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Journal : Journal on Mathematics Education

Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes Matitaputty, Christi; Nusantara, Toto; Hidayanto, Erry; Sukoriyanto
Journal on Mathematics Education Vol. 13 No. 3 (2022): 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.v13i3.pp393-414

Abstract

Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world. Therefore, this study aimed to examine in-service mathematics teachers' pedagogical content knowledge (PCK) to determine students’ mistakes in solving permutations and combinations problem and their teaching strategies to eliminate these errors. Data were collected by distributing vignettes, CoRe, and PaP-eRs to thirteen mathematics teachers from ten provinces in Indonesia after they finished an online professional teacher education program to determine their PCK in teaching permutations and combinations. The data collected were analyzed qualitatively using a content analysis approach to obtain categories inductively. The result showed that PCK of in-service mathematics in teaching permutations and combinations was observed by identifying student mistakes conceptually and procedurally, even though some could not determine their mistakes in permutations. On the other hand, the knowledge of instructional strategies can engage all students in active learning, but most of them only give general answers. Furthermore, an in-depth understanding of permutations and combinations topic is needed to support the development of teachers’ pedagogic competencies sustainably. The contribution of this research will be of interest to curriculum development and mathematics educators.
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.
How mathematics teachers' special knowledge changing: A case study in the Professional Teacher Education program Matitaputty, Christi; Nusantara, Toto; Hidayanto, Erry; Sukoriyanto
Journal on Mathematics Education Vol. 15 No. 2 (2024): 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.v15i2.pp545-574

Abstract

The COVID-19 pandemic has catalyzed the widespread adoption of distance learning, necessitating a comprehensive understanding of how teacher knowledge evolves within the context of Teacher Professional Education (TPE) programs. Some research endeavors may employ evaluation methodologies that inadequately capture the nuanced dimensions of knowledge, highlighting the necessity for greater incorporation of evidence-based approaches in the formulation and assessment of teacher development initiatives. This study employs a qualitative methodology to explore the evolution of Mathematics Teachers' Specialized Knowledge (MTSK) within the framework of a TPE program. Data were gathered through the engagement of three educators in the preparation and execution of lessons on permutation and combination via a Learning Management System (LMS), coupled with in-depth interviews. The findings underscore the TPE program's role in fostering collaborative learning environments through participation in online educational communities. Teachers are shown to be increasingly integrating technology into their pedagogical practices, albeit with varying degrees of proficiency. The presence of Professional Learning Communities (PLCs) is identified as instrumental in supporting educators in refining instructional strategies to enhance teaching effectiveness. Nevertheless, there remains a subset of teachers necessitating more profound and more comprehensive content knowledge about their subject matter. These insights emphasize the importance of designing TPE programs that offer sustained and adaptable professional development opportunities to facilitate continuous growth among educators. Consequently, it is recommended that online learning communities geared toward addressing the diverse learning requirements of students be established, thereby aiding in the identification and resolution of pedagogical challenges.
Co-Authors Abdur Rahman As’ari Abdur Rohim, Abdur Adinda Beauty Afnenda Andriyani, Fitria Apriliana Tezha Eka Faradina Ashiddiqi, Hasbi Aunga, Maria Marantika Awang, Mohd Isha Bachriani, Ellsa Natassa Bulgur Wibisono, Anang Cholis Sa’dijah Christi Matitaputty Desyandri Desyandri Dwi Jayanti, Mei Erry Hidayanto Farih Nur Hisyam Fatah, Zakiyah Fatikhah, Wulan Faula Rossydha Febyanti, Adinda Isna Fitriyah Nabila Gestiani, Anggun Hadi Mulyanto, Bayu Hamdani, Deni Hasanah, Firda Dyah Alvin Hendro Permadi Husna, Shely Anisa I Made Sulandra I Nengah Parta Ika Ujiana S Sugianto Indriati Nurul Hidayah Kasturi Kasturi, Kasturi Khoirudin, Mohammad Krisdarani, Novanda Lathiful Anwar Laurentcia Noviafta Widya Makbul Muksar Miswanto Miswanto Mohammad Archi Maulyda Mohammad Yusuf Randy Muhammad Erfan Mutina, Mutina Nabila, Fitriyah Nego Linuhung Ngadino, Dede Ngesti, Nisaa Arta Nurhayati Nurhayati Nurul Chamisah Permadi, Hendro Purwanto Purwanto Purwanto Purwanto Purwanto Puspita Ayu Damayanti Qohar, Abd. Rachmat Wasqita Radeni Sukma Indra Dewi Rahayu, Arimbi Ratna Ekawati Rianti Hidaiyah Riya Dwi Puspa Riya Dwi Puspa Rustanto Rahardi Sahadatina, Sahadatina Salman Alfarisi Sari, Marinda Rosita Sari, Noviana Puspita Satriya Adika Arif Atmaja Shabrina, Zayyan Shirly Rizki Kusumaningrum Sisworo Slamet Sri Rahayuningsih Sri Rahayuningsih Subanji Subanji Sudirman Sudirman Suteja, Maura Caesarani Toto Nusantara Umar Umar Utami, Nur Isnaini Viantasari, Erwinda Vita Kusumasari Vivi Rachmatul Hidayati Wahyuningtyas, Daniar Wulandari, Ninik Diah Zahro, Nafi'atuz Zirhannudin, Muhammad