july, 21-23 2011 - uny

ii

PROCEEDINGS International Seminar and the Fourth National Conference on Mathematics Education

Department of Mathematics Education, Yogyakarta State University

July, 21-23 2011 Held by: Departement of Mathematics Education Faculty of Mathematics and Natural Science Yogyakarta State University Published by: Departement of Mathematics Education Faculty of Mathematics and Natural Science Yogyakarta State University Karangmalang, Sleman, Yogyakarta Faculty of Mathematics and Natural Science UNY, 2012 1st Issue May 2012 Issue Katalog of The Issue (KDT) Reviewers : Prof. Dr. Ahmad Fuzan [et.al] – Yogyakarta, Mathematics and Natural Science Faculty Editors : Nur Hadi W [et.al] – Yogyakarta, Yogyakarta, Faculty of Mathematics and Natural Science Yogyakarta State University, 2012 The proceeding can be accessed at : http://eprints.uny.ac.id/view/subjects/prosiding.html ISBN : 978–979–16353–7–0

978-979-16353-7-0 Process editing of all the articles in proceedings is conducted by the Team Reviewer International Seminar and the Fourth National Conference on Mathematics Education from Departement of Mathematics Education, Faculty of Mathematics and Natural Science,Yogyakarta State University

iii

PROCEEDING International Seminar and the Fourth National Conference on Mathematics Education

Department of Mathematics Education, Faculty of Mathematics and Natural Science Yogyakarta State University July, 21-23 2011

This paper has been presented at International Seminar and the Fourth National Conference on Mathematics Education

“Building the Nation Character through Humanistic Mathematics Education” Department of Mathematics Education,Yogyakarta State University,

Yogyakarta, July 21-23 2011

Paper Reviewers : 1. Prof. Ahmad Fauzan (Padang State University) 2. Abdur Rahman As'ari, MA (Malang State University) 3. Dr. Cholis Sa’dijah, M.Pd,M.A (Malang State University) 4. Prof. Dr. Jozua Sabandar (UPI Bandung) 5. Prof. Yaya S. Kusuma, M.Sc., Ph.D. (UPI Bandung) 6. Dr. Turmudi (UPI Bandung) 7. Prof Dr. Sutarto Hadi (Lambung Mangkurat University) 8. Dr. Rahmah Johar (Syah Kuala University) 9. Dr. Yansen Marpaung (USD Yogyakarta) 10. Prof. Dr. Rusgianto H.S. (Yogyakarta State University) 11. Sukirman,M.Pd. (Yogyakarta State University) 12. Dr. Marsigit (Yogyakarta State University) 13. Dr.Agus Maman Abadi (Yogyakarta State University) 14. Dr. Hartono (Yogyakarta State University) 15. Dr. Djamilah B.W., M.Si (Yogyakarta State University) 16. Dr. Sugiman (Yogyakarta State University) 17. Dr. Ali Mahmudi (Yogyakarta State University) 18. Dr. Jailani (Yogyakarta State University) 19. Dr. Dhoriva Urwatul Wutsqo (Yogyakarta State University) 20. Dr. Heri Retnawati (Yogyakarta State University)

Department of Mathematics Education Faculty of Mathematics and Natural Science

Yogyakarta State University 2012

iv

Preface Assalaamu’alaikum Warahmatullaahi Wabarakatuh.

First of all, we would like to say alhamdulillah, thank to Alloh SWT, the most gracious and the most merciful, therefore the proceeding of The Fourth National Conference on Mathematics Education can be finished successfully. The conference was held on 21 – 23 July, 2011 for the cooperation of Universitas Negeri Yogyakarta (Yogyakarta State University) and and Indonesian Mathematical Society (IndoMS). It is an honor for us to be entrusted by IndoMS and UNY to organize The Fourth National Conference on Mathematics Education. The theme of the conference was “Building the nation character through humanistic mathematics education” and the aims were to be a forum for researchers, lecturers, teachers, students, and people who were care in mathematics education to share positive, constructive and creative ideas in relation to the development of the nation character through humanistic mathematics education.

We are very happy and proud, because we have seven invited speakers in their expertise, three invited speakers are from abroad (Prof. Christa Kaune, Germany; Prof. Isoda Masami, Japan; and Prof. Dr. Noor Azlan bin Ahmad Zanzali, Malaysia) and four invited speakers are from Indonesia (Dr. Ary Ginanjar Agustian, Prof. Jozua Sabandar, Ph.D., Prof. Dr. Sutarto Hadi, and Dr. Marsigit). We also very happy since we have numerous participants who are come from all parts of Indonesia and also from Malaysia. Alhamdulillah, there were 83 papers related to mathematics education that have been presented on parallel session of this conference.

We are very grateful to all reviewers who have been dedicated to review the articles of the proceedings. The reviewers are: Prof. Yaya S. Kusuma, M.Sc., Ph.D. (UPI Bandung), Prof. Jozua Sabandar, M.A., Ph.D. (UPI Bandung), Turmudi, M.Sc., Ph.D. (UPI Bandung), Prof. Sutarto Hadi, M.Sc., Ph.D. (UNLAM), Prof. Dr. Ahmad Fauzan (UNP), Dr. Rahmah Johar (UNSYIAH Aceh), Dr. Abdurrahman As’ari, M.A. (UM), Dr. Cholis Sa’dijah (UM Malang), Dr. Yansen Marpaung (USD Yogyakarta), Sukirman, M.Pd. (UNY), Dr.Marsigit, M.A. (UNY), Dr. Hartono (UNY), Dr. Djamilah B.W., M.Si (UNY), Dr. Sugiman (UNY), Dr. Ali Mahmudi (UNY), Dr. Agus Maman Abadi (UNY), Dr. Jailani (UNY), Dr. Dhoriva Urwatul Wutsqo (UNY)and Dr. Heri Retnawati (UNY).

The proceeding contains as many as 84 articles. The author of the article came from several institutions, namely: UNY, UTM Malaysia, UPI, UNJ, UNNES, UM, Unsyiah Kuala, PPs UNY, Sekolah Pascasarjana UPI, PPs UNJ, S2 Pengajaran Matematika ITB, UNIMED, UNHALU, UNSRI, UNRAM, Universitas Negeri Gorontalo, UNILA, UNS, Univeritas Tadulako, UIN Syarif Hidayatulloh Jakarta, STAIN Tulungagung, UII, UNISBA Bandung, USD Yogyakarta, Universitas Muhammadiyah Purworejo, STIKOM Surabaya, Universitas Muhammadiyah Bengkulu, Universitas PGRI Adi Buana Surabaya, UKSW Salatiga, Universitas PGRI Palembang, Universitas Widyadarma Klaten, STKIP Siliwangi Bandung, Universitas Veteran Bangun Nusantara Sukoharjo, STKIP Sebelas April Sumedang, SMA N 4 Tasik Malaya, Universitas Siliwangi Tasikmalaya, Universitas pelita Harapan Tangerang, SMA Lentera Harapan Lampung, UNIROW Tuban and IKIP PGRI Semarang.

We hope that the proceeding be useful, not only for the authors, but also can enrich the creative and innovative ideas that can support the advancement of mathematics education, especially in Indonesia.

Yogyakarta, May 2012 Chairman of the Committee Dr. Ali Mahmudi

v

CONTENTS

Cover i Publishing Statement ii Paper Reviewers iii Preface iv Contents v

Code Name Institution Title Page U - 1

Noor Azlan Ahmad Zanzali

Faculty of Education Universiti Teknologi Malaysia Email: [email protected]

Improving The Quality Of The Mathematics Education: The Malaysian Experience

M - 1

U - 2

Christa Kaune1, Edyta Nowinska2

1Institut für Kognitive Mathematik, Universität Osnabrück, Germany, 2Institute MATHESIS, Pyzdry, Poland

Development Of Metacognitive And Discursive Activities In Indonesian Maths Teaching A Theory Based Analysis Of Communication Processes

M-23

U - 3

Marsigit

Faculty of Mathematics and Science, Yogyakarta State University

Developing The Attitude And Creativity In Mathematics Education

M-34

U - 4

Sutarto Hadi

Department of Mathematics Education, Lambung Mangkurat University, Banjarmasin

Developing The Nation Character Through Realistic Mathematics Education

M-65

U – 5 Masami Isoda

University of Tsukuba, Japan Problem Solving Approaches in Mathematics Education as a Product of Japanese Lesson Study

M-77

P – 1

Abd. Qohar

Mathematic Department, State University of Malang, Indonesia

Mathematical Communication: What And How To Develop It In Mathematics Learning?

1

P – 2

Anggit Prabowo Marsigit Atmini Dhoruri

Yogyakarta State University E-mail: [email protected]

Improving The Understanding Of The Arithmetic Concept Through Realistic Mathematic Education (RME)

13

P – 3

Rustanto Rahardi

Faculty of Science and Mathematics Malang University Jl. Semarang 5 Malang, e-mail: [email protected]

Valsiner’s Zone Theory As The Teachers’ Zone Of Proximal Development

25

P – 4

Budi Mulyono

Mathematics Education Department Sriwijaya University email: [email protected]

Traditional Teaching About Angles Compared To An Active Learning Approach That Focuses On Students Skills In Seeing, Measuring And Reasoning, Including The Use Of Dynamic Geometry Software: Differences In Achievement

37

P – 5

Theresia Kriswianti Nugrahaningsih

Department of Mathematics Education Widya Dharma University Klaten e-mail: [email protected]

Using Metacognition In Learning Mathematics Toward Character Building

47

P – 6

Dasa Ismaimuza

Departement of Mathematics Education Tadulako University Palu, Central Sulawesi, e-mail:[email protected]

Creative Thinking Ability on Mathematics of Junior High School in Palu Based on School Levels

59

P – 7

Destiniar

Department of Mathematics EducationPGRI University of Palembang e-mail:

Effect of Contextual Learning Ability Against Students Understanding Math Concepts SMP

65

vi

[email protected] P – 8

Supriyono

Department of Mathematics Education Muhammadiyah University of Purworejo

Developing Mathematical Learning Device Using TTW (Think- Talk-Write) Strategy Assisted By Learning CD To Foster Mathematical Communication

73

P – 9

Nila Kesumawati

Departement of Mathematics Education, PGRI University of Palembang email: [email protected]

Development Mathematical Problem Solving Problems At Junior High School

85

P – 10

Dodi Syamsuduha

SMA Negeri 4 Kota Tasikmalaya e-mail: [email protected]

Pengaruh Pembelajaran Kooperatif Berbantuan Program Geometer’s Sketchpad Terhadap Peningkatan Kemampuan Berpikir Kritis Matematik Siswa SMP

95

P – 11

Kms. Muhammad Amin Fauzi

FMIPA Universitas Negeri Medan e-mail : [email protected]

Peningkatan Kemampuan Koneksi Matematis Dan Kemandirian Belajar Siswa Dengan Pendekatan Pembelajaran Metakognitif Di Sekolah Menengah Pertama

109

P -12

Gelar Dwirahayu

Department of Mathematics Education Faculty of Tarbiya and Teachers Tratining State University of Islamic Syarif Hidayatullah Jakarta [email protected]

Implementation Of Character-Building Education In Mathematics Teaching And Learning To Create Of Human Character

123

P – 13 Iis Margiyono1, Helti Lygia Mampouw2

1,2Program Studi Pendidikan Matematika FKIP, 2Pusat Studi Pendidikan Sains, Teknologi dan Matematika, Universitas Kristen Satya Wacana, Jl. Diponegoro 52-60 Salatiga 50711, Indonesia E-mail: [email protected]

Deskripsi Pedagogical Content Knowledge Guru Pada Bahasan Tentang Bilangan Rasional

133

P – 14

Kariyam Perdana, R.B.

Department of Statistics Islamic University of Indonesia e-mail: [email protected]

Factor Analysis Of Ordinal Data Based On Weighted Ranking And Its Application To Reduce Perception Variables To Math Lessons Of Senior High School Student

145

P – 15

Syahrir

Departement of Mathematics Education Teachers’ Training College of Mataram

Effects of the Jigsaw and Teams Game Tournament (TGT) Cooperative Learning on the Learning Motivation and Mathematical Skills of Junior High School Students

155

P – 16

Musthofa

Department of Mathematic Education, Yogyakarta State University

Some Creative And Easy Methods To Calculate A Multiplication Of Two Numbers

167

P – 17

Oktavianus Adi Nugraha 1, Sundo Nurbono 1, Dimas Adi Nugroho1, Handita Sari 2, Kriswandani3

Mathematics Education Study Program Education and Teaching Faculty Satya Wacana Christian University

Effort To Improve Student Achievement In Learning Through The Development Of Function Composition Method Of Discussion On The Approach To Contextual Teaching And Learning (CTL) In Class Xi IPA 1 Salatiga Christian Senior High School 1

173

P – 18

Ilfi Norman, Zaid Zainal Abidin, Md. Nor Bakar

Universiti Teknologi Malaysia

Secondary School Students’ Abilities Through Problem Posing Activities

187

P – 19 Kodirun Mathematics Department of Developing Students Ability To Write 199

vii

Faculty of Mathematics and Natural Sciences of University of Haluoleo Kendari Email: [email protected]

Mathematical Proof By Polya Method

P – 20

Yusuf Hartono

Department of Mathematics Education Sriwijaya University e-mail: [email protected]

Mathematics Learning Within Culture And Nation Character: Using Traditional Dance In Learning The Concept Of Symmetry At Grade IV Primary School

207

P – 21

Bambang Priyo Darminto

Mathematics Education Department, Muhammadiyah University of Purworejo e-mail: [email protected]

Developing Cultural And Character Nations Values Through Mathematics Learning

215

P – 22

Umy Zahroh

Department of Mathematics Education, State Islamic College (STAIN) of Tulungagung Mayor

The Influence Of Edutainment Method Towards The Mathematics’ Learning Achievement Of The Sixth Grade Students Of SDN I And SDN II Tanjungsari Boyolangu Tulungagung

223

P – 23

Abdul Muin

Department of Mathematics Education, Syarif Hidayatullah State Islmic University Jakarta e-mail: [email protected]

The Situations That Can Bring Reflective Thinking Process In Mathematics Learning

231

P – 25 Adi Nur Cahyono

Department of Mathematics, Semarang State University, Email: [email protected]

MatriksMovie: Building The Nation Character Through Movie-Based Realistic Mathematics Education

239

P – 25 Aning Wida Yanti

Department of Mathematics Education, State University of Malang [email protected]

Learning Mathematics To Grow Metacognitive Ability In Understanding And Mathematic Problems Solving On Limit

251

P – 26

Asep Ikin Sugandi STKIP Siliwangi Bandung Email : [email protected]

Developing National Character Through Mathematics Instruction Via Mathematics Instruction With Problem-Based Learning In Jigsaw Typed Cooperative Setting

263

P – 27

Darmawan1 Iwan Pranoto2 .

1)Teacher in Majalengka State High School 1 - Student of Master of Mathematics for Teaching, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Email: [email protected] 2)Lecturer in the Math Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Email: [email protected]

On The Teaching Of Analyzing The Effects Of Parameter Changes On The Graph Of Function

275

P – 28

Dylmoon Hidayat Ismail Daniel

Department of Mathematics Education, Universitas Pelita Harapan, Tangerang email: [email protected] and Sekolah Lentera Harapan, Lampung

Mathematics Teachers’ Performance In Teaching Using English At Secondary National Plus Schools

283

viii

email:[email protected] P – 29

Hapizah Trimurti Saleh

Department of Mathematics Education, University of Sriwijaya Inderalaya Ogan Ilir, e-mail: [email protected]

Developing The Teaching Module Of Initial Values And Boundary Problems For Students Of Mathematics Education Program

291

P – 30

Herry Agus Susanto1) Bambang Suharjo2)

1) Veteran Bangun Nusantara University of Sukoharjo 2) Muhamadiyah University of Gresik E-mail : [email protected]

Mathematics And Mathematics Education Values In Forming Someone’s Character

299

P – 31

Hongki Julie

Sanata Dharma University [email protected]

Development Guided Reinvention Principle In Pmri Approach In Use The Teacher Guide In Elementary School

311

P – 32

Iwan Gunawan1 Iwan Pranoto2

1) Student of Master of Mathematics for Teaching, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Email: [email protected]. 2) Lecturer in the Math Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Email: [email protected]

An Instruction Idea Connecting Integral Concepts In Senior High School With Irregular Area Measurement In Elementary School

321

P – 33

Kadir Eny Wulandari

Department of Mathematics Education FITK, Universitas Islam Negeri Syarif Hidayatullah Jakarta e-mail: [email protected]

The Implementation Of Multiple Intelligences Based Learning To Improve Students’ Learning Activities, Response, And Learning Outcome In Mathematics

333

P – 34

Lia Kurniawati

Departement of Mathematics Education, UIN Syarif Hidayatullah Jakarta

Developing Mathematical Reflektive Thinki NG Skills Through Problem Based Learning

335

P – 35

Mimih Aminah Jozua Sabandar

STKIP Sebelas April Sumedang e-mail: [email protected] Indonesia University of Education (UPI)

The Potency Of Metacognitive Learning To Foster Mathematical Logical Thinking

345

P – 36

Mujiyem Sapti Suparwati

Department of Mathematics Education, Muhammadiyah University of Purworejo e-mail: [email protected]

An Experiment Of Mathematics Teaching Using SAVI Approach And Conventional Approach Viewed From The Motivation Of The Students Of Sultan Agung Junior High School In Purworejo

357

P – 37

Mustamin Anggo

FKIP Universitas Haluoleo Kendari

The Metacognitive Process Of Teachers College Students In Solving Mathematical Problems

367

P – 38

Nyimas Aisyah

Department of Mathematics Education Sriwijaya University Km. 32 Indralaya Ogan Ilir email [email protected]

Values Implemented By Secondary Teachers In Mathematics Problem Solving

377

P – 39

Rasiman

Department of Mathematics Education, Faculty Mathematics and Natural Sciences Education IKIP PGRI Semarang

Leveling Of Students Critical Thinking Abilities In Mathematics Problem Solving In Line With Gender Differences

391

P – 40

Sudirman

Department of Mathematics State University of Malang

Penginvestigasian Objek Fungsi Sebagai Hasil Pengkapsulan Proses: Suatu Studi

401

ix

e-mail : [email protected]

Kasus Untuk NURI

P – 41

Supratman

Mathematics Education Courses And Pedagogy Faculty Of Education, University Of Siliwangi Tasikmalya e-mail: [email protected]

The Influence Of The Use Of E-Book And E-Learning Base In Students Achievement

415

P – 42

Tedy Machmud

Department of Mathematics Education Gorontalo State University e-mail: [email protected]

Scaffolding Strategy In Mathematics Learning

429

P – 43

Tjang Daniel Chandra

Department of Mathematics State University of Malang e-mail : [email protected]

Integrated Mathematics Teaching as an Effort to Teach Mathematics More Interesting

441

P – 44

Sri Hastuti Noer

Mathematics Education Lecturer in FKIP, Lampung University Email: [email protected]

Character Development In Mathematics Problem-Based Learning

449

P – 45

Winda Ramadianti

Yogyakarta State University Email: [email protected]

Improving Student’s Motivation To Learning Math By Cooperative Learning Technique Make A Match

457

P – 46

Abdur Rahman As’ari

Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, State University of Malang

Membangun Karakter Pebelajar Unggulan Melalui Pembelajaran Matematika

467

P – 47 Gaguk Margono

Universitas Negeri Jakarta, Kompleks UNJ Rawamangun Jakarta [email protected]

Internal Consistency Reliability Of Instruments Measuring Students Satisfaction As An Internal Customer (Application Of Factor Analysis)

479

P – 48

Sri Subarinah

Study Program of Mathematics Education, FKIP Universitas Mataram Email: [email protected]

Creating Joyful Atmosphere In Mathematics Learning For Elementary School Students By Implementing Kopermatik Aids

493

P – 49

Ali Mahmudi

Department of Mathematics Education Faculty of Mathematics and Natural Science Yogyakarta State University email: [email protected]

Developing Students’ Character Through Mathematics Teaching And Learning

503

P – 50

Atmini Dhoruri R. Rosnawati, Ariyadi Wijaya

Department of Mathematics Education, Yogyakarta StateUniversity e-mail: [email protected]

Developing Mathematics-Students Worksheet Based On Realistic Approach For Junior High School In Bilingual Program

511

P – 51

Elly Arliani

Faculty of Mathematics and Sciences, Yogyakarta State University [email protected]

Developing Teacher’s Character Through Lesson Study Activities

519

P – 52 I Nengah Parta

Jurusan Matematika FMIPA UM Email: [email protected]

Developing Mathematics Teaching Material “Investigative” for Pre-Service Mathematics Teacher

527

P – 53

Hasratuddin1

1State University of Medan Email: [email protected]

Improving Student’s Emotional Intelligence By Mathematics Learning2

539

P – 54

Ratu Ilma Indra Putri

Department of Mathematics Education, Sriwijaya University

Improving Mathematics Comunication Ability Of Students In Grade 2 Through

547

x

e-mail:[email protected] PMRI Approach P – 55

Cholis Sa’dijah

Department of Mathematics State University of Malang e-mail: [email protected]

Students’ Achievement In Developing Instructional Material Of Junior High School Mathematics In English Through Implementation Of Peer Assesment In Cooperative Setting

557

P – 56

Retno Subekti

Department of Mathematics Education FMIPA UNY [email protected]

Developing Students’ Entrepreneurial Spirit Through The Subject Ilmu Hitung Keuangan

567

P – 57

Achmad Mudrikah

Nusantara Islamic University (UNINUS) Bandung

Developing Teaching Materials By Using Computer-Assisted Problem-Based Learning

575

P – 58

Yumiati

Mathematics Education Studies Program, Department of Mathematics and Sciences Education Universitas Terbuka e-mail: [email protected]

The Implementation of Generative Learning With Open-Ended Approach to Improve Mathematics Student Achievements On Muhammadiyah 44 Pamulang

585

P – 59

Kadir

Department of Mathematics Education FITK, Universitas Islam Negeri Syarif Hidayatullah Jakarta Jl. H. Juanda 95, e-mail: [email protected]

A Pedagogical Value From Mathematical Mistakes

597

P – 60

Toto Subroto Indonesia University of Education Magister Student’s Dr. Setiabudhi 229 Bandung, email: [email protected]

The Use Of Cabri 3D Software As Virtual Manipulation Tool In 3-Dimension Geometry Learning To Improve Junior High School Students’ Spatial Ability

609

P – 61

Turmudi

Mathematics Education Department of UPI Email: [email protected] Dwi Haryanto SMP Lab School of UPI, Bandung

Creating And Solving Model Of Linear Equation Through The Balance At Junior Secondary Class

619

P – 62

Yansen Marpaung

Department of Mathematics Education, University of Sanata Dharma, e-mail: [email protected]

PMRI and Metacognitive Scaffolding

631

P – 63

Ary Woro Kurniasih

Department of Mathematics Semarang State University Kampus Sekaran, Semarango, e-mail:[email protected]

Identification Critical Thinking Stages Of Students’ Mathematics Education Study Program FMIPA UNNES For Solving Mathematics Problems

639

P – 64

Evi Suharyanti1, Theofelus Galih S.1, Margi Rahayu1, Kriswandani2

S1 faculty of Mathematic majoring teaching qualification and knowledge

Satya Wacana Christian University Email : [email protected]

Reforming Mathematic Through The Concept Of Cooperative Learning By Using The Technique Think-Pair-Share Focusing On Cube And Cuboid To Improve The Study Result And Activity Of Students From Banyubiru 1 State Middle School Class Of Viiie In Semarang District On Their Second Semester Year Of 2010/2011

651

P – 65

Iwan Junaedi

Department of Mathematics Education, Semarang State University Email: [email protected]

Improving The Quality Of Learning In Geometry Transformation Course To Encourage Students Learning Independence Through The Lesson Study Approach

663

P – 66

Lathiful Anwar

Universitas Negeri Malang

Supporting Student’s Thinking In Addition Of Fraction From Informal To More

675

xi

Formal Using Measuring Context P – 67

Dian Armanto Max Stephens

Department of Mathematics Education, The State University of Medan and The University of Melbourne (Australia) e-mail: [email protected] ; [email protected]

Developing Learning Trajectory For Enhancing Students’ Relational Thinking

689

P – 68

Anton Noornia

Jurusan Matematika FMIPA Universitas Negeri Jakarta

Cooperative Learning With Metacognitive Approach To Enhance Mathematical Critical Thinking And Problem Solving Ability, And The Relation To Self-Regulated Learning

711

P – 69

Hardi Suyitno

Jurusan Matematika FMIPA Universitas Negeri Semarang [email protected]

Value’s of Mathematics Education and Citizenship Education

723

P – 70

Warli

Departement of Mathematics Education, UNIROW Tuban Email: [email protected]

Improving Students’ Creativity In The Proving The Validity Of Arguments Through Learning Strategy ”What’s Another Way”

737

P – 71

Abdulloh Jaelani

Department of Mathematics Educatio, University of PGRI Adi Buana Surabaya [email protected]

Building Character Education In Learning Mathematic

749

P – 72

Supriyono

Department of Mathematic Education, Muhammadiyah University of Purworejo

Developing Mathematical Learning Device Using Think Talk Write Strategies Assisted Learning CD To Forcer Mathematical Communication

759

P – 73

Dina Ladysa, Sindi Amelia, Bobbi Rahman

Study Programme of Mathematics Education, Postgraduate Programme, Indonesia University of Education (UPI) Email : [email protected], [email protected], [email protected]

Pre-Service Teachers’ Views Toward Mathematics Anxiety

771

P – 74

Djamilah Bondan Widjajanti

Department of Mathematics Education Yogyakarta State University Email : [email protected]

Managing Students’ Math-Anxiety Through Humanistic Mathematics Education

777

P – 75

Euis Setiawati

Mahasiswa S3 Program Studi Pendidikan Matematika Sekolah Pascasarjana Universitas Pendidikan Indonesia

Hambatan Epistemologi (Epistemological Obstacles) Dalam Persamaan Kuadrat Pada Siswa Madrasah Aliyah

787

P – 76

Farida Nurhasanah

Department of Mathematics Education, Sebelas Maret University email:[email protected]

Junior High School Students’ Abstraction In Learning Geometry

801

P – 77

Kadir

Department of Mathematics Education at Haluoleo University, Kendari

The Use Of Coastal Potency In Learning Mathematics To Enhance Social Skills Of Junior Secondary School Students

813

P – 78

Nurina Happy, Endang Listyani

Universitas Negeri Yogyakarta

Improving The Mathematic Critical And Creative Thinking Skills In Grade 10th SMA Negeri 1 Kasihan Bantul On Mathematics Learning Through Problem-Based Learning

823

P – 79 Rahmah Johar Department of Mathematics Development Of Learning Material Of 835

xii

Education, Syiah Kuala University Banda Aceh e-mail: [email protected]

Pakem-Plus For Mathematics Lesson At Elementary School

P – 80

Risnanosanti

Department of Mathematics Education, Muhammadiyah University of Bengkulu Bali Street, email: [email protected]

The Effect Of Mathematics Self-Efficacy Toward Mathematical Creative Thinking Ability Of SMA Students In Bengkulu City

847

P – 81

Rusgianto H.S

Mathematics Education Department, Faculty of Mathematics and Sciences State University of Yogyakarta

The Relationship Between Reasoning, And Emotional Intelligence In Social Interaction With Mathematics Achievement

857

P – 82

Yani Ramdani

Universitas Islam Bandung Enhancement Of Mathematical Reasoning Ability At Senior High School By The Application Of Learning With Open Ended Approach

865

P – 83 Kamaliyah Rita Novita

Bilingual Master Program on Mathematics Education Sriwijaya University, Indonesia Padang Selasa 524 Palembang, email: [email protected]

Guided Reinvention In Proving The Sum Of The Angles Of Triangle

881

P – 84 Sanni Merdekawati, Himmawati Puji Lestari

Universitas Negeri Yogyakarta Developing Student Worksheet In English Based On Constructivism Using Problem Solving Approach For Mathematics Learning On The Topic Of Social Arithmetics

895

P – 85

M.J. Dewiyani S

Undergraduate Program of Information System, STIKOM Surabaya email : [email protected]

Solving Problems In Mathematics Using The Personality Types As A Means Of Developing The Nation’s Character

905

P – 86

Edy Tandililing

Jurusan PMIPA FKIP UNTAN Pontianak

The Enhancement of Mathematical Communication and Self Regulated Learning of Senior High School Students Through PQ4R Strategy Accompanied by Refutation Text Reading

917

PROCEEDING ISBN : 978 – 979 – 16353 – 7 – 0

This paper has been presented at International Seminar and the Fourth National Conference on Mathematics Education 2011 “Building the Nation Character through Humanistic Mathematics Education”. Department of Mathematics Education, Yogyakarta State University, Yogyakarta, July 21-23 2011

P – 49 Developing Students’ Character

Through Mathematics Teaching And Learning

Dr. Ali Mahmudi Department of Mathematics Education

Faculty of Mathematics and Natural Science Yogyakarta State University email: [email protected]

Abstract

The National Education System mandates that the national education serves to develop and shape the character and civilization of the nation. This confirms the quality of Indonesia's human to be developed by each educational unit. This normative national education goals need to be elaborated and implemented in the teaching and learning process, including mathematics teaching and learning. Mathematics teaching and learning should be well designed so that it can be used as a tool in developing positive character of students. Through the mathematics teaching and learning, implicitly or explicitly, can be developed variety of positive characteristics, such as critical thinking skills, logical thinking skills, analytical thinking skills, or meticulous. Such mathematics teaching and learning needs to be done consistently so will lead to habituation to the students that if beyond a certain limit, it belongs to the students' habits and entrenched in him. Key words: mathematics teaching and learning, character.

INTRODUCTION

Each individual faces a problem, in the narrow and broad-scale, simple or

complex. Complexity of the problem is growing as the swift currents of globalization

and increasingly complex challenges of life. Each individual requires capabilities and

strategic character to succeed in solving various problems and face many challenges, the

workplace and personal lives.

To succeed in the workplace and in personal lives, one does not only require technical

skills, but also non-technical skills. The importance of the non-technical skills that are

described by Beach (Tim Program Hibah Kompetisi Berbasis Institusi Universitas

Udayana, 2010) which showed that as many as 87% of people fail or have lost their jobs

because of unacceptable behavior.

One of non-technical skills that support the success of the individual is an

individual character. Educational institutions have the responsibility to develop students

character through teaching and learning process as mandated by National Education

System which states that education serves to develop and shape the character and

civilization of the nation. This confirms the quality of Indonesia's human to be developed by

each educational unit. This normative national education goals need to be elaborated and

implemented in the teaching and learning process, including mathematics teaching and

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International Seminar and the Fourth National Conference on Mathematics Education 2011 Department of Mathematics Education, Yogyakarta State University

504 Yogyakarta, July 21-23 2011

learning. Mathematics teaching and learning should be well designed so that it can be

used as a tool in developing positive character of students. Through the mathematics

teaching and learning, implicitly or explicitly, can be developed variety of positive

characteristics, such as critical thinking skills, logical thinking skills, analytical thinking

skills, or meticulous. Such mathematics teaching and learning needs to be done consistently so

will lead to habituation to the students that if beyond a certain limit, it belongs to the students'

habits and entrenched in him

DISCUSSION

This section describes the character and its development through mathematics

teaching and learning.

1. Character Development

Each individual requires a certain competence for success in the workplace and in the

personal lives. Based on their survey, Ruben and DeAngelis (Tim Program Hibah

Kompetisi Berbasis Institusi Universitas Udayana, 2010) identified the necessary

competence or character of an individual to succeed in the workplace and in the

personal lives. These characters are personal, social and organizational characters.

Meanwhile, according to Pulliam (2008), the competence of the most desired workplace

are communication skills, interpersonal skills, high motivation/initiative, honesty,

strong work ethic, work in teams skills, analythical thinking skills, flexibility and details

oriented.

NACE USA survey results (Tim Program Hibah Kompetisi Berbasis Institusi

Universitas Udayana, 2010) also mentioned the 14 characteristics of the individual to

succeed in the workplace. These characteristics are communication skills,

honesty/integrity, interpersonal skills, ethics, motivation/initiative, adaptability,

analytical skill, technological literacy, organization skill, details oriented, leadership,

confidence and friendly.

Tempo Data and Analysis Center (Tim Program Hibah Kompetisi Berbasis

Institusi Universitas Udayana, 2010) also conducted a survey on the champion

characters as presented in the following table.

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International Seminar and the Fourth National Conference on Mathematics Education 2011 Department of Mathematics Education, Yogyakarta State University Yogyakarta, July 21-23 2011 505

Table 1. Job Seeker Characters Rating Required by Workplace

No Champion Character Percentage 1 Willing to work hard 9,03 2 High confidence 8,75 3 Having a vision for the future 8,37 4 Ability to work in teams 8,07 5 Having a good and detailed plan 7,91 6 Ability to think analytically 7,82 7 Adaptable 7,12 8 Able to work under pressure 5,91 9 Proficient in English 5,27 10 Ability to organize work 5,26

Various characters described above should be used as a reference in carrying out

the teaching and learning that allows the growth of various student characters. It must

be recognized if these characters are not developed optimally in the school. Indeed, it is

not contained explicitly in the school curriculum. But, it should be understood that the

curriculum is not just a compilation of a number of subjects. The curriculum is an

educational plan to facilitate students a specific competence that has ben formulated

(Buchori,2000). Supposedly, teaching and learning activities is designed and

implemented to integrate the skills or characters.

2. Development of Character through Mathematics Teaching and Learning

Mathematics has a strategic role in the development of science and technology.

But, not solely because it mathematics needs to be learned. Mathematics educators need

to ask themselves: what is the purpose of mathematics teaching and learning? Is

intended to make students master all mathematics materials as much as possible? Or, is

that students become mathematician later? Of course not. Mathematics teaching and

learning is not only intended to make students smarter, but also that the students have

the good reasoning, personality and good character (Soedjadi, 1999). This is

understandable, because not all students who receive math lessons in the end will continue to

use or apply the mathematics they have learned. Though almost all students need good

reasoning and personality in everyday life

Through mathematics teaching and learning students are expected to think

logically, rationally, critically, honest, and have high integrity. These skills or characters

are indeed higly required individu to be able to survive in competitive global era.

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Students are not only prepared to have the skills associated with thinking and reasoning

skills, but also prepared to have a personality, integrity and good character. It is easy to

understand and be able to imagine what would happen to someone who has high

knowledge and skills, but not based on high attitude and morality.

Are the characters as mentioned above can be developed through the mathematics

teaching and learning? Mathematics teaching and learning that well designed can be

used as a tool to cultivate a variety of characters. As an illustration, in mathematics,

there are many definitions and theorems. Definition and theorem are basically an

agreement that must be obeyed (Mardiyono, 2005). Can be predicted what would

happen if the various agreements (the definition) and rules (theorems) is not referenced.

Of course it will cause confusion.The consistent use of this agreement and the rules

closely with the attitude and character. Thus, the mathematics teaching and learning has

a great opportunity to develop attitudes and character of students. Various other

characters such as rigor and critical thinking skills can be nurtured through the activity

of problem solving activity in the mathematics teaching and learning. While, various of

characters such as the ability to work in team, organize and appreciate the opinions of

others can be nurtured through learning activities in math class discussion setting. Thus,

mathematics teaching and learning can be used and functioned as a tool to develop the

intelligence, skills and to shape the character of students.

In the context of mathematics teaching and learning, positive characters that can

be developed is often termed a mathematical value. According to Bishop (1998), values

in mathematics education is the deep affective qualities which education fosters through

the school subject of mathematics. The values in the mathematics or in the mathematics

education are an important component in the mathematics teaching and learning. These

values can be learned by students either implicitly or explicitly in the mathematics

teaching and learning. For example, through a series of problem solving activities,

students are trained to be critical, careful, coherent, analytical, rational and efficient.

According to Taplin (2003), there are some values or characteristics that need to

be learned by students. These characters include: (1) honesty, (2) behave in a

completely true, accurate, efficient, healthy and frugal living, (3) peace, such as

tranquility, contentment, patience, concentration, optimism, self-acceptance, discipline

and confidence, (4) love, such as compassion, forgiving and tolerance, and (5)

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nonviolence, like virtue, cooperation, respect for diversity, respect life, respect property,

and pay attention to the ecological balance.

Aspects of characters that can be developed in the mathematics teaching and learning generally can be divided into two kinds, namely those aspects of character in education generally (also a growing generally in society) and aspects of character in mathematics (as well as in mathematics education). As an illustration, when teachers require students to act honestly in doing the test, then the values of honesty, good behavior, which is generally derived from the values of education in general, has introduced teachers to the students. Meanwhile, when students describe and compare several different proof of the Pythagorean theorem, mathematical values such as rationality, openness and accuracy has been introduced and trained to students.

Based on the above, actually to develop skills and positive character to students is not realized by giving certain new subjects, no need to increase the allocation of time, requiring no additional new teachers, but can be integrated into existing subjects. Learning democracy, for example, can be done through discussion activities and can also be attached substantially in certain mathematical material. For example, there are various definitions of a square that can be constructed by student. A square can be defined as a quadrilateral whose four sides are congruent and four right-angle. Square can also be defined as a rectangle whose sides are congruent. Also, square can also be defined as a rhombus whose right-angle. It can be emphasized to students that although it looks different, these definitions are the same in substance. This will train the students to appreciate other people's opinions and do not insist that only their own opinion right.

Here are given some examples of integration of the various characters in the mathematics teaching and learning. One way is through learning problem-solving activities. Problem solving is an important part and is one of the purposes of mathematics teaching and learning. Through problems solving activity, it is expected that students can develop critical and creative thinking skills. These skills are very important for students as a preparation for life’s challenges. Here is an example of problem that involves a lot of information that require students to sort out and use them in solving problems.

Last week Adi traveled with a train as far as 1093 km. The train left at 08.00. After traveling 4 hours with an average speed of 86 km / h trains stopped at the next station for 1 ½ hours. Then the train traveled again for 3 hours with an average speed of 78 km / h to stop at the last station. How many kilometers the distance traveled by train?

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To be able to solve problems like the above, students can not only use knowledge of their books. Students are required to be able to select relevant information that can be used to solve the problem.

Another way that can be used to develop the reasoning skills of students is by providing incomplete information in a problem. The problem is often referred to as Fermi problems (Taplin, 2003). By using the reasoning skills and experience, it is expected that students can obtain a rational answer to the problem. Problems like these would be better if resolved in the context of a group discussion or cooperative learning. Here are examples of Fermi problems that require students to have a concern for social issues.

How many liters of gasoline are required in your city every day? How many dollars can be saved if the people using public transport than

private vehicles? Fermi problems can also be used to develop values or humanitarian character

(Taplin, 2003). When a teacher will teach the topic of the value of money, he can first give a story about a child who was sad because it failed to persuade his parents to buy him an expensive sport shoes on his birthday. The boy felt his parents did not love her. His parents are so sad for that notion. They hope that their children understand the family's financial situation. They asked him, how much money must be spent for their needs? Unfortunately, the child can’t give an answer. Based on the story, the teacher can ask a few questions to students like this.

How much money spent by parents to meet your needs every year? How much money spent by parents to meet your needs up to now? The questions are an open question that allows obtaining the various answers. It is

expected that students realize that the money they receive from their parents is so great, something that sometimes they did not expect before. It is supposed to make students aware that his wishes do not always have obeyed others. It is expected to cultivate positive characters on students, such as efficient, emphaty, and care about the difficulties of others.

Teachers can also use non-routine problems to develop a variety of other positive characters. Non-routine problems can be used to encourage the development of logical thinking skills and develop problem-solving strategies that can be applied to other situations. Here is an example of non-routine problems that require higher-order thinking skills.

Specify a number that meets the following properties. If the remainder is 1 divided by 3

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If the remainder is 2 divided by 4 If the remainder is divided by 5 is 3 If the remainder is 6 divided by 4 One of the mathematical topics that can be used to develop caring attitude towards

the environment and energy saving are statistics, especially the presentation of data. To begin the mathematics teaching and learning, teachers can ask students to predict the amount of paper they use every week. Use tables to present data obtained by the students. Ask students, whether they be surprised. Do they use too much paper? Why use a paper on certain days or weeks more than days/weeks of the others? Do they have a better idea to save paper? Is the paper saving campaign will succeed? Discuss students’ responses. Students’ answers can be used as a basis for developing the character of saving/ efficiency and care for the environment.

Another way that can be used to develop human values is to introduce to the students about the biography of mathematician. One well-known mathematician is Maria Agnesi (1718-1799). She was an Italian mathematician who has contributed greatly to the development of Calculus. As a child, she often helps other children learn, in addition to completing her own study. At the age of twenty, she began a book project titled Analytic Institution. Sometimes, she encountered problems in completing the book. However, her mind is always working, even when she sleeps. Ever, in a state of sleep, she walked to his desk to write something and then go back to bed. In the morning, she had found the answer to his problems. The book is written makes it famous. In this book, she proves that the statement had put forward when she was 9 years old. In addition to mathematics, she also has an interest in other fields. She was hanging out and working with the poor community in the area where she lived. In fact, she asked her father to make some room for a private hospital. She also worked in a hospital until she died at the age of 81 years. She often helps people who are not lucky and did not get a chance. This biography may be used as a means to develop a positive attitude on students such as diligence, perseverance and social emphaty.

Jumsai (Taplin, 2003) suggest an alternative way to develop the values or characters in the mathematics teaching and and learning, namely by developing questions that contain positive characters, or rewording problems that already exist. Through the questions referred, it is hoped the message conveyed to students about the desired positive behavior. Suppose given the folloeing problem.

Mr. Hasan has 35 cows. A thief took 14 of the cows. What is the number of Mr. Hasan’s cow now?

The problem can be changed or reworded so that contain positive values as follows.

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Mr. Hasan has 35 cows. He was very generous. He gave 14 cows to others who need it. What is the number of Mr. Hasan’s cow now? Messages to be delivered to students through these questions is the development

of positive characters on students, such as generous, empathetic, helpful, and so forth. A variety of positive character traits will be more effectively fostered in a social

context, through class discussion. Students will be easier to reach an understanding on many mathematical topics if they are given the opportunity to work together in pairs or small group discussions. CONCLUSION Mathematics teaching and learning is well designed can be used to develop students' character as the critical thinking, creative thinking, logical thinking, to think coherently, to think systematically, and consistent in attitude, even to develop human values. The mathematical teaching and learning needs to be done consistently so entrenched in the student REFERENCES Bishop, A. et al. 1998. Values in Mathematics Education: Making Values Teaching

Explicit in The Mathematics Classroom. [Online]. Tersedia; http://www.aare.edu.au/99pap/ bis99188.htm. [9 September 2008]

Buchori, M. 2000. Peranan Pendidikan dalam Pembentukan Budaya Politik di Indonesia. Article of National Seminar titled “Quo Vadis Pendidikan di Indonesia” at Sanatha Dharma University Yogyakarta, 21 – 23 August 2000.

Mardiyono, S. 2005. Inovasi Pembelajaran Matematika dan Sistem Evaluasinya Berdasarkan Kurikulum Berbasis Kompetensi. Article of National seminar at Himpunan Mahasiswa Pendidikan Matematika FMIPA UNY, Yogyakarta, March 27, 2005.

Soedjadi, R. 1999. Kiat Pendidikan Matematika di Indonesia (Konstatasi Keadaan Masa Kini Menuju Harapan Masa Depan). Jakarta: Ditjen Dikti Depdikbud.

Taplin, M. 2003. Teaching Values through a Problem Solving Approach to Mathematics. [Online] Available at: http://www.mathgoodies.com/articles/ teaching_values.shtm. [9 September 2008].

Pulliam, M. G. (2008). Skill Employer Seek. Career Corner, Exelsior College. [Online]. Available at: http://www.excelsior.edu/Excelsior_College/Publications/Skills_Employers_Seek_16.pdf. [3 April 2011].

Tim Program Hibah Kompetisi Berbasis Institusi Universitas Udayana. 2010. Konsep Pengembangan Panduan Evaluasi Pengembangan Soft-Skill Mahasiswa melalui proses Pembelajaran di Universitas Udayana. Udayana: Udayana University Bali

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