developing students' spatial ability in understanding three-dimensional representations universitas

339 Pages·2017·15.85 MB·English

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DEVELOPING STUDENTS’ SPATIAL ABILITY
IN UNDERSTANDING THREE-DIMENSIONAL
REPRESENTATIONS

MASTER THESIS

Aan Hendroanto
137785069

UNIVERSITAS NEGERI SURABAYA
PROGRAM PASCASARJANA
PROGRAM STUDI PENDIDIKAN MATEMATIKA
2015
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DEVELOPING STUDENTS’ SPATIAL ABILITY IN UNDERSTANDING
THREE-DIMENSIONAL REPRESENTATIONS

MASTER THESIS

A Thesis submitted to
Surabaya State University Postgraduate Program
As a Partial Fulfillment of the Requirement for the Degree of
Master of Science in Mathematics Education Program

Aan Hendroanto
NIM 137785069

UNIVERSITAS NEGERI SURABAYA
PROGRAM PASCASARJANA
PROGRAM STUDI PENDIDIKAN MATEMATIKA
2015
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APPROVAL OF SUPERVISORS

Thesis by Aan Hendroanto, NIM 137785069, with the title Developing Students’
Spatial Ability in Understanding Three-Dimensional Representations has been
qualified and approved to be tested.

Supervisor I, Date,

Prof. I Ketut Budayasa, Ph.D. ………………………….

Supervisor II, Date,

Dr. Abadi, M.Sc. ………………………….

Acknowledged by
Head of the Mathematics Education Study Program,

Dr. Agung Lukito, M.S.
NIP 196201041991031002
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APPROVAL

Thesis by Aan Hendroanto, NIM 137785069, had been defended in front of the
Board of Examiners on June 29, 2015.

Board of Examiners

Name Signature Position

Dr. Agung Lukito, M.S. ………………… Chairman/Member

Prof. I Ketut Budayasa, Ph.D. ………………… Member/Supervisor I

Dr. Abadi, M.Sc. …………………. Member/Supervisor II

Prof. Dr. Siti Maghfirotun Amin, M.Pd. …………………. Member

Dr. Siti Khabibah, M.Pd. ………………..... Member

Acknowledged by
Director of Postgraduate Program,

Prof. I Ketut Budayasa, Ph.D.
NIP 195712041994021001
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DEDICATION

I dedicate this thesis to my family and those who support me endlessly:
My mother, Roisah
Who teaches me to balance my life and pursue my dreams.
My father, Joyo Suprapto
Who shows me how to not give up this life.
My sisters, Eli Ernawati and Iin Dwi Susanti
Who inspire me in many ways.

I WILL ALWAYS LOVE MY FAMILY
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ABSTRACT

Hendroanto, Aan. 2015. Developing Students’ Spatial Ability in Understanding
Three-Dimensional Representations. Thesis, Mathematics Education Study
Program, Postgraduate Program of Surabaya State University. Supervisors: (I) Prof.
I Ketut Budayasa, Ph.D. and (II) Dr. Abadi, M.Sc.

Keywords: Spatial Ability, Spatial Visualization, Spatial Orientation,
Understanding 3D representations, Realistic Mathematics Education
(RME), Design Research.

Spatial ability is known as the main key to develop students’ ability in
understanding three-dimensional (Abbreviated as 3D) representations that becomes
the anchor of the development of 3D geometry thinking. Therefore, to develop
students’ ability in understanding 3D representations, we must develop their spatial
ability. The present study aims to design a sequence of activities to help young
learners developing their ability in understanding 3D representations. To develop
such activities, spatial visualization task and spatial orientation task are combined
with the aspects of understanding 3D representations. The sequence is also designed
based on the characteristics of Realistic Mathematics Education (RME) and
students’ learning style. In addition, the present study also targets to contribute to
the local instruction theory of developing students’ spatial ability such as how the
design works and how students’ learning goes. Accordingly, design research is
chosen as the research approach in order to produce both the instructional materials
and also the theory. We conducted two implementations of teaching experiment
involving 30 third-grader students of SD Laboratorium UNESA, Surabaya. The
result of the first implementation showed that the activities need some
improvements to have better support for the students. After the second trial, the
activities indicated a better support to the development of students’ spatial ability
in understanding 3D representations. These activities are identifying pictures in
photography activity and also drawing and constructing objects of building blocks
in reporting temples activity. During the implementation, these activities gave
students chance and guided them to explore the views of 3D objects and their
representations. Students’ learning progress is also in line with the hypothetical
learning trajectory.
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ABSTRAK

Hendroanto, Aan. 2015. Developing Students’ Spatial Ability in Understanding
Three-Dimensional Representations. Tesis, Program Studi Pendidikan Matematika,
Program Pascasarjana Universitas Negeri Surabaya. Pembmbing: (I) Prof. I Ketut
Budayasa, Ph.D. and (II) Dr. Abadi, M.Sc.

Kata Kunci: Kemampuan Spasial, Spasial Visualisasi, Spasial Orientasi,
Memahami Representasi 3D, Pendidikan Matematika Realistik,
Design Research.

Kemampuan spasial dikenal sebagain kunci utama untuk mengembangkan
kemampuan siswa dalam memahami representasi tiga dimensi (disingkat 3D) yang
merupakan dasar dalam perkembangan berpikir geometry 3D. Oleh karena itu,
untuk mengembangkan kemampuan siswa dalam memahami representasi 3D, kita
harus mengembangkan kemampuan spasial siswa. Penelitian kali ini bertujuan
untuk mendesain serangkaian kegiatan untuk membantu siswa mengembangkan
kemampuan mereka dalam memahami representasi 3D. Untuk mendesain kegiatan
ini, tugas atau kegiatan yang berkaitan dengan spasial orientasi dan spasial
visualisasi dikombinasikan dengan aspek-aspek dalam memahami representasi 3D.
Serangkaian kegiatan ini juga dikembangkan berdasarkan karakteristik dari
Pendidikan Matematika Realistic (RME) dan gaya belajar siswa. Sebagai
tambahan, penelitian kali ini juga bertujuan untuk berkontribusi dalam
mengembangkan lokal teori untuk mengembang kemampuan spasial siswa seperti
bagaimana kegiatan berjalan and bagaiman respon siswa serta perkembangannya
berjalan. Sesuai dengan tujuan ini, design research dipilih sebagai pendekatan
dalam penilitian untuk menghasilkan baik kegiatan dan teorinya. Penelitian ini
melaksanakan dua kali implementasi yang melibatkan 30 siswa kelas 3 dari SD
Laboratrium UNESA, Surabaya. Hasil dari implementasi pertama menunjukan
bahwa kegiatan yang didesain memerlukan beberapa perbaikan untuk lebih
meningkatkan kualitas kegiatan bagi siswa. Setelah implementasi kedua, kegiatan
yang didesain mengindikasikan hasil yang lebih baik dalam membantu siswa untuk
mengembangkan kemampuan spasial untuk memahami representasi 3D. Kegiatan
yang didesain ini terdiri dari mengidentifikasi foto-foto dalam kegiatan fotografi
dan kegiatan menggambar dan mengknstruksi objek-objek dari blok-blok kayu
dalam kegiatan melaporkan candi. Selama implementasi, kegiatan-kegiatan yang
didesain memberikan siswa kesempatan dan menuntun mereka untuk mengeksplore
objek-objek 3D dan representasinya. Progres belajar siswa juga sesuai dengan
trajek belajar yang telah diprediksikan (HLT).
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PREFACE

Assalamu’alaikum Wr.Wb.
Alhamdulillah to The Almighty, Allah SWT, so that I can finally finish this
thesis without much difficulties. Blessing and greetings to the prophet Muhammad
SAW who inspires people in the world to be wise and merciful among the others.
This thesis is one of my great works that I have ever achieved in my short
life. Of course, I would not be able to complete it without assistance, guidance,
motivation and support from the people involved in this study. Therefore, I would
like to thank and express my gratefulness to:
1. Prof. I Ketut Budayasa, Ph.D., Dr. Abadi, M.Sc. and Dr. Agung Lukito, M.S.
from the State University of Surabaya as my supervisors and supporting
lecturer who had helped, guided, and assisted me from the beginning of my
study till the end. All their advices had helped me through the writing and the
analyzing process of the present study.
2. Dr. F.H.J Frans van Galen, and Dr. H.A.A. (Dolly) van Eerde from Freudenthal
Institute of Utrecht University, who had assisted and guided me during the very
early phase of my study, designing process, developing activities, and building
the framework of the theory. They are not only professional but also friendly
as a lecture. They even helped and assisted me to do skating. Thank you very
much!
3. Dr. M.L.A.M. Dolk, the coordinator of the International Master Program on
Mathematics Education (IMPoME). He never stopped to push and motivate me
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no matter what happened. He was the one who was responsible for what I had
achieved including this study.
4. PMRI Center Board for giving me a very big opportunity to be one of the
awardees of IMPoME scholarship. I and my family really thank for the
chances.
5. All lecturers and staff of postgraduate program of the State University of
Surabaya and Utrecht University for their supports during my study in both
Surabaya and Utrecht.
6. Daluri, S.Pd as the regular mathematics teacher and the students of grade 3B
and 3C of SD Laboratorium UNESA as the participants involved in the present
study. Without them, the research would never be finished.
7. Last but not least, my family and my friends for their endless motivation and
technical or non-technical support during the study.
I do hope this study will contribute to the development of mathematics
education, especially in Indonesia. Finally, I fully realize that the present study still
has so many weakness in many aspects. Therefore, any critics, comments, and
suggestions are really welcomed.
Surabaya, June 2015
Author,

Aan Hendroanto
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TABLE OF CONTENTS

COVER ……………………………………………………………………… i
APPROVAL OF SUPERVISOR ………………………………………….. iii
DEDICATION ...........………………………………………………………. v
ABSTRACT ...………………………………………………………………. vi
ABSTRAK ………………………………………………………………….. vii
PREFACE .........................………………………………………………….. viii
TABLE OF CONTENTS …..………………………………………………. x
LIST OF FIGURES ……………….……………………………………….. xii
LIST OF TABLES ………………….…………………………………….... xv
LIST OF APPENDICES …………………………………………………… xvi
LIST OF FRAGMENTS ……..…………………………………………….. xvii

CHAPTER I INTRODUCTION …………………………………….....….. 1
A. Research Background ………………………………………………… 1
B. Research Question ……………………………………………………. 5
C. Aims of the Research …………………………………………………. 5
D. Definition of Key Terms ……………………………………………… 6
E. Criteria of the Study …………………………………………………... 8
F. Significance of the Research ………………………………………….. 9

CHAPTER II THEORETICAL FRAMEWORK ……………………...…. 10
A. Spatial Ability …………………………………………………………. 10
B. Spatial Ability in Understanding 3D representations …………………. 15
C. Spatial Ability in Indonesian Curriculum ……………………………... 21
D. Realistic Mathematics Education ……………………………………... 21
E. The Role of Students’ Learning Style in the Design ………………….. 25
F. The Role of Teachers in RME classroom ……………………………... 27
G. Design Research ………………………………………………………. 30
H. The Present Study and the Outline of Hypothetical Learning Trajectory 36

CHAPTER III RESEARCH METHOD …………………………………... 39
A. Research Method and Timeline of the Study …………………………. 39
B. Subject of the Study …………………………………………………... 43
C. Data Collection ……………………………………………………….. 44
D. Data Analysis …………………………………………………………. 48

CHAPTER IV RESULT AND DISCUSSION ………………………….… 53
A. Preliminary Teaching Experiment ……………………………………. 53
1. Preparation and Designing Phase ….………………………………. 53