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ARGUMENTASI MATEMATIS SISWA DALAM MENYELESAIKAN

MASALAH GEOMETRI : STUDI FENOMENOLOGI PADA SISWA SMP

Tesis

Diajukan untuk memenuhi sebagian dari syarat memperoleh gelar magister

program studi pendidikan matematika

Oleh :

Devi Fitri Noviyanti

NIM. 1706318

PROGRAM STUDI PENDIDIKAN MATEMATIKA

SEKOLAH PASCASARJANA

UNIVERSITAS PENDIDIKAN INDONESIA

2019

Devi Fitri Noviyanti, 2019 ARGUMENTASI MATEMATIS SISWA DALAM MENYELESAIKAN MASALAH GEOMETRI : STUDI FENOMENOLOGI PADA SISWA SMP

Universitas Pendidikan Indonesia I repository.upi.edu I perpustakaan.upi.edu

ARGUMENTASI MATEMATIS SISWA DALAM MENYELESAIKAN

MASALAH GEOMETRI : STUDI FENOMENOLOGI PADA SISWA SMP

Oleh

Devi Fitri Noviyanti

S.Pd Universitas Singaperbangsa Karawang, 2016

Sebuah Tesis yang diajukan untuk memenuhi salah satu syarat memperoleh gelar

Magister Pendidikan (M.Pd) pada Program Studi Pendidikan Matematika

© Devi Fitri Noviyanti 2019

Universitas Pendidikan Indonesia

Agustus 2019

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ABSTRAK

Devi Fitri Noviyanti (1706318) Argumentasi Matematis Siswa dalam

Menyelesaikan Masalah Geometri : Studi

Fenomenologi pada Siswa SMP

Argumentasi matematis tidak datang secara alamiah melainkan diperoleh melalui

latihan dengan cara menyelesaikan suatu masalah. Geometri tidak hanya

mempelajari definisi, sifat-sifat dan konsep geometri itu sendiri lebih lanjut dapat

digunakan untuk mengembangkan kemampuan siswa dalam berargumentasi matematis. Penelitian ini bertujuan untuk mendeskripsikan argumentasi matematis

siswa dan hambatan siswa dalam beragumentasi matematis ketika menyelesaikan

masalah geometri berdasarkan learning obstacles. Penelitian ini menggunakan penelitian kualitatif dengan pendekatan fenomenologi dimana pengumpulan data

dilakukan melalui tes, wawancara dan analisis dokumentasi yang dilakukan

terhadap 40 siswa kelas VII di salah satu SMP di kabupaten Karawang. Argumen

dituliskan dalam kalimat, gambar dan angka digunakan siswa untuk memudahkan menyelesaikan masalah geometri yang diberikan. Argumen dari jawaban siswa

sudah memuat objek, transformasi, dan konsep matematis. Siswa mampu

beragumentasi matematis dengan baik dalam menjelaskan makna terkait dengan hubungan diantara dua konsep geometri dan menganalisis hubungan antara dua

konsep geometri dengan disertai alasan yang mendukung. Dengan demikian, siswa

mampu beragumentasi matematis dengan baik ketika menyelesaikan masalah yang berkaitan dengan definisi dan hubungan diantara dua konsep geometri.

Pengetahuan geometri yang belum dikuasai dengan baik, bentuk soal non rutin dan

terbiasa dengan pertanyaan yang mengitung dan menentukan ukuran, tahapan

penyajian materi geometri serta keterbatasan siswa dalam mengaplikasikan aturan geometri dalam konteks yang berbeda menjadi hambatan bagi siswa dalam

beragumetasi matematis ketika menyelesaikan masalah geometri.

Kata kunci : argumentasi matematis, geometri, learning obtacles



ABSTRACT

Devi Fitri Noviyanti (1706318) Student’s Mathematical Argumentation in

Solving Geometry Problems : a

phenomenology study for student’s junior

high school

Mathematical arguumentation does not come naturally but is acquired through

practices by solving a problem. Studies geometry not only learning concept, definition, and properties it self further can use promote student’s mathematical

argumentation ability. This study aims to describe student’s mathematical

argumentation dan student’s difficulties in mathematical argumentation when solving geometry problems based on learning obstacles. This study used

qualitative research with a phenomenological study where data collection was

carried out through tests, interviews and documentation analysis was conducted on

fourthy seventh grade students in one of junior high schools in Karawang. Arguments written in sentences, images and numbers are used by students to make

it easier to solve geometric problems. The argument from the students' answers

already contains objects, transformations, and mathematical concepts. Students abled to give mathematical argument well in explained meaning about relationship

between two geometric concept and analyzed relationship between two geometric

concept with supporting reasons. Students were abled to provide a good

mathematical argumentaion when solving problems related to definition and relationship between two geometric concepts. Knowledge of geometry that has not

been well mastered, non routine problem and usually questions are given to count

and determine size, the stages of presentation of geometry material, and limitations of students in applied geometric rules in different contexts become obstacles for

students in gave an mathematical argumentation when solving geometry problems.

Keywords : mathematical argumentation, geometry, learning obstacles



DAFTAR ISI

LEMBAR PENGESAHAN

PERNYATAAN i

ABSTRAK ii

ABSTRACT iii

KATA PENGANTAR iv

UCAPAN TERIMAKASIH v

DAFTAR ISI vi

DAFTAR TABEL viii

DAFTAR GAMBAR ix

DAFTAR LAMPIRAN x

BAB I PENDAHULUAN

1.1 Latar belakang masalah 1 1.2 Tujuan penelitian 9 1.3 Pertanyaan penelitian 9 1.4 Manfaat penelitian 9

BAB II KAJIAN PUSTAKA 10

2.1 Argumen dan argumentasi matematis 10

2.2 Hambatan belajar (Learning Obstacles) 14

2.3 Concept image dan concept definition 16

2.4 Segiempat dalam pembelajaran geometri 17

2.5 Studi fenomenologi 18

2.6 Teori yang relevan 19

2.6.1 Teori Van Hiele 19

2.6.2 Teori Argumentasi Toulmin (TAP) 21

2.7 Penelitian yang relevan 21

2.7 Definisi operasional 22

BAB III METODOLOGI PENELITIAN 24

3.1 Desain penelitian 24

3.2 Prosedur penelitian 24

3.3 Subjek dan tempat penelitian 25

3.4 Instrumen penelitian 26

3.5 Teknik pengumpulan data 26

3.6 Teknik analisis data 27

BAB IV HASIL DAN PEMBAHASAN 29

4.1 Hasil Penelitian 32

4.1.1 Argumentasi matematis siswa dalam menyelesaikan 32

masalah geometri

4.1.1.1 Hasil argumentasi matematis siswa berdasarkan 35

kriteria argumentasi yang baik

4.1.1.2 Struktur argumentasi Toulmin dalam jawaban tes 59

argumentasi matematis siswa

4.1. 1.3 Komponen argumen jawaban tes argumentasi 64

matematis siswa



4.1.2 Kesulitan siswa dalam beragumentasi matematis ditinjau 67

dari learning obstacles

4. 2 Pembahasan Hasil Penelitian 72

BAB V KESIMPULAN DAN SARAN 82

5.1 Kesimpulan 82

5.2 Saran 83

DAFTAR PUSTAKA 85

LAMPIRAN 92



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