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KONEKSI MATEMATIK DALAM PEMBELAJARAN MATEMATIKA DI SEKOLAH MENENGAH PERTAMA Sugiman Sugiman
PYTHAGORAS Jurnal Pendidikan Matematika Vol 4, No 1: Juni 2008
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Koneksi matematik merupakan salah satu kemampuan yang menjadi tujuan pembelajaran matematika. Koneksi matematik terjadi antara matematika dengan matematika itu sendiri atau antara matematika dengan di luar matematika. Dengan kemampuan koneksi matematik, selain memahami manfaat matematika, siswa mampu memandang bahwa topik-topik matematika saling berkaitan. Dalam artikel ini dikaji mengenai koneksi matematik yang meliputi pengertian, peran dalam pembelajaran matematika, dan kemampuan koneksi matematik dari siswa kelas 3 sebuah SMP . Kata kunci: Koneksi matematik.

Optimasi perencanaan produksi bahan bakar minyak dengan fungsi kendala fuzzy menggunakan metode goal programming Wiwiet Widyaningsih; Sri Andayani
PYTHAGORAS Jurnal Pendidikan Matematika Vol 13, No 1: June 2018
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Dalam perencanaan produksi PT. Pertamina (Persero) TBBM Boyolali, perusahaan tersebut hanya mendistribusikan BBM sesuai dengan permintaan SPBU tanpa melakukan perhitungan matematis apakah pendapatan yang diperoleh sudah optimal dengan semua faktor dan kendala yang ada, seperti harga setiap jenis BBM, jam kerja mesin pengisian BBM di New Gantry System (NGS), moda transport mobil tangki, dan tingkat keselamatan mobil tangki. Untuk itu, penelitian ini bertujuan untuk melakukan optimasi perencanaan produksi BBM menggunakan metode goal programming agar perusahaan dapat memperoleh pendapatan yang maksimal dengan memperhatikan faktor-faktor dan kendala yang ada. Metode goal programming merupakan perluasan dari linear programming yang dapat menyelesaikan optimasi dengan banyak tujuan. Pada penelitian ini, selain dengan fungsi kendala biasa, metode goal programming juga digunakan untuk menyelesaikan permasalahan yang sama ditambah dengan satu fungsi kendala fuzzy, yaitu tingkat keselamatan mobil tangki, yang proses defuzzifikasinya menggunakan metode mamdani. Hasil penelitian menunjukkan, kedua penyelesaian metode goal programming baik dengan kendala biasa maupun dengan kendala fuzzy memberikan keluaran jumlah BBM dan jumlah pendapatan yang sama, yaitu produk premium () sebanyak 1016 kl, bio solar () sebanyak 1200 kl, pertamax () sebanyak 596 kl, dan pertalite () sebanyak 1632 kl dengan pendapatan sebesar Rp33.022.000.000,00. Optimization planning of fuel oil production with fuzzy constraint using goal programming method AbstractIn the production planning of PT. Pertamina (Persero) TBBM Boyolali, it only distributes fuel in accordance with the demand for gas stations without performing mathematical calculations whether the revenue obtained was optimal with all the factors and obstacles that exist, such as the price of each type of fuel, working hours of filling machine fuel in New Gantry System (NGS), transport modes of the tank car, and the tank car’s safety level. Therefore, this study aims to optimize the production planning using goal programming method so that the company can obtain maximum income by considering the factors and constraints. The goal programming method was an extension of linear programming that can accomplish optimization with many goals. In this study, in addition to the ordinary constraint function, goal programming method was also used to solve the same problem which includes one fuzzy constraint, namely the level of tank car safety, which the defuzzification process using Mamdani method. The result of the study shows that solution of goal programming method both with ordinary and fuzzy constraint give the same amount of fuel output and the same amount of revenue, that is premium () as much 1016 kl, bio diesel () as much 1200 kl, pertamax () as much 596 kl and pertalite () as much 1632 kl with the revenue is Rp33.022.000.000,00.

Analisis kemampuan menyelesaikan soal HOTS model TIMSS dan kepercayaan diri siswa sekolah menengah pertama Gity Wulang Mandini; Hartono Hartono
Pythagoras: Jurnal Matematika dan Pendidikan Matematika Vol 13, No 2: December 2018
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Penelitian ini bertujuan menganalisis kemampuan siswa SMP di Kabupaten Wonosobo dalam menyelesaikan soal HOTS model TIMSS dan mendeskripsikan kepercayaan diri siswa SMP di Kabupaten Wonosobo. Penelitian ini termasuk penelitian survei. Populasi penelitian adalah seluruh siswa kelas VIII SMP di Kabupaten Wonosobo pada tahun pelajaran 2016/2017. Pengambilan sampel menggunakan metode stratified proportional random sampling dan diperoleh 99 siswa sebagai sampel yang terbagi dalam 4 sekolah, yaitu 1 sekolah kategori tinggi, 2 sekolah kategori sedang, dan 1 sekolah kategori rendah. Hasil penelitian menunjukkan kemampuan menyelesaikan soal HOTS model TIMSS siswa SMP Kabupaten Wonosobo dalam kategori sedang (85,9%). Selanjutnya dilihat untuk masing-masing indikator dari soal HOTS model TIMSS, indikator memadukan/ mensintesis, menganalisis, memberikan alasan, dan menyelesaikan masalah non-rutin berada pada kategori sedang, hanya terdapat 1 indikator yang berada pada kategori rendah yaitu menggeneralisasi. Sedangkan untuk kepercayaan diri siswa SMP di Kabupaten Wonosobo berada pada kategori sedang (56,6%). Bila dilihat untuk masing-masing aspek, bahwa aspek keyakinan akan kemampuan diri, optimis, objektif, dan bertanggung jawab berada pada kategori sedang, untuk aspek rasional dan realistis berada pada kategori rendah An analysis of junior high school students’ability in solving HOTS model TIMSS and self-confidence AbstractThe purpose of this study were to analyze the ability of junior high school students in Wonosobo to solve the HOTS model TIMSS problem and to describe the self-confidence of junior high school students in Wonosobo. This study was a survey. The population was all 8th grade of Wonosobo Junior High School in the academic year 2016/2017. Sampling used was stratified proportional random sampling method. The samples consisted of 99 students from 4 representative schools, namely 1 school for high category, 2 schools for medium cateogry, and 1school for low category. The results showed that the ability to solve the HOTS model TIMSS problem of junior high school students in Wonosobo was in the medium category (85.9%). Furthermore, for each indicator of HOTS model TIMSS problem, found that indicators integrate/ synthesize, analyze, justify, and solve non-routine problems were in medium category, there was only 1 indicator that in low category that is generalization. As for self-confidence of junior high school students in Wonosobo was in medium category (56.6%). When viewed from each aspects, aspect of belief in self-ability, optimist, objective, and responsible were in medium category, aspect of rational and realisticis was in low category.

Pengembangan Perangkat Pembelajaran Geometri SMP dengan Pendekatan Open-Ended Berorientasi Kemampuan Berpikir Kritis Astuti Ariani; Djamilah Bondan Widjajanti
PYTHAGORAS Jurnal Pendidikan Matematika Vol 8, No 1: June 2013
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Penelitian ini bertujuan untuk menghasilkan perangkat pembelajaran geometri bangun ruang sisi datar kelas VIII SMP. Perangkat pembelajaran tersebut terdiri atas: Rencana Pelaksanaan Pembelajar-an (RPP), Lembar Kegiatan Siswa (LKS) dan tes hasil belajar. RPP dan LKS menggunakan pendekatan open-ended dengan berorientasi kemampuan berpikir kritis. Penelitian ini merupakan penelitian pengembangan (R D) yang dikembangkan oleh Borg dan Gall dengan modifikasi. Hasil penelitian disimpulkan bahwa perangkat pembelajaran yang dikembangkan dinyatakan: (1) valid berdasarkan penilaian ahli/praktisi, (2) praktis digunakan berdasarkan: (a) observasi keterlaksanaan pembelajaran, (b) penilaian guru, dan (c) angket respons siswa, dan (3) efektif berdasarkan hasil tes kemampuan berpikir kritis siswa.Kata Kunci: pengembangan, perangkat pembelajaran geometri, pendekatan open-ended, kemampuan berpikir kritis. Developing the Learning Kits for the Topics of Geometry Using Open-Ended Approach with Critical Thinking Ability Orientation at Junior High School AbstractThis study aims at developing the learning kits for the topics Polyhedral of geometry at grade 8th in Junior High School. The learning kits consist of the Lesson Plans, the Student Worksheets, and the learning achievement test. The Lesson Plans and Student Worksheets use open-ended approach with critical thinking ability orientation. This is a research and development (RD) study by modifying Borg and Gall’s procedures. The result of study can be concluded that: (1) the learning kits are valid based on experts evaluation, (2) they are practical based on the result of: (a) the learning observation, (b) the teachers evaluation, and (c) the students’ responses questionnaire, and (3) they are effective based on the result of students’ critical thinking ability test.Keywords: develop, learning kits of geometry, open-ended approach, critical thinking ability.

Efektivitas model pembelajaran Relating, Experiencing, Applying, Cooperating, Transferring (REACT) dan reciprocal teaching berbantuan game edukasi Niswatun Hasanah; Achmad Buchori; Dina Prasetyowati; Farida Nursyahidah
PYTHAGORAS Jurnal Pendidikan Matematika Vol 14, No 1: June 2019
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Penelitian ini bertujuan untuk mendeskripsikan efektivitas model pembelajaran Relating, Experiencing, Applying, Cooperating, Transferring (REACT) berbantuan Game Edukasi dan Reciprocal Teaching berbantuan Game Edukasi ditinjau dari kemampuan pemecahan masalah matematis siswa. Penelitian ini adalah quasi experiment dengan posttest only control design. Populasi dalam penelitian ini adalah siswa kelas VIII MTs Sultan Fatah Gaji Demak tahun ajaran 2017/2018 dan kelas VIII-A, VIII-B, dan VIII-C dipilih sebagai sampel penelitian. Hasil penelitian menunjukkan bahwa (1) terdapat perbedaan signifikan rata-rata kemampuan pemecahan masalah matematis antara siswa yang mendapatkan pembelajaran dengan model REACT berbantuan Game Edukasi, model Reciprocal Teaching berbantuan Game Edukasi, dan model pembelajaran konvensional (ekspositori); (2) kemampuan pemecahan masalah matematis siswa yang belajar menggunakan model pembelajaran REACT berbantuan Game Edukasi lebih baik dari pada siswa yang belajar dengan pembelajaran konvensional; (3) kemampuan pemecahan masalah matematis siswa yang belajar menggunakan model Reciprocal Teaching berbantuan Game Edukasi lebih baik dari pada siswa yang belajar dengan pembelajaran konvensional; (4) pembelajaran dengan model REACT dan Reciprocal Teaching berbantuan Game Edukasi sama-sama efektif ditinjau dari kemampuan pemecahan masalah dengan rata-rata kemampuannya signifikan di atas 70; dan (5) terdapat pengaruh positif keaktifan siswa pada kelas yang belajar menggunakan model REACT dan Reciprocal Teaching berbantuan Game Education terhadap kemampuan pemecahan masalah matematis siswa. The effectiveness of the Relating, Experiencing, Applying, Cooperating, Transferring (REACT) and reciprocal teaching model assisted by educational gameAbstractThis research aimed to describe the effectiveness of Relating, Experiencing, Applying, Cooperating, Transferring (REACT) learning models assisted by Educational Game and Reciprocal Teaching assisted by Educational Game in terms of students’ mathematical problem-solving abilities. This study was a quasi-experiment with a posttest only control design. The population in this research was students of 8th-grade of MTs Sultan Fatah Gaji Demak, Indonesia in the academic year 2017/2018 and class VIII-A, VIII-B, and VIII-C were selected as research samples. The results showed that (1) there was a significant difference in the average mathematical problem-solving ability between students who received learning with the REACT model assisted by Educational Game, the Reciprocal Teaching model assisted by Educational Games, and conventional learning models (expository); (2) the mathematical problem-solving ability of students who learn using REACT learning models assisted by Educational Games was better than conventional learning; (3) the mathematical problem-solving ability of students who learn using the Reciprocal Teaching model assisted by Educational Game was better than conventional learning; (4)The learning with the REACT and Reciprocal Teaching models assisted by Educational Games was equally effective in terms of problem solving skills with an average ability significantly above 70; and (5) there was a positive correlation between the activeness of students in class learning using REACT and Reciprocal Teaching models assisted by Game Education on students’ mathematical problem-solving abilities.

Keefektifan Pendekatan CTL dan Problem Solving Ditinjau dari Prestasi Belajar Matematika dan Religiusitas Siswa Tri Wijayanti; Sugiman Sugiman
Pythagoras: Jurnal Matematika dan Pendidikan Matematika Vol 8, No 2: December 2013
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Penelitian ini adalah penelitian eksperimen semu dengan desain nonequivalent controlgroup design. Populasi penelitian ini adalah siswa kelas VII di sekolah berbasis pesantren yaitu SMP Muhammadiyah Boarding School (MBS) Yogyakarta. Sampel penelitian adalah kelas VII C, VII D, dan VII E. Instrumen penelitian ini adalah angket religiusitas siswa dan tes prestasi belajar matematika. Data dianalisis secara multivariat dengan taraf signifikansi 5% untuk pengujian kesamaan rata-rata kelompok dan ditindak lanjuti dengan analisis univariat pada taraf signifikansi 5%. Hasil penelitian menunjukkan bahwa (1) pendekatan CTL efektif ditinjau dari prestasi belajar matematika dan religiusitas siswa, (2) pendekatan problem solving efektif ditinjau dari prestasi belajar matematika dan religiusitas siswa, dan (3) pendekatan CTL tidak lebih efektif dibandingkan pendekatan problem solving ditinjau dari prestasi belajar matematika dan religiusitas siswa.Kata kunci: pendekatan contextual teaching and learning (CTL), pendekatan problem solving, prestasi belajar matematika, religiusitas siswa The Effectiveness of CTL and Problem Solving Approach in Terms of Student’s Mathematics Achievement and Religiosity AbstractThis study is aquasi-experimental research design with nonequivalent control group design. The study population was a class VII student of SMP Muhammadiyah Boarding School (MBS) Yogyakarta as islamic boarding school. Samples were class VIIC, VIID, and VIIE. The research instrument was a questionnaire religiosity students and mathematics achievement tests. Data were analyzed by the multivariate analysis at the significance level of 5% for the average similarity testing groups and followed up by a univariate analysis at the significance level of 5%. The results showed that (1) CTL approach effective in terms of student’s mathematics achievement and religiosity, (2) problem solving approach effective in terms of student’s mathematics achievement and religiosity, and (3) CTL approach is not more effective than problem solving approach in terms of student’s mathematics achievement and religiosity.Keywords: contextual teaching andlearning(CTL) approach, problem solving approach, mathematics achievement, studentreligiosity

Pengembangan Perangkat Pembelajaran Bangun Ruang SMP dengan Pendekatan SAVI (Somatik, Auditori, Visual, dan Intelektual) Supiyati Supiyati; Jailani Jailani
PYTHAGORAS Jurnal Pendidikan Matematika Vol 9, No 2: December 2014
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Tujuan penelitian ini adalah untuk menghasilkan perangkat pembelajaran bangun ruang SMP dengan menggunakan pendekatan SAVI yang layak yaitu valid, praktis, dan efektif. Jenis penelitian ini adalah pengembangan. Penelitian pengembangan ini menggunakan model 4-D yang dikembangkan oleh Thiagarajan, Semmel dan Semmel. Pengembangan perangkat terdiri dari tahap analisis awal-akhir, analisis siswa, analisis materi, analisis tugas, spesifikasi tujuan pembelajaran, pemilihan media, pemilihan format, desain produk, uji ahli, uji coba terbatas dan uji coba lapangan. Subjek penelitian ini adalah 52 orang yang terdiri dari dua kelas yang berasal dari siswa SMPN 5 Sumbawa Besar dan SMPN 2 Unter Iwes. Instrumen penelitian yang digunakan terdiri dari lembar validasi, lembar observasi keterlaksanaan pembelajaran, lembar penilaian sisiwa, lembar penilain guru, dan tes prestasi belajar. Analisis data dilakukan secara deskriptif. Hasil penelitian ini menunjukkan bahwa perangkat pembelajaran berupa silabus, Rencana Pelaksanaan Pembelajaran (RPP) dan Lembar Kegiatan Siswa (LKS) yang dikembangkan memenuhi kriteria valid, praktis dan efektif serta Tes Prestasi Belajar (TPB) yang valid dan reliabel.Kata kunci: pengembangan, perangkat pembelajaran, bangun ruang, pendekatan SAVI Developing the Solid Geometry Teaching Kit for Junior High School Using SAVI Approach (Somatic, Auditory, Visual, and Intellectual) AbstractThe aim of this study was to produce the solid geometry teaching kit for junior high schools which use SAVI approach that is valid, practical, and effective. This was a developmental research using a 4-D model by Thiagarajan, Semmel and Semmel. The developmental process consisted of front-end analysis, learner analysis, task analysis, concept analysis, specifying instructional objectives, format selection, product design, expert validation, small try-out, and field try-out. There were 52 subjects from two junior high schools namely SMPN 5 Sumbawa Besar and SMPN 2 Unter Iwes. This research instruments consisted of validation sheets, learning observation sheets, students evaluation sheets, teachers evaluation sheets and test. The data were analyzed descriptively.This research results revealed that the syllabus, lesson plan, and student work sheet which were developed are valid, practical, and effective, and achievement test is valid and reliabel.Keywords: developing, teaching kit, solid geometry, SAVI approach

Keefektifan Pembelajaran Menggunakan Pendekatan Problem Posing dan Pendekatan Open-Ended Ditinjau Dari HOTS Dasih Lelani Nurina; Heri Retnawati
Pythagoras: Jurnal Matematika dan Pendidikan Matematika Vol 10, No 2: December 2015
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Penelitian ini bertujuan untuk mendeskripsikan keefektifan pembelajaran trigonometri dengan menggunakan pendekatan problem posing dan pendekatan open-ended ditinjau dari HOTS siswa. Penelitian ini merupakan penelitian eksperimen semu. Penelitian ini menggunakan satu kelompok eksperimen dan satu kelompok kontrol. Populasi penelitian ini adalah seluruh siswa kelas X SMA Negeri 3 Bantul. Sampel penelitian sebanyak dua kelas yang dipilih secara acak. Instrumen penelitian yang digunakan adalah instrumen tes HOTS. Data dianalisis menggunakan uji one sample t-test dan two independent sample t-test. Hasil penelitian menunjukkan bahwa: pendekatan problem posing efektif ditinjau dari HOTS; pendekatan open-ended efektif ditinjau dari HOTS; Pendekatan open-ended tidak lebih efektif dibandingkan dengan pendekatan problem posing ditinjau dari HOTS.Kata Kunci: problem posing, open-ended, higher order thinking skills (HOTS) The Effectiveness Using Problem Posing Approach and Open-Ended Approach in Terms of the HOTS AbstractThis study aims to describe the effectiveness of teaching Trigonometry using the Problem Posing Approach and Open-Ended Approach in terms of the HOTS of High School Students. This research was a quasi-experimental. The research population comprised nine classes of Year X student of SMA Negeri 3 Bantul. The sample consisted of two classes that were randomly established. The instruments used in the research was HOTS test. The data analysis techniques consisted of the one sample t-test and two independent sample t-test. The results of the research show that: the problem posing approach is effective in terms of HOTS; the open-ended approach effective in terms of HOTS; and there is no difference in effectiveness between the problem posing approach and open-ended approach in terms of HOTS.Keywords: problem posing, open-ended, higher order thinking skills (HOTS)

INTEGRAL HENSTOCK-STIELTJES FUNGSI BERNILAI VEKTOR Umi Mahnuna Hanung; Ch. Rini Indrati
PYTHAGORAS Jurnal Pendidikan Matematika Vol 5, No 2: Desember 2009
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

This paper discusses about the generalization of the Henstock-Stieltjes integral for vector-valued functions which are defined on a closed interval [a,b]R. The generalization has been done up to the existance of this integral.Key words: Henstock-Stieltjes integral, vector-valued function and bounded function.

Pengaruh Pembelajaran Bangun Ruang Sisi Lengkung Melalui CTL dan Open Ended terhadap Hasil Belajar Kognitif, Sikap, dan Keterampilan Yamti Yamti
PYTHAGORAS Jurnal Pendidikan Matematika Vol 11, No 1: June 2016
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Tujuan penelitian ini adalah untuk menemukan (1) pengaruh pembelajaran pada bangun ruang sisi lengkung dengan strategi pembelajaran kooperatif Contextual Teaching and Learning (CTL) dan Open Ended terhadap hasil belajar kognitif siswa, (2) pengaruh pembelajaran pada bangun ruang sisi lengkung dengan strategi pembelajaran kooperatif CTL dan Open Ended terhadap sikap siswa, dan (3) pengaruh pembelajaran pada bangun ruang sisi lengkung dengan strategi pembelajaran kooperatif CTL dan Open Ended terhadap keterampilan matematika siswa. Jenis penelitian adalah eksperimen semu. Populasi penelitian adalah seluruh siswa kelas IX SMP Muhammadiyah 8 Yogyakarta tahun pelajaran 2014/2015, sedangkan sampel penelitian adalah siswa kelas IX D dipilih secara acak. Hasil penelitian menunjukkan bahwa terdapat pengaruh pembelajaran bangun ruang sisi lengkung dengan strategi kooperatif CTL dan Open Endedterhadap hasil belajar kognitif, sikap, dan keterampilan siswa.Kata Kunci: contextual teaching and learning, open ended, hasil belajar kognitif, hasil belajar sikap, hasil belajar keterampilan The Influence of the Space Curved Side Up Learning Through CTL and Open Ended toward the Learning Result of Cognitive, Attitude, and Skill AbstractThe aims of this research was to investigate: (1) the influence of the space curved side up learning with CTL cooperative learning strategy and Open Ended toward the students learning result of cognitive, (2) the influence of the space curved side up learning with CTL cooperative learning strategy and Open Ended toward the students learning result of attitude, and (3) the influence of the space curved side up learning with CTL cooperative learning strategy and Open Ended toward the students learning result of mathematical skills. This research was quasi experiment. The population of research was all students grade IX SMP Muhammadiyah 8 Yogyakarta, while the sample of research was students in class IX D selected randomly. The results show that the space curved side up learning with the of contextual teaching learning and open ended has influence toward the students learning result of cognitive, attitude, and skills.Keywords: contextual teaching and learning, open ended, the learning result of cognitive, the learning result of attitude, the learning result of skills.

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