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Journal : Journal on Mathematics Education

Causes of proof construction failure in proof by contradiction Hamdani, Deni; Purwanto; Sukoriyanto; Anwar, Lathiful
Journal on Mathematics Education Vol. 14 No. 3 (2023): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v14i3.pp415-448

Abstract

Failure to deduce false suppositions in proof by contradiction is still considered “more difficult” than proving the conditional to in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure hypothesis specifically used in proof by contradiction. The research data were collected and analyzed from the work of students who have agreed to be research participants, a total of 83 students. The results of the analysis of student work successfully identified four types of failures, namely formulating suppositions, constructing and manipulating suppositions, identifying contradictions, and disproving suppositions. These four types of failures then became the material for the development of the hypothesis framework of a failure to construct proof by contradiction, which consists of 17 hypothesis nodes divided into three main hypotheses, namely: operational (action), affective (emotional), and foundational (logical reasoning). The failure hypothesis framework justifies that the sources of the failure of proof construction in proof by contradiction are understanding of the act of producing a proof by contradiction, emotionality towards the coherence of the construction steps, disproving suppositions, beliefs, use of appropriate definitions-theorems and axioms, and cognitive tension in proof by contradiction; and formal logic of the act of producing a proof by contradiction, as well as differences in the underlying logic with other acts.
Comparing model-building process: A model prospective teachers used in interpreting students’ mathematical thinking Sapti, Mujiyem; Purwanto; Irawan, Edy Bambang; As’ari, Abdur Rahman; Sa’dijah, Cholis; Susiswo; Wijaya, Ariyadi
Journal on Mathematics Education Vol. 10 No. 2 (2019): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students' mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students' work with their knowledge or thought.
Exploring mathematical representations in solving ill-structured problems: The case of quadratic function Santia, Ika; Purwanto; Sutawidjadja, Akbar; Sudirman; Subanji
Journal on Mathematics Education Vol. 10 No. 3 (2019): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and meaningfulness of what they learn, they also are connected with their prior knowledge. The focus of this research is exploring the used of mathematical representations in solving ill-structured problems involving quadratic functions. The topic of quadratic functions is considered necessary in mathematics teaching and learning in higher education. It's because many mathematics education students have difficulty in understanding these matters, and they also didn’t appreciate their advantage and application in daily life. The researchers' explored mathematical representation as used by two subjects from fifty-four mathematics education students at the University of Nusantara PGRI Kediri by using a qualitative approach. We were selected due to their completed all steps for solving the ill-structured problem, and there have different ways of solving these problems. Mathematical representation explored through an analytical framework of solving ill- structured issues such as representing problems, developing alternative solutions, creating solution justifications, monitoring, and evaluating. The data analysis used technique triangulation. The results show that verbal and symbolic representations used both subjects to calculate, detect, correct errors, and justify their answers. However, the visual representation used only by the first subject to detect and correct errors.
Generalization strategy of linear patterns from field-dependent cognitive style Setiawan, Yayan Eryk; Purwanto; Parta, I Nengah; Sisworo
Journal on Mathematics Education Vol. 11 No. 1 (2020): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students’ failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors’ components such as the experience of field-dependent type students. For this reason, this study was carried out to explore the thinking process of students who fail and investigate the thinking processes of students who succeed in generalizing linear patterns. The results of this study provide an effective learning strategy solution for field-dependent students in generalizing linear patterns. This study employed a qualitative approach with a case study design to junior high school students. The results indicated that students in the field-dependent cognitive style looked at pattern questions represented in the form of geometric images globally without looking at the structure of the image. Two strategies for generalizing linear patterns used by field-dependent students were examined, namely recursive and different strategies.
Semiotic reasoning emerges in constructing properties of a rectangle: A study of adversity quotient Suryaningrum, Christine Wulandari; Purwanto; Subanji; Susanto, Hery; Ningtyas, Yoga Dwi Windy Kusuma; Irfan, Muhammad
Journal on Mathematics Education Vol. 11 No. 1 (2020): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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Abstract

Semiotics is simply defined as the sign-using to represent a mathematical concept in a problem-solving. Semiotic reasoning of constructing concept is a process of drawing a conclusion based on object, representamen (sign), and interpretant. This paper aims to describe the phases of semiotic reasoning of elementary students in constructing the properties of a rectangle. The participants of the present qualitative study are three elementary students classified into three levels of Adversity Quotient (AQ): quitter/AQ low, champer/AQ medium, and climber/AQ high. The results show three participants identify object by observing objects around them. In creating sign stage, they made the same sign that was a rectangular image. However, in three last stages, namely interpret sign, find out properties of sign, and discover properties of a rectangle, they made different ways. The quitter found two characteristics of rectangular objects then derived it to be a rectangle’s properties. The champer found four characteristics of the objects then it was derived to be two properties of a rectangle. By contrast, Climber found six characteristics of the sign and derived all of these to be four properties of a rectangle. In addition, Climber could determine the properties of a rectangle correctly.
Co-Authors Abdillah Mahdi Abdul Hakim Abdul Rahman Abdul Rohman Abdur Rahman As’ari Abu-Hussin, Mohd Fauzi Ade Eka Anggraini Ade Evriansyah Lubis Ade Wahyudin, Ade Adha, Arfa Adhytia Nugraha Aditya Hani Affida, Maulina AFIFAH, UMI Agung Aditya Agus Prima Aspa Agus Sriyanto Agustina Styawan, Anita Agustinus Astono Ahmad Farhan Fasya Ahmad Gafan Abdillah Ahmad Hanif AHMADI Aidil Syaputra Ajeng Anggreny Ibrahim, Ajeng Anggreny Alfyananda Kurnia Putra Amany Hidayah Amat Komari Amrina Yulfajar Amsari Damanik Ana Mardiyaningsih Andrew, Febren Andri Firmansyah Andri Gemaini Angkoso, Sutanto Prasetyo Anindya Bidasari Anissa Yuniar Larasati Anita Kartika Sari Anna Gustina Aprilina Dwi Astuti Aqni, Bima Vitrana Ardhia Salsabilla Pramesti Azzahra Ardian Setio Utomo Arfa Adha Arief, Maria Odelia Vania Arieff Salleh Rosman Arifin Arisman Ariyadi Wijaya Arjita, Rendra Aryo Subroto Avifahtur Nur Rohma Ayu Sandra Dewi Bambag Teguh Handoyo Bambang Hermanto Bambang Sulistyo Bambang Teguh Handoyo Bangkit Ary Pratama Bannu Bayinah, Lafi Ni’matul Bayyinah, Lafi Na'imatul Befika Fitriya Dewi Benazir Bona Pratamawaty Benyamin Lakitan Bidhari, Lesty Ayu Binekas, Bani Budi Handoyo Budi Lestari Budi Prakoso Budi Purnomo cahyani, Ida Cahyo Sasmito Cakranegara, Pandu Adi Cakti Indra Gunawan Caplow, Julie A. Catur Daminto Chanifah CHARLYNA S. PURBA Cholis Sa’dijah Christina Bagenda Chusnul Zulaika Crista, Ngudi Hari Dahlan, Charly Dayana, Ismi Deni Sanjaya Dewanti, Vita Nuraini Dewi Kusumaningsih Diah Wulansari Hudaya, Diah Wulansari Dian Novitasari Dian Novitasari Diky Al Khalidy Diyanto, Rahmad Dora Bernadisman Dwiyono Hari Utomo Dzaky CP, Vicky Edora Edy Bambang Irawan Efta Dhartikasari Eka Danik Prahastiwi Eka Deviany Widyawaty Elistiana Eneng Nuraini Erry Hidayanto Erwien Christianto Etin Puspita Sari Eunike Yusmaliani Evi Maria Ezar Amrullah Faiq Asro’ie Fajar Fauziah, Fifit Fanny Dwi Puspitasari Farida Rahmawati Faridh Arganatha Diwangkara Farisya Nurhaeni Fatiya Rosyida, Fatiya Febriana Ardiyanti Ferry Firmawan Fiqoh, Latifah Nisa Fisa Wisnu Wijaya Fitah, Alqurani Aliyu Fitra Gustiar, Fitra Fitri Ramadhani Fitri Wulandari Fitriana, Nur Indah Fitriany, Rifda Fitriyani, Yeny Fortuna, Nadhifa Dewi Franciscus Xaverius, Franciscus Xaverius Gambriyanto, Kusumo Gautam Kumar Jha Hadi Karyono Halimah, Lili Hamdani, Deni Hana Hanifa Hanapia, Cepi Hanifa, Hana Hanum Sasmita Hartika, Wiwi Haryati, Prasasti Wahyu Hediati, Febri Noor Hendrit, Ade Heni Nurani Hartikayanti Herlina Vika Safriyani HERMAWAN Hery Susanto Heryanti, Ajeng Nuraeni Hidayat Sulistyo Hifdzi Romadloni I Made Sulandra I Nengah Parta Ibnu Siswanto Ibrahim Ida Hayu Dwimawanti Ida Sugeng Suyani Ifan Deffinika Ika Santia Ike Sari Astuti Ikram, Muhammad Ilzam, Moch Ilzam Imansyah, Salmaa R. N Imawan Taufiqy Imroatun Isna Nur Fadhilah Inayatullah, Muhamad Iqbal Indra Saputra Indriani, Lisna Intan Wulandari Iqbalulhadi, Mochammad Iramie Duma Kencana Irianto Irawaty Isawal, Ajun Islami, Miranda Ismangil Itsnaini, Nurul Ivan Wagner ivy, Tan Geok Chin Jaka Wisnu Wardana Jandra , Mifedwil Jatmiko, Rinto Wahyudi Jihan Fitrianti Suci Ramdani Joko Setiawan Joko Tri Haryanto kamil, khumaidi Kana Saputra S Khalimaturrofi’ah Kohar Krismiyarsi Krisno, Gama Aji Kristiadi, David Kunarto Kurnia, Alfi Kusuma, Fahmi Adi Kusumah, Krisnawati Baby Kusumastuti, Dyah Kyungsuk Bae Laeli N, Yuniar Lafi Na’imatul Bayyinah Lafi Na’imatul Bayyinah Laili Syarifah Larasati, Anissa Yuniar Larassati, Dian Sukma Lathiful Anwar Lestari, Okda Leyder, Raymond A. Lia Mulyani, Lia Lieanto, Caroline Lilik Ariyanto Listyo Yudha Irawan Loekas Susanto Lulut Julianto M Pudail M. Pudail M. Yogi Riyantama Isjoni Made wedaswari Mahmudah P. F Malik, Muhamad Ibnu Maria Dewi Christiyawati Marieieva, Tetiana Mario Zulhadi Amrullah Markus Suryoutomo Maryani, Neni Maskuri, Said Masvika, Hendra Memmase, Joice Zhenrike Minatika, Euis Naely Mochammad Imron Awalludin Muda, Strayker Muhammad Andri Radiany Muhammad Dezan Adistira Dezan Muhammad Gunawan Wibisono Muhammad Irfan Muhammad Muchlish Huda Muhammad Rif'an Muhayan Mujiyem Sapti Mukaromatus Sholihah, Lailatul Muliasutisna, Asep Muna, Nailatul Mundirin Murbaningsih , Ari Mintarti Musarofah, Unun Mutiah, Nurmila Mu’tafiqul haqiqi Mu’tashimbillah, Muhammad Nadaa Syifa’ Abyan Rizqi Nadila Putri Effendi Nanik Purwiningsih Natasya Yunita Sugiastuti Nindy Sevirasari Ningtyas, Yoga Dwi Windy Kusuma Nisa, Riatun Novika Adi Wibowo Nunung , Nurjanah Nur Ainia Nur Hayati, Nilam Nur Kusumawati, Heni Nur Rochmah, Eva Nurhayati, Tita Nuriswara, Rakhmad Hidayat Nurkomar Hidaya Nurshanti, Dora Nurtama Aditya Nugraha Nurti Kusuma Anggraini Oedjijono Poly Endrayanto Eko Christmawan Ponco, Catur Pranoto, Gusti Adi Prasetyo, Deigo Adit Dwi Pratama, Rama Adi Pratiwi, Ayu Hardianti Pratiwi, Visna Shalsa Pratomo, Sunu Arsy Prawira, Akvian Erie Prayitno, Arif Dio Esa Prinandari, Ajeng Ayu Probokusumo Pua Upa, Fatmawati Pudail Purba, Regius Ovianto Purwanti, Hani Purwono Hendradi Puspita, Rafika Tri Puspitaningrum, Cynthia Ayu Dian Putra, Rendi Pratama Putri Putri Mahanani, Putri Qarlina, Cherly Dwi Qohar, Abd. R. Suharyadi Rahayuani Ratnaningsih, Hanim Rahayuaningsih Ratnaningsih, Hanim Rahmad Diyanto Rahmah, Nunung Aini Rahmatulloh, Aang Rahmawati, Heni Ramadhani, S.Pd., M.Pd, Irham Rani Zahra Ratmini, Niluh Ratna Asmah Susidarti Ratnaningsih, Hanim Rahayuani Ratri Noorhidayah Ratri, Anugrah Januar RB. Hendri Kuswantoro Reno Warni Pratiwi Resmaya Agnesia Mutiara Sirait Retno Sunu Astuti Retnoasih, Agustina Ria, Rofiqoh Rifai, Fuad Yanuar Akhmad Rifki Ahmad Rifki Andi Novia Rika Yuliastanti Rini Setiawati Riri Trinanda Risqa Naila Khusna Syarifah Rivandi A, Muhamad Arvan Riyoldi Rizar, Fitra Rizki Indrawan Rohmawati, Windi Romli Romli, Romli Rosi Widarawati Rosi Widarawati Rosidah, Nikmatur Rosimanidar Ruly Eko Kusuma Kurniawan Rurianto Rusmanto Rustam s, solihin S, Wedi Sabani, Jessica Mei Sahri, Rafida Ramania Sahrina, Alfi Salsabilah Samuel Marpaung Sanudin Saputra, Dicky Alga Sari, Anita Kartika Sari, Endah Murtiana Sarjito, Agus Saryana Sastradipraja, Usman Shobikin Siswadi Sisworo Siti Hidayati Siti Komariyah Siti Nabilah Siti Nurchasanah Siti Sarifah Siti, Siti Sarifah Soelistijo, Djoko Sofa, Eros Meilina Sofin Imaratul Aini Solikhin Son , Haji Sri Dewi Astuty Ilyas Sri Hastuti Sri Mulyani SRI RAHAYU Sri Wahyuni Sri Winarso Martyas Edi Subandi Subandi Subanji Subechan, M Arif Sudarno utomo Sudirman Sugeng Riyadi Sugeng Utaya Suhadi Suhendar Sukamto, Ika Sumiyarsi Sukoriyanto SUMANTO Sumarmi Sunarsa Sundjoto Sunu Arsy Pratomo Suprayitno suprayogi Suprihati Supriono Suryaningrum, Christine Wulandari Susilawati Susiswo Sutar Sutawidjadja, Akbar Sutini Suyanto Syahrial, Yoppi Syakirin, Rafialdi Syamsir Dewang Syamsul Bachri Syaputra, Aidil Talitha Zhafira Talitha Zhafira Tang, Adelina Taufik Dani Temmy Hastian Tenovita Sari, Fajar Tituk Utari Toto Suharto Triana Dewi Purnama Sari Trias Widorini Tuti Hardianti Tuti Mutia Udin, Mahrudin Ujianto, Anang Dwi Umi Sarjiatun Upa, Fatmawati Pua Ustadz, Damar Irsyad Uswatun Chasanah Verawaty , Marieska Vicky Dzaky Cahaya Putra Wahdi, Agung Hilmi Wahid, Defrio Saka Wahjoedi, Tri Wahyu Hadikristanto Wahyu Tri Utomo Wahyuni, Sr Wardani, Rahmalia Kurnia Wardiyan, Chandra Warno Wedi S Wibowo, Furqon Edi Widiyawati, Ema Nurkholisa Widodo, Joehananto Djoko Teguh Widodo, Risriki Widyastari, Sri Wiguna, Edo Wijayanti, Ariyani Wahyu Wilujeng Hidayati Winarni, Ida Windarsih, Anjar Wisang Elang Fajar Nisnala Wiwi Hartika Wulakada , Imam Al Ghozali Hide Wulandari, Jessi Aprilia Yanthy Leonita Perdana Simanjuntak Yatmihatun, Sri Yatmihatun, Yayan Eryk Setiawan Yenny AS Yohanes Yulia, Mukhafatul Sifa Yuniar Laeli Nur Faizah Yunus Yunus Yuono, Sukma Setyo Yusuf Suharto Yusup Rohmadi Zaenal Muttaqin Zainul Mu’ien Husni Zihni Ihkamuddin Zihni Ihkamuddin Zulandi, Muhamad Rahmal Zulfa Amalia Rachim