance at a certain time, then the distance is summed. In this activity, students are asked to use the fraction bar in the process of finding the result of the sum of fractions. Pictures of student activity can be seen in Figure 4.

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Figure 4. Activities of students on student activity sheet 3

In Figure 4 student add fractions with the different denominator using the fraction bar. Students are asked to follow the directions in which the first fraction is represented by a fraction bar A and bar B. The next second the students cut and placed the bar B on bar A so that they get the results of the two distances. Here's a transcript of the conversation.

T : Why does it show athlete number 5?S : I measure it, the result is half of the poolT : How do you know that is a half of the pool?S : Because in the middle of the poolT : Is there any other way? Using the bar?S : We can fold itT : How can it show the results by folding?S : Previously it was 2. After folded it changes into halfT : Which bar are used to represent athlete number 8?S : This one, because it shows a quarter, it still stands when folded and folded again, still

stands and then folded again, folded again. Done.T : Oh.. how are the rest after you fold that?S : 1(Rafi cutting the bar)T : What bar that you hold?

S : 12 , then I stick it to another one

T : so, how long is it?

S : 34

Conversations Transcript 4. The student’s answer on student activity sheet 3

After the students work on the third LAS, students are asked to work on the final phase of the test (post-test) individually. The assessment of post-test showed different results with a pre-test. Students no longer need to include the denominator when summing two pieces of fractions with different denominators. In discussions with students during the pilot experiment, the students said that by using a fraction bar, learning becomes more interesting and less boring. Students can also instantly understand that the numerator of the fraction cannot be added directly, but rather must be

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synchronized first. This is consistent with the theory who say that one model that can be used in learning fractions are the long model with a bar or strip [10].

Discussion

The purpose of this research is to contribute to developing a Local Instructional Theory (LIT) by designing a series of learning activities to help students understand fractions addition operation. Based on the design of learning trajectories that have been designed, there are three sequential learning activities that determine the fractional part of an athlete, summing a total distance of an athlete, and add up the distance between two athletes. Learning activities begins with providing contextual issues often encountered by students, especially at the pool activities.

A series of activities were designed based on the principles and the five PMRI characteristics, namely:a. Use of contexts for phenomenologist exploration

An activity learning begins with a problem that closes to the students, students answer questions relating to the position of athletes in the pool. In this case, the students' answers refer to the introduction of fractions in a simple manner.

b. Using models and symbols for progressive mathematization use of models and symbols in completing problems do students during the process of resolving the problem in this study using a fraction bar to help students in add fractions.

c. Using students own contribution and production The teacher gives an appreciation of the contributions of students in the learning process in both the group and individual activities. Learning becomes more meaningful, few of the reasons are because of the many variations of answers and different solution strategies of each group as well as individuals. At this phase, students solve their problems with each way which they consider easier, for example, there are students who use the method of folding the bar and there are students who tore the bar.

d. InteractivityInteractivity not only between teachers and students but also with fellow students, the shape of these interactions can be a discussion, explaining, communication, cooperation, and evaluation.

e. Intertwining mathematics concept, aspects, and unit Aspects and units mean that the mathematics taught to students would be more meaningful if it is relevant to the topic of learning.

CONCLUSION

Based on the results of the discussions that have been described, it can be concluded that the activities in the student activity sheet that has been designed actually can help students understand and resolve problems in addition of fraction from informally intuitive to the formal problem-solving. In the operation of learning fractions, learning path traversed by students include 3 activities that determine the fractional part of the whole, add fractions with the same denominator, and add fractions with the different denominator. The usage of swimming context and fraction bar make students more interested in learning addition of fraction.

ACKNOWLEDGEMENT

Reseacher would like to thank Prof. Dr. Zulkardi, M.I.Komp, M.Sc and Prof. Dr. Ratu Ilma Indra Putri, M.Si as a mentor who has guided researcher to finally be able to complete the pilot phase of this experiment. As well thank you very much for the University Technology of Malaysia

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that has given the authors the opportunity to present the results of this study.

REFERENCES

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