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Journal : Journal on Mathematics Education

Exploring quantitative relationship through area conservation activity Sari, Puspita; Ng, Swee Fong
Journal on Mathematics Education Vol. 13 No. 1 (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.v13i1.pp31-50

Abstract

Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in early algebra can be explored through area conservation activities. Understanding area conservation is said to be fundamental in developing the concept of area measurement. In this study, a ten-year old pupil was observed during her involvement while comparing area of two polygons that can be decomposed into equivalent triangles. Data for this study include the pupil’s written artefacts, and video recordings of the activities and interviews. Findings from this study show that the area conservation activity has the potential to build the notion of quantitative relationships in early algebra. The quantitative relationship between the unit of measurement and the result of measurement of a shape can also be explored, that is, the smaller the unit of measurement, the larger the result of measurement. Hence, this study can provide a groundwork for further studies in the relation between quantitative relationship in algebra and area conservation in geometry at the elementary school level.
The ‘mound-hollow’ model for solving integer addition and subtraction problems Sari, Puspita; Dindyal, Jaguthsing; Shutler, Paul Maurice Edmund
Journal on Mathematics Education Vol. 16 No. 1 (2025): 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.v16i1.pp365-382

Abstract

Understanding integer operations is a fundamental yet challenging concept for elementary students, often requiring effective visual models to support their comprehension. Despite various instructional models, many students continue to struggle with integer addition and subtraction, particularly when negative numbers are involved. Addressing this gap, this study explores the potential of the mound-hollow model to facilitate students’ understanding of integer addition and subtraction concepts intuitively. This study aimed to examine how three sixth-grade students utilized the mound-hollow model to solve integer addition and subtraction problems. Data were collected from students' written tests and individual interviews conducted after a teaching experiment involving 25 sixth graders in Indonesia. The findings indicate that the mound-hollow model provides a meaningful analogy for solving addition problems of types x+(-y) and (-x)+y (where x>y and x,y are natural numbers) and subtraction problems of types x-(-y) and (-x)-y. All three students successfully employed the model to solve the addition problems by neutralizing every mound-hollow pair and to solve the subtraction problems by creating mound-hollow pairs. Additionally, students demonstrated the ability to justify their solutions and correct errors through the mound-hollow representation. The use of a single mound or hollow to represent larger integers enhanced students’ proficiency in solving integer operations and reinforced their understanding of the relationship between addition and subtraction, such as x-(-y)=x+y and (-x)-y=(-x)+(-y). These findings highlight the effectiveness of the mound-hollow model as an alternative instructional tool for teaching integer operations, providing students with an intuitive framework to construct abstract mathematical concepts. The implications of this study contribute to mathematics education by offering insights into the design of visual models that support conceptual understanding in integer arithmetic.
The neutralization on an empty number line model for integer additions and subtractions: Is it helpful? Sari, Puspita; Hajizah, Mimi Nur; Purwanto, Swida
Journal on Mathematics Education Vol. 11 No. 1 (2020): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

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

Abstract

The number line and the neutralization model have been used very extensively in teaching integer additions and subtractions for decades. Despite their advantages, issues concerning subtractions on these models are still debatable. Therefore, the neutralization on an empty number line (NNL) model is proposed in this research to help students better understand the meaning of integer subtractions as well asadditions. This report is a part of a design research study conducted in a classroom of 28 elementary school students at the fifth grade. Data were gathered by collecting students’ written work, conducting interviews and observations during the teaching experiment. This paperfocuses on students’ perceptions of the NNL model and what factors that might contribute to students’ achievements in understanding integer additions and subtractions. The analysis revealed that most students overemphasized on the use of the NNL model as a procedural methodinstead of as a model for thinking. Moreover, students’ mathematical beliefs and conceptions on the use of the column strategy and theabsence of a discussion on the need of using the model are found to be some factors that could cause students’ misunderstandings. However, with a thorough planning, the NNL model has a potential to help students developing a meaning of integer additions and subtractions.
Co-Authors - Wiendartun . Asparian, . . Sukatiningsih . Sukatiningsih A.R, Rahmi Abi, Antonius Remigius Achmad Subagio Adelina Fitri Adi Santoso Aditya, Amalina Cahya Aditya, I Kadek Adma, Arinaldo Afrinaldi, Rolly Ahera Ashari , Ahera Ashari Albari, Rahmat Rafi Alviani, Tantri Rizki Amany, Natasya Zalta Amimr, Andy Amiratun, Silvia Anabela, Aisha Anak Agung Gde Rai Arimbawa Andre Rachmat Scabra Andriani, Rina andriyani, fatimah Anisa Anisa Anriana, Nina Antari, Dwi Apriliyasaragih, Enzel Arachman, Beryl Khalif Arif Rahman Aristo, . Armaidi Darmawan Arseto, Dedy Dwi Ashar Nuzulul Putra Aspadiah, Vica Asrinawaty, Andi Nur Asrul Sani Astutik , Widya Aulia, Sevina Azhar Azhar Azhari, M. Rifqi Azmi , Muhammad Ali B.P, Herman Baehaqi Bafadal, Mentarry Bakti Setyadi Bangun, Ika Agustina Br Barokatun Hasanah, Barokatun Baroroh Lestari Boy Arief Fachri Budesri, Puja Budi Aswin Butar, Marta Butar Butar-butar, Marta C Hanny Wijaya Cholisoh, Siti Nur Citra Asmara Indra CM Simatupang, Ervina D Sitanggang, Hendra Dahlia Dahlia Dani Gustaman Syarif Dedi Irwanto, Dedi Derniati, Neris Desmelati Desmelati Dewi Astuti Purnama Sari Dewi Fadilasari Dian Agustia Dianita, Dianita Dindyal, Jaguthsing Dondin Sajuthi Effendi, Firman Efitra Eka Daryanto, Eka Eksi Utari Ely Susanti Evy Wisudariani Fahri, Chairul Faisal, Atikha Fakhraini Fajrina Hidayati Fauzan, Nabil Febrianti S., Anisa Putri Frihatin, Gita Fristiohady, Adryan Fuji Kurniawati Futri, Selli Gaol, Miranda Lumban Gina Andyka Hutasoit Ginting, Irma Kristiani Br Girsang, Monica Evi Fania Guspianto Guspianto Gustiawati, Resty Hadiyan, Aris Hajizah, Mimi Nur Halim, Rd. Haqqi, M Hibatul hartadi, alvin febri Hasanah, Putri Amalia Hasibuan, Khadijah Helmi Suryani Nasution Hendra Dhermawan Sitanggang Hero Gunawan Herwansyah Herwansyah, Herwansyah Hidayana, Nur Hubaybah, Hubaybah Hulaila, Saskia Husain, Farid Husnarika Febriani, Husnarika Ibrahim, Agus Malik Imelda Yolanda Nayoan Ina Indah Puspasari Kiay Demak Indah Zhafirah, Annisa Intan Sari Iriantini, Sri Irma Purwati Islamiwati, Dian Ismah, Iffah Zatil Ismi Nurwaqiah Ibnu Isnalita Isnalita, Isnalita J. Tandirerung, Fistra Jay Jayus Johan, Muhammad Juaidah Agustina, Juaidah Juliana, Fitri Julianti Julianti, Julianti Kasyani, Kasyani Kemimaro, Fathannah Khaerurrafiah, Ery Khairuna Khairuna Khairunnisa Khairunnisa Kiay Demak, Indah Pupasari Kumala Sari, Filma Kusumawati, Nila La Ode Reskiaddin Lasmana, Mienati Somnya LITBAGAY, ANNE JULITZA Liviana, Theresia Liyanti, Lisda Luthfi Al Ansyari, Muhammad M. Irsyad M. Ridwan M. Ridwan M. Ridwan M. Ridwan M. Ridwani, M. 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Asfiandi Marbun, Tesalonika Graciella Marga Neo Pratama Marliana, Nanda Marta Butar Butar Maryanto - Mashuri Mashuri Maulidya Istiqomah, Nuralifah Medianto, Felix Meilinda Meilinda Meliani, Meliani Mochtar Marhum Muammar, Lalu Muhammad Abib mudjisusatyo, yuniarto Muhammad Alwi Muhammad Iqbal Muhammad Ridwan Muhammad Rifqi Azhary muhammad rizky, muhammad Muhammad Syukri Muhti, Rahmadillah Mukhammad Fauzi Muzuni, Muzuni Nadia Nadia Nadwa, Zafira Nadwa, Zavira Naibaho, Tyoma Saryance Nainggolan, Septri Monalisa Nani Yulianti Nasrun Nasrun Nasution, Helmi Suryani Natalia, Igles Natami, Rehan Tri Na’Im, Andiko Neonbeni, Yohanes Ng, Swee Fong Ningsih , Vinna Rahayu Ningsih, Sri Tuti Ningsih, Vina Rahayu Norhapifah , Hestri Novita Eka Rini, Willia novita, willia Novramanda, Atisa Nugraha, Deden Novan Setiawan Nugroho, Alfan Nur Fadhilah Nur Muhammad Firmanda Nurfadila Nurhayati Nurhayati NURIYAH Nuriyah, Rini Putri Nursaimatussaddiyah, Nursaimatussaddiyah Oka Lesmana, Oka Padalia, Andi Padang, Chusnul Maqfira Andi Padang, Chusnul Maqfirah Andi Pamulaan, Alif Bahtiar Prabawati, Dewi Purno, Marhaendro Purwantiningsih Sugita Purwanto, Swida Putra, Adrian Tri Putra, Aldrian Tri Putra, Iwan Putri, Fitria Eka Rachman, Dendy Januari Rahayu Ningsih, Vinna Rahmadani, Dwika Rahmadani, Nurfadillah Raiyasmi, Dean Ramadhani, Riski Saskia Ramadhani, Rizky Barkah Rambe, Ade Mahri Kurniawan Rambe, Multisari Rangkuti, Irsan Reinaldo, Poldo Rekiaddin, La Ode Restu Restu Rezer, Yuni Dita Rianti Ridha, Irfan Rika P, Prasetyan Rina Nofri Enis Rinaldi, Shirin Ebadi Riono, Yoyon Risnawati Risnawati Rizky Adiputra Rosnelli, Rosnelli Rozalia Rumaisha-Zuhriansyah, Rayya Rupawan, I Kadek Rusdianto, Fahrul Rusmiyati Rusmiyati, Rusmiyati Rusyan, Susiyanti Sadila, Andi Safutro, Syaifudin Hadi Sahidin . 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