Learning Proportional by Comparing Costs in Secondary School

Evie Nurmala Dewi

1,a

, Zulkardi

2,b

and Yusuf Hartono

2,c

Senior High School Negeri 1 Babat Toman , Jalan Sekolah No. 1 Kecamatan Babat Toman, Musi Banyuasin , Indonesia

Sriwiyaya University, Jalan Palembang-Prabumulih Km.32, Indralaya Ogan Ilir,, Indonesia

Keywords: Proportional, PMRI, Design Research, Context, Comparison.

Abstract: This study aims to determine students' understanding of proportional learning in comparing costs through

the PMRI approach. The research participants consisted of 32 grade VII junior high school students using

the Research design method which consisted of three stages: initial design, experimental design (pilot

experiment and teaching experiment) and retrospective analysis. This study produced a Learning Trajectory

(LT), which contains a series of learning processes that help students find cost comparison concepts that can

be seen in everyday life. A Hypothetical Learning Project (HLT) was developed in activities using the

Actual Learning Flow of students (ALT) during the teaching experiment. The results of the study indicate

that the price comparison concept is the starting point in the comparison of values.

1 INTRODUCTION

Value comparison is the ratio of two values or more

than a similar quantity. The use of comparative

material can be applied and unwittingly often used

in everyday life. Proportion is defined as the

equality of two ratios, for example

(Silvestre and da Ponte, 2012; Ellis, 2013). Value

comparison is one of the subjects studied in grade

VII which one of the basic competencies is to use

comparisons to solve problems.

One way to make material can be done by

exploring its contents from users which will help

students learn more (Cramert and Post, 1993; Van de

Walle, 2008). Comparison informal, students make a

solid foundation on which they make their own

approaches, which can be explored and cover

situations that involve measuring prices, geometry or

other visual contexts and varying degrees can be

used to teach comparisons (Wijaya, 2013), that use

context in explicit between context and

mathematical ideas is also useful for students to

support development of mathematical thinking.

Zulkardi (2002) explained that context leads

students to understand mathematics from what can

be used for something formal can be written with

symbols through the mathematical process. In this

study, using the context of tekwan as one of

Palembang's special foods that can explore national

and local culture into the concept of learning

mathematics through everyday life, so as to make a

lesson more meaningful and interesting so as to

motivate students to study harder (Retta et al.,

2013). In general, comparison problems are

categorized into two types, namely missing value

problems and comparison problems (Sumarto et al.,

2013).

PMRI has five characteristics that are in

accordance with the characteristics of RME

( Gravemeijer, 2006; Zulkardi, 2002; Putri, 2013 ),

in the learning process with Realistic Mathematics

Education that must be improved, namely:

(a) using the context for exploration (use of contexts

for phenomenon exploration), (b) using

models to construct mathematical concepts (use of

models for mathematics concept construction), (c)

using student contributions (use of students'

creations and contributions), (d) student

activities and interactivity in the learning process

(students activity and interactivity on the learning

process), and (e) integrated with other learning

topics (intertwining mathematics concepts, aspects,

and units).

This study aims to produce a learning trajectory

of proportional concept using the context of tekwan

in seventh grader of junior high school. Through the

identification stage, students can understand the ratio

of a comparison value based on the conditions and

situations obtained through the price of different

technicians and what materials will be used.

Nurmala Dewi, E., Zulkardi, . and Hartono, Y.

Learning Proportionality through Price Comparison in Secondary School.

DOI: 10.5220/0009995100002499

In Proceedings of the 3rd Sriwijaya University International Conference on Learning and Education (SULE-IC 2018), pages 199-203

ISBN: 978-989-758-575-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

199

Learning is designed using RME approach which

can be related to other learning in the form of the

context of tekwan food as one of the typical foods in

Palembang.

2 METHOD

This study used design research method which is an

appropriate way to answer researchers' questions and

achieve the objectives of the research as those who

will design comparative material with RME

approach through the making of tekwan in grade VII

of SMP Negeri 3 Rantau Bayur, Banyuasin.

According to Gravemeijer and Cobb (2006),

there are three stages in the implementation of

research as follows.

1. Preparing for the experiment and preliminary

design. It is the preparation and preliminary stage in

the form of literature studies in the form of

understanding comparisons, RME approaches and

analysis of mathematics curriculum materials

through discussions with classroom teachers

regarding the state of the classroom and the way in

which research is carried out, research needs through

observation in accordance with the schedule.

Designing the suspected learning trajectory of this

stage is learning trajectory and hypothetical learning

trajectory (HLT). HLT is designed to be dynamic so

that a cyclic process can be formed that can change

and develop during the teaching process.

2. Designing experiment. At this stage the pilot

experiment is carried out (cycle 1) through HLT

trials which will have been designed for students in

small groups to collect data in adjusting and revising

the initial HLT to be used in the teaching experiment

(cycle 2) later. Students taken from 9 students. based

on 3 different low, medium and high abilities that

the model teacher will choose. The results of the

HLT pilot experiment phase that has been fixed are

tested again in a class consisting of students as many

as the number of classes as the subject of the study.

Eye teacher students as model teachers and

researchers conduct communication learning

activities. The overall activities carried out by

students will be used as data in the study.

3. Retrospective Analysis. At this stage, an analysis

of the results of the study conducted by comparing

Hypothetical Learning Trajectory (HLT) with the

learning trajectory of students in the actual learning

process so that the results were obtained in student

learning activities to answer the problems in the

study.

The data collection techniques in this study were

carried out by comparing observations during the

learning process with HLT which was designed in

the preliminary design phase. The data obtained

through observation, making video recordings of

student activities, looking at students' abilities

through Student Activity Sheets (LAS), giving initial

tests and final tests and student interviews. Then

compare HLT and ALT to find out if the active

student is not active during the activity.

Analysis of the data based on the initial data

validation of student’ activity sheets and student’

learning recordings so that the results of the research

can be finally concluded.

3 RESULT AND DISCUSSION

3.1 Result

This research is used to produce learning trajectories

about comparative material in solving problems in

everyday life by using the context of tekwan through

RME approaches in junior high school. Through

various stages in the initial preparation, namely

reviewing the literature and designing HLT by

making direct observations on student learning

activities

Where this stage the researcher prepares the

activities of the literature in research through

activities in the form of discussion about the

comparison material of the comparison with the

concept - the basic concept. In addition, students can

find out that the context used is tekwan which is a

typical food Palembang also provides knowledge

that in every sale of tekwan the price sold is not all

the same varies from the experiment students know

what ingredients are the main subject and additions

through size on basic materials during the making of

tekwan and carried out in several activities before

and after several tests.

Table 1. Name of student in pilot experiment

Student Name Abilit

Karnia Hi

Yenita High

Farida Mediu

Nuni

Mediu

Wisma Low

Winda Low

The researcher himself will act as a model

teacher along with 6 students with different abilities,

where the ability consists of high, medium, and low

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level abilities divided into 2 groups where Group 1

(student 1, student 2, and student 3) and group 2

(student 2, student 4 and student 6). the names of

students in Table 1.

Before the learning in cycle 1 will be carried out

the initial test for the six students, the test is carried

out to see the students 'initial ability to measure the

extent to which students understand the prerequisite

material and also see students' ability to solve

problems related to comparison material which will

be taught next . Specifically on the answer sheet of

the initial test the researcher knows how students in

answering each given question related to the

comparison material using the tekwan making

contest. Students are given a written test of four

initial test questions, and in completing this initial

test students work individually, following the

situation of students in doing the initial test can be

seen in Figure 1.

Figure 1: Students are working on pre-test.

The first problem given to students in cycle 1 is

by using the context of the researcher through the

components of the material related to the

comparison material through conversation.

from the picture above?

Figure 2: Problem number 1.

Figure 1 is the first problem given to students in

the above questions, in the form of food ingredients

that will be used to make tekwan consisting of

milled fish and sago, students are told to think,

besides the ingredients above, there are ingredients

that can be used so that the food can be made.

To find out the strategies used in resolving the

comparison problems given, researchers who act as

teachers conduct interviews with each group.

Teacher : what picture do you see?

Group 2 : fish, sago is lacking, the water is not there ?

teacher : oh yeah, what should we do?

Group 2 : it seems like it's for empek -empekk

student 2 : not empek - empek

Teacher : besides Pempek there is another?

student 2 : tekwan mom ...........

student 4 : why don't we make a technician we need a

container?

teacher : how to make a technician .......

student 6 : if 1 kg of fish, 1 kilogram of sago 1500 sago

and water is 600 ml

students 4 :when I'm a fish, 800 grams of sago and water

is only 400 grams

student 2 : we don't usually have a lot of ingredients

plus more results

teacher : what does that feel like that?

student 2 : he must be different mom

Conversational transcription above shows that

students (group 2) use intuitively to solve the

comparison problem given. They have not given a

reason mathematically using the procedure in giving

strong reasons even though the answer is correct.

The second comparison problem given is to

compare three containers or comparison situations

with three factors compared. The theme given is

tekwan food with good taste, not tasty. Students are

given several ingredients with sizes and sizes

between 1500 gr sago, 1500 gr milled fish and 300

ml water with the provision that the three containers

are loaded with the same size and other materials of

different sizes in each container. Fill the ingredients

above into the container provided ? explain your

reasons ?

Figure 3: Problem number 2.

Figure 4. Student teaching experiment

Figure 4. Shows that in the experimental teaching

students do the practice by making tekwan food

from the ingredients that have been prepared and

divide into several groups that are seen are groups 1

and 3 and start mixing some of the ingredients

Learning Proportionality through Price Comparison in Secondary School

201

divided in the three containers. Here is teacher

interviews with group 4.

Teacher : what if you want to have a different taste

student 1 : we divide it if the fish and 1500 grams of

sago are divided like 500 grams each and

the water

student 3 : if you see it the value is the same

teacher : we want to get a different taste

student : the meaning is divided into 3 parts

teacher : do fish have to be the same for the part

student 5 : sago and water, yes mom

teacher : yeah kid .......

student 1 : let it be meaningful that there are 250

grams, 750 grams and 500 grams

student 3 : water is 150ml, 50ml and 100ml

Teacher : yes right, so how do you taste feel from the

three containers

Student 5 : There tastes good, it's quite tasty and

doesn't taste good

Teacher : Try to conclude from the results you have

obtained

Student3 : Good , that distinguishes the taste is the

amount of sago and water that is given in

each container

The conversation transcription shows that group

4 has started reasoning in solving comparison

problems. They give reasons and prove their alleged

answers. The concept of comparison used by

students 1 and 3 is to look for comparisons in each

ingredient and there are 2 differences in answers that

are better in the answer of student 3 there is a

comparison value in Figure 5 below.

Figure 5. Strategy of the answers to group 4 students in

solving the Comparison problem

That way students can produce the material then

they begin to work on the results so that the tekwan

which tastes good, medium and unpleasant

Restropective Phase Cycle Analysis 1

Based on the activities carried out by students in

cycle 1, a retrospective analysis was conducted on

why students subtracted by the same number,

namely 250. They replied that in order for all

materials to be deducted proportionally, they had to

be deducted by the same number. In this case

students have not been said to reason in comparison

because students still use the concept of addition and

subtraction in a comparison situation rather than the

concept of multiplication and division. In addition, the

comparison situation given is difficult to model. So

that revisions are made to the problems given to

students in the teaching experiment (cycle 2).

3.2 Discussion

The use of tekwan food context is the context of

Pelembang traditional food culture in comparative

learning on comparison material can help students to

understand mathematics in everyday life, besides

students can reason in solving problems given,

reasoning processes occur when students can find

the concept of comparison to look for price and

amount. for example there is a portion of food in one

portion of the ingredients used are the staple

ingredients of tekwan food and other ingredients will

increase proportionally and the amount of tekwan

food produced and conversely if one ingredient

increases, the portion of tekwan food in one bowl

and taste value will increase and different prices and

resolve the problems given in LAS. Zulkardi (2002)

stated that mathematics learning is a human activity

and mathematics must be clearly connected to the

concept of student's daily life as a source of

development and to the context of everyday life as a

source of development and as an application area

through mathematical processes both horizontally

and vertically. In the development through approach

through formal and informal stages.

4 CONCLUSION

In this study stated that the concept of tekwan can be

an ingredient in learning mathematics where each

learning process takes place activities that help

students in solving problems in mathematics

learning, especially determining the value of price

comparisons that have been the question of what

causes the price of tekwan to vary even though the

basic ingredients are the same namely fish also

become students better understand the problems that

are given especially everyday life.

Researchers hope that with the context of the

tekwan can make other studies using Palembang

specialties which are local and national cultural

contexts to be a learning process that can lead

students to be more active in learning.

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