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Journal : Jurnal Elemen

KESULITAN SISWA DALAM MEMBUKTIKAN MASALAH KESAMAAN DAN KETIDAKSAMAAN MATEMATIKA MENGGUNAKAN INDUKSI MATEMATIKA Astawa, I Wayan Puja; Sudiarta, I Gusti Putu; Suparta, I Nengah
Jurnal Elemen Vol 6, No 1 (2020): Jurnal Elemen
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Mathematical similarities and inequalities are common mathematical statements related to numbers whose truth can be proven by mathematical induction. Proving by mathematical induction involves two main steps, namely the basic step and the induction step. The study of mathematical induction related to similarity and inequality is very important and is still relatively limited in quantity. This study aims to determine whether there are significant differences in students' ability to prove mathematical statements using mathematical induction on mathematical similarities and inequalities problems and identify misconceptions. The study was conducted with a mixed method. A sample of 117 students from two high schools in the city of Singaraja was selected by a random cluster technique to obtain quantitative data. Meanwhile, the research subjects were two students selected based on the misconceptions shown to obtain qualitative data. Quantitative data on the ability to prove the similarity and inequality problems using mathematical induction was collected by written tests and qualitative data on misconceptions were collected by interview. Quantitative data were analyzed by a paired group t-test and by z test for proportions. Meanwhile, qualitative data were analyzed by content analysis of students' works to identify their misconceptions. The results showed that proving the mathematical induction of the inequality problem was more difficult than proving the similarity problem. This difficulty occurs both in the basic step and the induction step. Misconceptions arise due to the fallacy of analogies and interpretations of mathematical notation.
Kesulitan Siswa dalam Membuktikan Masalah Kesamaan dan Ketidaksamaan Matematika Menggunakan Induksi Matematika I Wayan Puja Astawa; I Gusti Putu Sudiarta; I Nengah Suparta
Jurnal Elemen Vol 6, No 1 (2020): January
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/jel.v6i1.1746

Abstract

Mathematical similarities and inequalities are common mathematical statements related to numbers whose truth can be proven by mathematical induction. Proving by mathematical induction involves two main steps, namely the basic step and the induction step. The study of mathematical induction related to similarity and inequality is very important and is still relatively limited in quantity. This study aims to determine whether there are significant differences in students' ability to prove mathematical statements using mathematical induction on mathematical similarities and inequalities problems and identify misconceptions. The study was conducted with a mixed method. A sample of 117 students from two high schools in the city of Singaraja was selected by a random cluster technique to obtain quantitative data. Meanwhile, the research subjects were two students selected based on the misconceptions shown to obtain qualitative data. Quantitative data on the ability to prove the similarity and inequality problems using mathematical induction was collected by written tests and qualitative data on misconceptions were collected by interview. Quantitative data were analyzed by a paired group t-test and by z test for proportions. Meanwhile, qualitative data were analyzed by content analysis of students' works to identify their misconceptions. The results showed that proving the mathematical induction of the inequality problem was more difficult than proving the similarity problem. This difficulty occurs both in the basic step and the induction step. Misconceptions arise due to the fallacy of analogies and interpretations of mathematical notation.
Co-Authors ., DR. I WAYAN SADRA, M.Ed. ., Gede Purwandika ., I Komang Widanto ., I Made Yoga Emma Prasetya ., I Pt Ade Andre ., I PUTU ADE ANDRE PAYADNYA ., I PUTU EDITIA MIUSENA ., I Wayan Kumarayasa ., IDA AYU IKA TRISNA DEWI ., IDA AYU NGURAH SULASMINIYATI ., KADEK YUDISTA WITRAGUNA ., MADE WIDYA SURYAPRANI ., NI KOMANG WIRASTI ., NI LUH TIA RAHMAWATI ., Ni Made Erlinta Devi ., Ni Made Irma Dwi Purnamayanti ., NI PUTU MEINA AYUNINGSIH ., NI WAYAN SANJIWANI UTAMI ., NI WAYAN SRI WIDHYANTARI ., NI WAYAN YUNIK WIDIA ASTUTI ., PANDE GEDE SUBIKSA BRAHMA RANDRA ., PUTU YULI SUWASTINI A. M. Sari Ade Dwi Utami Adi Saputra, Putu Resya Agustiari, Pande Kadek Rai Agustini, Kadek Trisna Anak Agung Lilyk Cahyani . Anak Agung Lilyk Cahyani ., Anak Agung Lilyk Cahyani Anak Agung Ngurah Gde Sapteka Annadhifi, Muhammad Ilham Nurfaizi Apriyanti, Muda Aritisna, Ni Made Tarisa Dian Bgeholz, Susanne Budayana, I Made Cahyani, Ni Putu Candra D. Dafik Dewa Ayu Oka Setiawati Dewi, Putu Kartika Dr. I Made Sugiarta, M.Si. . Dr.I Wayan Sadra,M.Ed . Drs.Djoko Waluyo,M.Sc . Eliska Juliangkary Findayani, Ni Kadek Gde Suweken Gede Purwandika . Gede Suweken Ghoffari, Lalu Hasan Gusti Ayu Mahayukti I Dewa M. Agus Ariawan I Dewa Made Agus Ariawan I Gede Adhitya Wisnu Wardhana I Gst Nyoman Yudi Hartawan I Gst Putu Sudiarta I GUSTI AGUNG EKA SURYANTARI . I Gusti Ngurah Pujawan I Gusti Nyoman Yudi Hartawan I GUSTI PUTU ARI SUGIANTARA . I Gusti Putu Suharta I Gusti Putu Suharta I KETUT GEDE BIRAWA ANURAGA . I Komang Sukendra I Komang Widanto . I Made Ardana I Made Chandra Adi Purnama I Made Satria Wiguna I Made Suarsana I Made Suarsana I Made Sumerta Yasa I Made Yoga Emma Prasetya . I MADE YOGA WICAKSANA . I Nyoman Gita I Nyoman Sukajaya I Pt Ade Andre . I Putu Ade Andre Payadnya I PUTU EKA IRAWAN I Putu Eka Irawan I Putu Wisna Ariawan I WAYAN EKA ARYASUTA . I Wayan Kumarayasa . I Wayan Muderawan I Wayan Puja Astawa I Wayan Sadra Ida Ayu Purnama Bestari Iswara, Dw. Md. Ananda Dian Juliangkary, Eliska K. DEADY IRMAWAN . Kadek Amerta Yasa Kadek Pasek Budarsini KANISIUS MANDUR . Komang Agus Widyatmika Komang Tri Purnamayanthi Lestari, Sahin Two LUH DE IRIN PRADNYAWATI . Luh Mitha Priyanka Luh Putu Sri Lestari Made Widya Suryaprani Matthiesen, Finn Muhammad Naoval Husni Muhammad Turmuzi N. K. Nuraini N. L. T Rahmawati Narita, Ni Luh Putu Dinna Surya Narottama, Anak Agung Ngurah Made Ni Kadek Findayani Ni Kadek Suryantini Ni Komang Wirasti Ni Luh Dewi Sintiari Ni Luh Putu Dinna Surya Narita Ni Luh Suciari . Ni Luh Suciari ., Ni Luh Suciari Ni Made Erlinta Devi . Ni Made Irma Dwi Purnamayanti . Ni Made Sri Mertasari Ni Made Suastini Ni Made Suastini, Ni Made Ni Made Suwarnisi Ni Nyoman Parwati Ni Nyoman Riantini W. Ni Putu Ari Wiratini Ni Putu Darmayanti Ni Putu Nova Andriani Ni Putu Santhi Widiasih NI PUTU WIWIN SURYANTARI . Ni Wayan Ekayanti Ni Wayan Mei Ekayanti Ni Wayan Sanjiwani Utami . Ni Wayan Sri Maeti Pande Kadek Rai Agustiari Partayasa, Wayan Payadnya, I Putu Ade Andre Periandani, Putu Novi Pratiwi, Kadek Ayu Mutiara Priyanka*, Luh Mitha Purnama, I Made Chandra Adi Purnamayanthi, Komang Tri Putra, Dewa Made Krisna Dharma Putra, Komang Hendri Nugraha Putu Adhitya Santika Dharma Putu Kartika Dewi Putu Nanci Riastini, Putu Nanci Putu Novi Periandani Putu Resya Adi Saputra Rahmawati, N. L. T Rani Darmayanti Riantini W., Ni Nyoman Riza Aldira Robiatul Adawiyah Sapteka, Anak Agung Ngurah Gde Sapteka Sariyasa . SEBASTIANUS FEDI . Setiawan, Kadek Aldi Setiawati, Dewa Ayu Oka Srinivasa, Putu Winy Suarningsih, Ni Luh Putu Ayu Intan Sudiarta, I Gst. Putu Suryantini, Ni Kadek Suryaprani, Made Widya Suweken, Gde Ulya, Viki Himatul Waluyo, D. Wayan Partayasa Wayan Sadra Wicaksana, I Made Yoga Widiantari, Ni Kadek Kasi Widiasih, Ni Putu Santhi Wikasari, Ayu Wirasti, Ni Komang