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Aan Putra
Institut Agama Islam Negeri Kerinci
Religion Humanities Biochemistry, Genetics & Molecular Biology Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Environmental Science Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Medicine & Pharmacology Physics Social Sciences Other

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Journal : Jurnal Elemen

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Secondary students’ informal strategies in solving enumeration problems prior to formal combinatorics instruction Putra, Aan; Zulkardi; Putri, Ratu Ilma Indra; Laswadi
Jurnal Elemen Vol 11 No 4 (2025): October
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/jel.v11i4.31088

Abstract

Although enumeration problems are fundamental in combinatorics, little is known about how students intuitively approach such enumeration problems before receiving formal instruction. This exploratory qualitative study investigated the initial strategies employed by twelve-grade students in solving enumeration problems prior to formal instruction on enumeration rules. Fifteen students from a public senior high school in Kerinci, Indonesia, who had not yet learned combinatorics in the curriculum, participated in this study. Data were collected through students’ written responses to three combinatorial problems presented in different real-life contexts and further explored through semi-structured interviews. Only responses demonstrating coherent and interpretable strategy were analyzed. The findings reveal three dominant strategies: listing all possible arrangements, generalizing patterns, and applying the multiplication principle. These findings indicate that students possess intuitive approaches that can serve as a foundation for formal combinatorial reasoning. The study aligns with the Realistic Mathematics Education (RME) perspective, emphasizing the importance of guided reinvention and contextual mathematization, and proposes implications for designing learning trajectories that build on students’ informal reasoning in secondary mathematics education.
Co-Authors Aditya Harisman Agung Tri Prasetia Amanda, Nurul andina, Andina Andri Defrian Andriani, Medi Anisyak Islami Asdamayanti, Nurul Bayu Okta Orizal Dela Kristia Delsa Sepnila Delviana, Reza Dewi, Mella Permata Dosi Juliawati Egha Ardhia Pramesty Elita, Geni Sri Elly Susanti Engla Wetri Fadhilah, Ulfa fadhillah, ulfa Fahira, Popy Faradilla, Hanifa Farid Imam Kholidin Febria Ningsih Feni Okti Yolanda Fitri, Anisa Fitrisa Syelitiar Florensia Betyka Geci Oktari Geni Sri Elita Gito Kurniawan Gunawan, Rilla Gina Gustin, Liza Hafis, M Hendra Syarifuddin Hengki Yandri Hesti, Nadiya Ice Dwi Novelza Icmi Santry Nova Ijce Hormadia Ines Feltia Milenia Intan Bela Yulia Juliani, Rezki Putri Kesi Afrilia Laswadi Laswadi M Hafis Maila Sari Mella Permata Dewi Melsita, Holdia Mesi Oktafia Mhmd. Habibi Mulya Novita Mulyani, Tami Muthia Roza Nelpita Ulandari Nia Monika Sari Norhaslina, Norhaslina Nova, Icmi Santry Novelza, Ice Dwi Nurfauziah Nurfauziah Nurul Amanda Nurul Amelia Nusantara, Duano Sapta Oktafia, Mesi Pitri, Afnesa putri, latifa intan brilian Putri, Rahmi Putri, Rani Manisa Rahayu, Atika Rahmadhani, Aulia Sefti Rahmi Putri Ratni Yanti Ratu Ilma Indra Putri Rema Anggralia Rema Anggralia Rencitia Renza Puspitasari Reri Seprina Anggraini Reza Delviana Ria Deswita Ria Deswita Rosi Nopela Rusliah, Nur Sari, Anjli Bisna Sari, Maila Sari, Nada Afrima Sertika, Suci Sisfarina Hafifah Sustipa, Widya Syarifuddin, Hendra Syarifuddin, Hendra Thania Wulansari Ulandari, Nelpita Wahyudi Wahyudi Wahyuni, Annisa Tri Wike Pratiwi Vitaloka Wulandari Wulandari Yatti Fidya Yessi Yulanda Yetiona Tensa Yudela, Shintia Zulfah Zulfah Zulkardi Zulkardi Zulkardi