The Effectiveness of Realistic Mathematics Education by using the Context

of Toba Batak Culture

Sinta Dameria Simanjuntak

and Imelda

Department of Mathematic Education, Catholic University of St,. Thomas, Setia Budi, Medan, Indonesia

Department of Mathematic Education, The Catholic University of St. Thomas, Medan, Indonesia

Keywords: Realistic Mathematic Education, Learning Effectiveness, Toba Batak Culture

Abstract: Facts and research results show that the 2013 curriculum implementation has not been effective. The

contributing factors are teachers and students. The teacher is not able to manage student-centered learning

because it is used to teacher-centered learning. Students are not able to follow the learning because they are

familiar with teacher-dominated learning. Consequently, learning becomes ineffective. The alternative

solution to the problem is learning realistic mathematics education using context that is close to students.

The context applied is the context of the student's culture, namely the Toba Batak culture. The results of the

study show that students meet the minimum completeness criteria that have been set by the government, the

teacher is able to manage learning well, students gived positive responses to the learning carried out. In

accordance with the indicators of learning effectiveness, it can be concluded that the learning of realistic

mathematics education using the context of the Toba Batak culture is effective.

1 INTRODUCTION

The government has continuously carried out some

socialization and training on the implementation of

the 2013 curriculum. However, in reality there are

still many educators and students who feel confused

about implementing it in the learning process. Thus,

the implementation of the 2013 curriculum in

schools has become less effective. This is proven

through several research results that refer to the

evaluation of the effectiveness of the 2013

curriculum implementation.

The studies conducted on the measurement of the

effectiveness of the implementation of the 2013

Curriculum generally reveal that the implementation

of the 2013 curriculum is less effective. Riptiani

Manik, et al who conducted the research in 2015

revealed that the implementation of 2013 curriculum

was less effective in terms of input aspects, the

implementation of 2013 curriculum was less

effective in terms of product aspects and concluded

that public elementary schools in rural areas of

Badung regency were less effective in implementing

2013 curriculum. Next, research conducted by Ni

Luh Karnita Dewi, et al in 2015 reported that the

implementation of the 2013 Curriculum on state

elementary schools in the outskirts of Badung

Regency was less effective.

Basically, the lack of effectiveness of the

implementation of the 2013 curriculum began with

educators. This is in line with the results of research

revealed by I Nyoman Ruja and Sukamto in 2015

which revealed that teachers experienced problems

in implementing the 2013 Curriculum. The problem

faced by teachers in the implementation of the 2013

National Curriculum was that teachers in the field

were not ready and teachers were still having

difficulties in making lesson plans despite the

teacher's syllabus and books.

The same research on the difficulties of teachers

in implementing the 2013 Curriculum was also

revealed by research carried out by Ayuk

Kusumastuti, Sudiyanto and Dini Octoria in 2016.

The study revealed that teachers experienced several

obstacles in implementing the 2013 Curriculum. The

results showed that teachers had difficulties in three

aspects of learning. These three aspects are learning

planning, learning implementation, and learning

assessment.

Simanjuntak, S. and Imelda, .

The Effectiveness of Realistic Mathematics Education by using the Context of Toba Batak Culture.

DOI: 10.5220/0009498503730380

In Proceedings of the 1st Unimed International Conference on Economics Education and Social Science (UNICEES 2018), pages 373-380

ISBN: 978-989-758-432-9

373

Other studies revealed that there were some

obstacles experienced by teachers in the

implementation of the 2013 Curriculum. The

research was research conducted by Heri Retnawati

in 2015. The study produced 4 research results. The

results of the first study revealed that training and

socialization had not been able to provide a good

and thorough understanding of the 2013 Curriculum.

The results of the second study revealed that

teachers had difficulty managing time in planning

learning, planning learning, planning attitude

assessments, and sorting knowledge and skills in the

preparation of assessment instruments. The results of

the third study revealed that time in the

implementation of learning, difficulties related to

learning devices, and difficulty activating students.

The results of the latest research revealed that the

assessment system in 2013 Curriculum was

complicated and needed a long time to compile

reports.

The difficulties faced by teachers in

implementing the 2013 curriculum have a significant

impact on students. As a result of the teacher's

inability, students become difficult to learn. Students

are as if placed on a ship without a skipper. Students

become confused and student learning activities

become passive.

Based on the problems that arise in the

implementation of the 2013 Curriculum, researchers

are interested in developing effective learning in

accordance with the demands of the 2013

curriculum. The development of learning carried out

will be a solution or answer to the confusion of

educators in designing learning in accordance with

the demands of the 2013 Curriculum. The

development of learning produced is also expected

to be a model or reference for educators in designing

learning through the context that is close to the

student's self. Thus, the learning process that

provokes students to be active in learning does not

become a difficult job because students are brought

to a real and contextual learning environment.

The development of learning that will be used to

produce effective learning in accordance with the

demands of the 2013 Curriculum is, the

development of realistic mathematical approaches

using the cultural context of the Toba Batak tribe.

This learning approach was chosen because it has

characteristics that are in accordance with the

scientific learning approach suggested by the 2013

curriculum. One of the main characteristics of the

scientific approach is based on facts or phenomena

and is not imaginary which is a characteristic of a

realistic mathematical approach. In addition, in

realistic mathematical approaches students are

facilitated to construct their own knowledge so that

students appear to be new inventors in accordance

with the philosophical basis of the 2013 Curriculum.

The next reason for the selection of the development

of realistic mathematical approaches is because

realistic mathematics contains steps the learning set

out in the 2013 curriculum is 5M activities which

include observing, asking, reasoning, trying and

building networks.

The context used in the development of this

learning is the cultural context of the Toba Batak

tribe which consists of cultural forms owned by the

Toba Batak tribe. Involving the cultural context in

the development of this learning approach is based

on the philosophy of developing the 2013

curriculum which reveals that education is rooted in

national culture and is a process of national cultural

inheritance. In the end, through this analysis the

context of the Toba Batak ethnic culture was applied

in the development of this learning.

As an illustration, here is an example of how the

development of learning a realistic mathematical

approach by using the cultural context of the Toba

Batak tribe to be designed. In the algebraic addition

material, the teacher usually gives an example "2x +

3y + 5x + 2y = 7x + 5y". With the development of

learning to be carried out, the material will be given

the cultural context of the Toba Batak tribe. So that

the example would be "Togap, Bonar, Poltak,

Maruhum each assigned to the teacher to bring 2

ulos sadum, 3 ulos ragihotang, 5 ulos sadum and 2

ulos ragihotang for the teacher's day program. What

are the ulos sadum and ulos ragihotang they bring? "

The answers that will be obtained are 7 ulos sadum

and 5 ulos ragihotang.

2 THEORICAL FRAMEWORK

2.1 Definition of Learning and

Mathematics Learning

Learning activities must be done by all humans.

Humans have been learning since their wombs.

Learning can be interpreted as an effort made by

someone to make changes in behavior, attitudes,

habits, knowledge, skills and so forth. So that in

learning happens a change from not knowing to

know, from not being skilled to being skilled and

from not being able to do something to be able to do

something (Khairani, 2013).

The word "learning" has an understanding of

doing learning activities. So the word "learning"

contains the process or events of the learning verb.

UNICEES 2018 - Unimed International Conference on Economics Education and Social Science

374

In other words, the term learning is a process related

to learning.

Mathematics can be interpreted as a branch of

science in which there is a logical thinking process

in accordance with certain principles, properties,

postulates and theorems. By connecting this

understanding to the notion of learning, mathematics

learning can be interpreted as the process of learning

about the development of logical thinking in

accordance with certain principles, properties,

postulates and theorems.

2.2 Batak Tribe Culture

Understanding culture can be defined descriptively,

historically, normatively, psychologically,

structurally and genetically. However, in general the

definition has the same meaning. Based on these

definitions, it can be summarized that culture is the

totality of inheritance that is passed down from

generation to generation in regulating behavioral

patterns and actions that must be maintained, so that

the community within them can meet their material

and emotional needs.

Every culture has a form of cultural results. This

form of culture consists of cultural systems, social

systems and physical culture. The form of culture in

the cultural system are ideas, ideas, values and

norms that bind the supporting community. The

form of culture in the social system is the overall

activities and actions of people who are patterned in

the supporting community. Whereas the form of

culture in the form of physical culture is the concrete

objects produced by the culture that can be seen and

can be touched.

The form of culture in the form of a cultural

system in the Toba Batak tribe are 7 living

philosophies inherited by ancestors. The seven

philosophy of life as outlined by Tinambunan are

mardebata (having God), marpinompar (having

children), martutur (having kinship), maradat

(having customs), marpangkirom (having hope for

hasangapon / being respected in society, hagabeon /

glory, hamoraon / wealth), marpatik (has rules and

laws) and maruhum (has law).

The form of culture in the social system of the

Toba Batak tribe is the result of cultural activities.

The results of these cultural activities are

(genealogy), Toba Batak language, marsiadapari

(mutual cooperation), Toba Batak dance (Tortor),

partuturon (kinship), writing Batak Toba, national

anthem batak (O Tano Batak), umpasa (quote) and

umpama (idiom).

The form of culture in the form of physical

culture in the Toba Batak tribe is the result of unique

and valuable works. The form of physical culture is

ruma sopo (traditional house), mats of pandan leaves

as a place to sit, gondang sabangunan (a set of

drums), monuments, sigale-gale (wayang) and ulos

(woven cloth).

2.3 Realistic Mathematic Education

The RME approach has special characteristics that

are different from other learning approaches. This

particular characteristic lies in the aspects that are

owned by PMR. De lange (in Sutarto Hadi, 2017:

38) states that mathematics learning with the RME

approach includes the aspects : (1) start a lesson by

asking "real" problems for students in accordance

with their level of experience, so that students

immediately engage in meaningful learning, (2)

problems given must be directed in accordance with

the objectives to be achieved in the lesson, (3)

students develop or create symbolic models

informally of the problems raised, (4) teaching takes

place interactively which means that students

explain and give reasons for the answers given,

understand the answers of their friends, agree to the

answers of their friends, express disapproval, seek

alternative solutions and reflect on every step taken

or the results of the lesson .

Each learning model or approach has the syntax

or steps in its implementation in the learning

process. The steps of the mathematics learning

process with RME are as follows: (1) understanding

contextual problems, (2) resolve contextual

problems, (3) compare and discuss answers, and (4)

attract conclusions.

2.4 Learning Effectiveness

Effective learning that actually has a meaning that is

far more important than just the achievement of

learning goals. According to Chris (2007: 96),

“Learning is an activity of construction, handled

with (or in the context of) others, driven by learner's

agency. Effective learning is the best of their best

plus the monitoring and context. Effective learning

can be seen as a virtuous cycle of effective learning

advances, effective learning processes, distinctions

between process and outcome decrease. Outcomes

include knowledge (of things, people, actions), skills

(with things, ideas, people), actions, feelings and

emotions, success, satisfaction, ideas and strategies

about learning, affiliation to learning, a sense of

oneself, including self as a learner, a sense of others

and interacting with them, a sense of membership of

a community”.

Based on the quotations that have been

described, it can be concluded that there are at least

The Effectiveness of Realistic Mathematics Education by using the Context of Toba Batak Culture

375

4 things that must be possessed by a learning process

so that it is said to be effective. The four things that

are meant are learning is the formation of student

activities so that in effective learning students must

be active, learning is controlled and directed by a

facilitator so that in effective learning the teacher

must be able to manage the learning process,

learning activities require supervision and evaluation

so that effective learning is needed observation of

the learning process and learning outcomes.

The effectiveness of learning in this study will

be directed according to the theory expressed by

Chris. Referring to Chris's statement, the

effectiveness of learning will be reviewed from 4

aspects:

1. The achievement of expected learning

objectives that meet the Minimum

Completeness Criteria. Indicators of

achievement of learning objectives in

accordance with indicators set by the

Department of Education and Culture of

Indonesia. Each student is said to have finished

his study (individual completeness) if the

proportion of students' correct answers is ≥

65%, and a class is said to have completed their

learning (classical completeness) if there are ≥

85% of students who have completed their

study (Depdikbud in Trianto, 2010: 241).

2. The activeness of students in listening to the

teacher / friend's explanation, writing (making

notes on solving problems, making

summaries), discussing / asking questions with

friends / teachers, organizing and finding

relationships from the information provided.

3. The ability of teachers to manage the learning

in an effort to find out student learning

readiness, provide explanations / provide

information, observe and motivate students to

do learning tasks, provide assistance and guide

student work.

4. Students' responses in terms of interest and

interest in learning components and activities.

3 RESEARCH METHODS

This type of research is development research. The

study was conducted at SMP Budhi Dharma Balige

Jl. Ki Hajar Dewantara Soposurung Balige which is

located in Toba Samosir Regency. The subjects of

this study were students at Secondary School Budhi

Dharma Balige 8

class on 2017/2018 academic

year. The object of this research is the effectiveness

of learning realistic mathematics education with the

context of Toba Batak culture.

The variables involved in this study are learning

effectiveness, student learning outcomes, student

activities, the ability of teachers to manage learning

and the student response. Learning outcomes are

scores obtained by students from the test of learning

outcomes that are measured using the test

instruments that have been compiled. Student

activity is an activity carried out by students during

the teaching and learning process. Student activities

will be observed using observation sheets of student

activities. The ability of teachers to manage the

learning is the score obtained by the teacher when

carrying out the activities of the teaching and

learning process. The ability of teachers to manage

the learning is measured using teacher observation

sheets. Student responses are students' responses to

learning that has been carried out. Student responses

will be measured using a questionnaire.

The instruments used in this study were learning

outcomes tests, observation sheets and

questionnaires. The observation sheets provided are

activity observation sheets for students, activity

observation sheets for teachers and learning

management observation sheets. Students'

Questionnaire responses to the components and

activities of learning about the subject matter,

student activity sheets, student books, ways of

learning, and the way the teacher teaches.

The results obtained were analyzed to check

whether the development of learning using a realistic

mathematics learning approach that has an effective

cultural context of the Batak Toba tribe in

accordance with the indicators that have been set.

These indicators include the validity of learning

devices and learning instruments as well as the

effectiveness of learning developed. Furthermore,

effectiveness is measured through indicators of

learning completeness, student activity, teacher's

ability to manage student learning and response.

The learning developed is said to be valid if the

level of validity produced is valid. If the level of

validity of the developed learning is lower than

valid, then a revision needs to be made to obtain a

valid level of validation.

Learning that is developed is said to be effective

if the level of effectiveness produced is high. If the

level of effectiveness of the developed learning is

lower than high, it is necessary to revise it to obtain

a high level of effectiveness.

The teacher is stated to be able to manage the

learning well if the score obtained by the teacher is

in a pretty good category. If the categories obtained

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376

below are good enough, the learning and tools are

re-reviewed for revision and the teacher is briefed to

improve the quality before a retest.

Student and teacher responses are measured by

the number of responses that are positive or negative

based on each questionnaire category that has been

provided. A positive response means expressing

happy, new, interested and interested and interested

in developing learning activities in realistic

mathematical approaches using the context of the

Toba Batak culture. Conversely a negative response

means stating the opposite condition of a positive

response. If a positive student response is greater

than or equal to 80%, then the achievement of

learning goals is stated to be achieved.

4 ANALYSIS

4.1 The Value of Learning Outcomes

The subject learned in realistic mathematics

education that uses the culture of the Batak Toba

culture in this study is the number pattern. This

material is taught as many as seven meetings. The

material discussed is special number pattern,

arithmetic sequence, geometry sequence, arithmetic

series and arithmetic series.

The learning procces ends with a test to measure

students' abilities and to analyze student

achievement. The test consists of 3 questions.

Question number one consists of 3 problems.

Question number two consists of 4 problems and

question number 3 consists of 3 problems. The

indicator of question number one determines the

type of number sequence, determine the general

formula for the sequence of numbers and determine

the pattern of convergencies sequences. The

indicator of question number two determines the

arithmetic sequence, determine the first term of the

arithmetic sequence, determine the arithmetic series

and calculate the number of n first arithmetic series.

The indicator of question number three is

determining the geometry sequence, determining the

first n term of the geometry sequence and

determining the number of the first n terms of the

geometry series.

The number of students that follow the exam is

40 students. The results of the test can be seen in the

following table:

Table 1: Summary of Student Exam Results

Value

The number of students 40

Lowest score 40

Highest score 100

Mean 80.7

Standard Deviation 15.9

Number of students who

has score same or lower

than 65

From the table above obtained information that

the lowest value obtained by students is 40. the

highest value obtained by students is 100. the

average class of students is 80.7. large distribution

of student value data is 15.9. the number of students

who have a value equal to or greater than 65 there

are 35 students. percentage of students who have a

value equal to or greater than 65 is 87.5%.

4.2 The Observation Sheet of Teacher

Ability to Manage Learning

Learning process of number pattern is carried out in

7 meetings. At each meeting, an observer observes

the activities carried out by the teacher. The

activities observed are preliminary activities, main

activities, closing activities and time management.

In the preliminary activity, the observer observes the

teacher's activities in opening learning which

consists of 4 activities. In the main activities,

observers observe the activities carried out by the

teacher in delivering learning material consisting of

15 activities. In the closing activity, the observer

observes the activities carried out by the teacher

when closing learning which consists of 2 activities.

In time management, observers observe how

teachers use learning time well.

Observations of the teacher's ability to manage

the learning can be seen in the following table:

Table 2: The Ability of Teacher

ic Cate

Odd Numbe

4.00

(

Good

)

Even and Square Numbe

4.09 (Good)

Rectangle and Triangle Numbe

4.00 (Good)

Pascal Triangle 4.00 (Good)

Arithmetic Se

uence and Series 4.04

(

Good

)

Geometr

uence 4.18

(

Good

)

Geometry Series 4.13 (Good)

Average 4.04 (Good)

From the table above, it can be seen that the

teacher's ability to manage the learning is in a good

category with an average of 4.04.

4.3 The Observation Sheet of Student

Activity

Student activities observed by observers were 7

meetings. The activities observed are activities in the

The Effectiveness of Realistic Mathematics Education by using the Context of Toba Batak Culture

377

preliminary stage, the stage of the main activities,

the closing stage and time management. Activity

was observed in the preliminary stage is how student

feedback to the teacher in starting learning which

consists of 4 activities. In the main activity stage,

what is observed is student feedback on the learning

activities presented by the teacher. Student activities

observed at the core activities consist of 15

activities. In the closing activity stage, what is

observed is student feedback to the teacher when

closing learning activities. In the time management

phase, the activity observed is how students use the

available learning time well.

The following is the result of observing student

activities observed by observers:

Table 3: The Activity of Student

ic Cate

Odd Numbe

3.95

(

Enou

)

Even and Square Numbe

3.95 (Enough)

Rectangle and Triangle Numbe

3.95 (Enough)

Pascal Trian

le 4.04

(

Good

)

Arithmetic Se

uence and Series 4.22

(

Good

)

Geometr

uence 4.27

(

Good

)

Geometry Series 3.95 (Enough)

Average 4.04 (Good)

From the table above, it can be seen that the

student’s activity is in a good category with an

average of 4.04.

4.4 The Student Response

Student responses were measured using a

questionnaire. The questionnaire used consists of

two choices, namely "yes" or "no". The

questionnaire contains 4 aspects namely feeling of

pleasure, novelty, feeling of interest and desire.

Aspects of pleasure and novelty contain 4 indicators

namely subject matter, student activity sheet, the

way of learning and the way the teacher teaches.

Interested aspects of learning consist of indicators

interested in participating in further learning

activities with realistic mathematics education

activities using the context of Toba Batak culture.

Aspects of desire consist of desire in language, the

appearance of the writing, illustration of the teacher

and the location of the image contained in the

student activity sheet.

The following is a summary of the results of the

student response questionnaire on learning realistic

mathematics using the context of the Toba Batak

culture that has been implemented.

Table 4: Results of Student Response Questionnaire

Indicato

Cate

ppy

Not Ha

ppy

Yes No

Lesson 97.5% 2.5%

Worksheet 97.5% 2.5%

How to Stud

95% 5%

How Teacher to Teach 100% 0%

Avera

e 97.5% 2.5%

New Not New

Lesson 97.5% 2.5%

Worksheet 100% 0%

How to Stud

82.5% 17,5%

How Teacher to Teach 97.5% 2.5%

Avera

e 94.4 5.6

Interested in participating in

further learning activities with the

learning mathematics education

activities using the context of

Toba Batak culture.

97.5% 2.5%

Desire in the language, writing

appearance, teacher illustration

and the location of the picture

contained in the student activity

sheet.

100% 0%

The percentage of students who were happy with

realistic mathematics education with the context of

Toba Batak culture as much as 97.5% and students

who were not happy with realistic mathematics

education with the context of Toba Batak culture as

much as 2.5%. Based on these results, in accordance

with the indicators that have been determined, it can

be said that students have a positive response to the

learning carried out. In this case, the percentage of

students' positive response is 97.5% > 80%. Thus, it

is concluded that students feel happy with learning

realistic mathematics education using the context of

Toba Batak culture.

The percentage of students who stated realistic

mathematics education with the context of the new

Toba Batak culture for these students was as much

as 94.38% and students who did not feel new with

learning realistic mathematics education using the

context of Toba Batak culture as much as 5.62%. So

the responses of student to the learning are positive.

In this case, the average percentage of students'

positive response is 94.38% > 80%. Thus, it is

concluded that realistic mathematics learning with

the context of Toba Batak culture is new to students.

The percentage of students who are interested in

participating in further learning activities with

realistic mathematics education activities using the

context of Toba Batak culture is as much as 97.5%

and students who are not interested in learning

realistic mathematics education using the context of

the Toba Batak culture for the next lesson are 2.5%.

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378

So it can be said that students have a positive

response to learning that is carried out with a

percentage of students' positive response of 97.5% >

80%. Thus, students are interested in participating in

further learning activities with realistic mathematics

learning activities using the context of Toba Batak

culture.

The percentage of students who are interested in

language, writing appearance, teacher illustration

and the location of the picture contained in the

worksheet is as much as 100%. Thus, it can be said

that students have a positive response to learning

carried out with a percentage of students' positive

response of 100% > 80%. Thus students are

interested in language, writing appearance, teacher

illustration and the location of images contained in

worksheet learning realistic mathematics education

using the context of Toba Batak culture.

5 RESULT AND DISCUSSIONS

Effective learning indicators in this study are

reviewed from 4 indicators in accordance with what

was revealed by to Chris (2007: 96). These

indicators are students' completeness in learning, the

ability of teachers to manage learning, student

activities and student responses.

Sum of students who have scores equal to or

greater than 65 from the results of the study is 35

people. If presented in percent, the percentage value

is 87.5%. Minimum individual completion and

completeness of the drinking class according to the

Ministry of National Education are 65 and 85%.

Based on these indicators, the individual

completeness and class of students in this study meet

the stipulated conditions.

The ability of teachers to manage the learning in

this study obtained an average score of 4.04. The

value if presented in quality, then the ability of

teachers to manage the learning is in a good

category.

Good learning is learning that is able to activate

student activities. Based on observations obtained

information that the average value of student activity

is 4.04. This value in the form of quality means

good. So, the activities of students in realistic

mathematics education using the context of the Toba

Batak culture are good. In other words students are

actively participating in learning activities.

The results of the analysis for student response

aspects which consist of happy or not happy, new or

not new, interested or not interested and having the

desire or not having desire all show positive results.

Students enjoy learning realistic mathematics

education with the context of Toba Batak culture.

Learning realistic mathematics with the context of

Toba Batak culture is new learning for students.

Students are interested in participating in further

learning activities with realistic mathematics

learning activities using the context of Toba Batak

culture. Students are also having a desire in

language, writing appearance, teacher illustration

and the location of the images contained in the

student activity sheet used. From the achievement of

these four aspects it was concluded that students had

a positive response to realistic mathematics learning

using the context of Toba Batak culture.

6 CONCLUSIONS

The results of the study show that students meet the

minimum completeness criteria that have been set by

the government, the teacher is able to manage

learning well, students actively follow learning and

positive student responses to the learning carried

out. based on these four results, it can be concluded

that learning realistic mathematics using the context

of Toba Batak culture is effective.

ACKNOWLEDGEMENTS

Thank you from the author, to the Kementerian

Riset Teknologi dan Pendidikan Tinggi

(Kemristekdikti) of the Republic Indonesia for the

support and assistance of research funds in the

Penelitian Dosen Pemula scheme which has been

granted with an agreement number 227 / K1.1 /

LT.1 / 2018. Hopefully the results of this study are

useful for the development of Indonesian education

science.

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