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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)

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

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.
REPRESENTASI SISWA SMA DALAM MEMECAHKAN MASALAH NILAI OPTIMUM BERDASARKAN GAYA KOGNITIF FILD INDEPENDENT DAN FIELD DEPENDENT Santia, Ika
Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika Vol 1 No 1 (2015)
Publisher : Program Studi Pendidikan Matematika, Universitas Nusantara PGRI Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (238.652 KB) | DOI: 10.29407/jmen.v1i1.125

Abstract

Rendahnya kemampuan siswa  memecahkan masalah nilai optimum adalah kurangnya ragam representasi yang dimiliki siswa. Kemampuan representasi menjadi penting dalam suatu pembelajaran matematika. Perbedaan  kemampuan representasi siswa dalam memecahkan masalah dimungkinkan adanya perbedaan gaya kognitif siswa. Untuk itu dilakukan suatu penelitian kualitatif yang  bertujuan mendeskripsikan:  (1)  representasi siswa  SMA  dengan gaya  kognitif Field Dependent dalam  memecahkan masalah nilai optimum (2) representasi siswa  SMA  dengan gaya  kognitif Field Independent dalam  memecahkan masalah nilai optimum. Pengumpulan data dilakukan dengan  pemberian tugas TPM dan wawancara. Teknik pemeriksaan keabsahan data yang digunakan  adalah triangulasi. Subjek penelitian adalah siswa SMA kelas XI sebanyak 2 orang. Hasil  penelitian  ini  menunjukkan  bahwa  subjek dengan gaya  kognitif Field Dependent merepresentasikan idenya untuk memecahkan masalah nilai optimum adalah dengan cara: memahami informasi dan apa yang ditanyakan dengan membuat gambar, membuat rencana penyelesaian dengan membuat persamaan matematika, memanipulasi persamaan tersebut dan mengecek kembali hasil akhir yang didapatkan dengan mensubstitusi kembali jawaban akhir ke persamaan awal. Sedangkan subjek dengan gaya kognitif Field Independent merepresentasikan idenya untuk memecahkan masalah dengan cara: memahami informasi dan apa yang ditanyakan dengan menuliskan persamaan matematika menggunakan simbol formal, membuat rencana penyelesaian dengan membuat persamaan matematika, memanipulasi persamaan tersebut dan menggunakan cara coba-coba serta tidak melakukan pengecekan kembali hasil akhir yang diperoleh. Kata Kunci: Representasi, Pemecahan Masalah nilai optimum, Gaya Kognitif
CARA BERPIKIR GEOMETRIS SISWA DALAM MENENTUKAN HUBUNGAN ANTAR BANGUN SEGIEMPAT MELALUI PEMBELAJARAN MATEMATIKA REALISTIK DIDASARKAN PADA TINGKAT KEMAMPUAN MATEMATIKA SISWA Santia, Ika
Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika Vol 1 No 2 (2015)
Publisher : Program Studi Pendidikan Matematika, Universitas Nusantara PGRI Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (180.615 KB) | DOI: 10.29407/jmen.v1i2.233

Abstract

Penelitian ini bertujuan menjabarkan cara berpikir geometris siswa berkemampuanmatematika rendah, sedang dan tinggi dalam menentukan hubungan antarbangunsegiempat dilihat melalui pembelajaran PMR. Penelitian ini termasuk penelitiankualitatif dan bersifat eksploratif. Subjek diambil dari kelas VIII SMP yang beradapada level deduksi informal berdasarkan level berpikir gometris van Hiele.Selanjutnya untuk menguji kredibilitas data, dilakukan triangulasi waktu. Hasilpenelitian menunjukkan bahwa (1) siswa yang berkemapuan matematika tinggi (GT)merangkai 12 hubungan antarbangun segiempat yang mungkin  dari 15 hubunganantarbangun segiempat yang mungkin dan cenderung menggunakan danmemperhatikan 4 unsur pada kegiatan menggambar bangun datar segiempat yaituposisi, ukuran sisi, bentuk dan besar sudut (2) siswa yang berkemapuan matematikasedang (GS) merangkai 5 hubungan antarbangun segiempat dari 15 hubunganantarbangun segiempat yang mungkin dan cenderung hanya menggunakan danmemperhatikan 3 unsur pada kegiatan menggambar bangun segiempat yaitu bentukgambar, ukuran sisi dan sudut. Sedangkan (3) Siswa yang berkemapuan matematikarendah (GR) tidak dapat merangkai hubungan antarbangun segiempat dari 15hubungan antarbangun segiempat karena hanya memperhatikan 1 unsur padakegiatan menggambar bangun segiempat yaitu bentuk gambar.Kata Kunci: hubungan, antarbangun segiempat, PMR, kemampuan matematika
Students’ mental construction in cube and cuboid concepts based on mathematical ability differences Rofiki, Imam; Anam, Ahmad Choirul; Sari, Putri Eka; Irawan, Wahyu Henky; Santia, Ika
Al-Jabar: Jurnal Pendidikan Matematika Vol 11 No 1 (2020): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v11i1.5946

Abstract

Understanding of cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies of students’ understanding of these concepts have posited a gap between the students’ surface area and volume conceptions of its and students’ understanding. The study aims to describe the students’ mental constructions in APOS (Action, Process, Object, and Schema) theory framework. This study used analysis of students as subject to three junior high school students who have differences in mathematical abilities with a qualitative approach. Data were collected by the task sheet and interview. The result of this study evidences that subject who has high mathematical ability could solve problems about cube and cuboid concepts correctly in the action stage. In the process and object stage, subject could provide detailed explanations of how steps to assess the surface area and volume of cube and cuboid. She compared two shapes with different sizes of cube and cuboid. In the schema stage, she made systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject who has medium mathematical ability explained her mental construction in action and process stage well, despite the error in the process stage. Next stage, she had compared two different shapes of cube and cuboid to found their ratio. The last stage, she had not completed her explanation. The subject has low mathematical ability could solve the problems about cube and cuboid concepts. At the process, object, and schema stage, she had not completed its indicators to show cube and cuboid concepts.
INOVASI MEDIA PEMBELAJARAN GAME QUARTET CARD PADA MATERI BANGUN RUANG SISI DATAR KELAS VIII SMP Anggraini, Novia Afriana; Santia, Ika; Hima, Lina Rihatul
Pendas : Jurnal Ilmiah Pendidikan Dasar Vol. 10 No. 02 (2025): Volume 10, Nomor 02 Juni 2025 publish
Publisher : Program Studi Pendidikan Guru Sekolah Dasar FKIP Universitas Pasundan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23969/jp.v10i02.27863

Abstract

The purpose of this research is to develop quartet card learning media on flat-sided space building material. This research uses the Research and Development (R&D) method with the ADDIE model which consists of 5 stages, namely Analysis, Design, Development, Implementation, and Evaluation. The data collection techniques used are interviews, questionnaires, and observations. The validity of the quartet card learning media is seen from the results of the expert validation test with a percentage score obtained of 89.6% from media experts, 81.3% from material experts, and 92.3% from practitioners who are included in the category of very valid learning media can be used without revision. The results of student responses on small-scale trials obtained a percentage of 82% and large-scale trials obtained a percentage of 83% with a very interesting category, meaning that the attractiveness of quartet card learning media is very good. The quartet card learning media is declared valid and interesting to use in learning mathematics on flat-sided space building material.
DRAGLANDTICS: INOVASI MEDIA PEMBELAJARAN BERBASIS ANDROID DENGAN ELEMEN GAMIFIKASI EDUKATIF Sulistyo, Bagus; Handayani, Aprilia Dwi; Jatmiko; Nurfahrudianto, Aan; Santia, Ika
Jurnal Ilmiah Pendidikan Citra Bakti Vol. 12 No. 3 (2025): Jurnal Ilmiah Pendidikan Citra Bakti
Publisher : STKIP Citra Bakti

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.38048/jipcb.v12i3.5886

Abstract

Kesulitan siswa dalam memahami konsep operasi pecahan masih menjadi tantangan di SDN Batuaji 1, meskipun materi ini telah diajarkan sejak kelas IV. Hambatan ini muncul akibat terbatasnya penggunaan media pembelajaran yang interaktif dan dominasi metode ceramah dalam kegiatan belajar mengajar. Tujuan kajian ini guna mengembangkan sarana pembelajaran matematika berbasis aplikasi Android bernama DragLandTics yang menerapkan unsur gamifikasi, serta mengkaji tingkat kevalidan, kemenarikan, dan efektivitas penggunaannya dalam pembelajaran operasi pecahan. Meliputi tahap analisis, perancangan, pengembangan, implementasi, evaluasi pada proses pengembangan dengan pendekatan model ADDIE. Hasil validasi menunjukkan bahwa media ini teridentifikasi sebagai kategori sangat valid dengan skor rata-rata 4,56, dan respon siswa menunjukkan tingkat kemenarikan tinggi dengan skor 4,26. Selain itu, terlihat adanya kemajuan hasil belajar siswa yang menonjol setelah penggunaan media, berdasarkan perbandingan nilai pretest dan posttest. Implementasi elemen gamifikasi seperti tantangan, penghargaan, dan visual interaktif dalam DragLandTics terbukti meningkatkan motivasi belajar siswa, Penelitian ini merekomendasikan pengembangan lanjutan dengan menambah fitur serta penyempurnaan tampilan agar semakin menarik dan optimal dalam akativitas edukatif.
Peningkatan Hasil Belajar Barisan Aritmatika Siswa SMK Melalui Pembelajaran Open Ended Problems Putri, Like Rizky; Hima, Lina Rihatul; Santia, Ika
Polinomial : Jurnal Pendidikan Matematika Vol. 4 No. 3 (2025)
Publisher : Papanda

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56916/jp.v4i3.1880

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This study aims to improve students’ learning outcomes in arithmetic sequences through the implementation of the open-ended problems learning model. The background of the research highlights students' difficulties in understanding mathematical concepts, particularly arithmetic sequences, due to teacher-centered learning methods and limited student engagement. A total of 88.88% of students in class X-TKJ at SMK Arrahmah Papar did not meet the Minimum Mastery Criteria (KKM) of 75 in the Mid-Semester Exam. The open-ended problems approach was chosen based on its proven effectiveness in enhancing students' critical and creative thinking skills (Nazareth & Mukhlis, 2022). This study used a quantitative approach with a One Group Pretest-Posttest Design. The research subjects consisted of 36 students. Data were collected through mathematics pretest and posttest, teacher observation sheets, and student response questionnaires. The results showed a significant improvement in learning outcomes, with the average score increasing from 61.39 (pretest) to 82.36 (posttest). The Paired Sample t-test yielded a significance value of 0.000 (< 0.05), indicating a significant difference between pretest and posttest scores. Teacher activity was rated very good with an average of 88.15%, while student responses were positive with an average of 81.18%. The study concludes that the open-ended problems learning model is effective in improving both the learning outcomes in arithmetic sequences and students’ critical and creative thinking abilities
PENGARUH MODEL PEMBELAJARAN STEM-PBL TERHADAP KEMAMPUAN BERPIKIR KRITIS SISWA DALAM MATERI STATISTIKA Wida, Ovilia Nur; Candraningtyas, Tsatsabilla Diannira; Widyawati, Irma; Santia, Ika
ELIPS: Jurnal Pendidikan Matematika Vol 6 No 2 (2025): ELIPS, September 2025
Publisher : Universitas Pancasakti

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47650/elips.v6i2.1989

Abstract

Penelitian ini berfokus pada rendahnya kemampuan berpikir kritis yang dimiliki oleh siswa SMA dalam menyelesaikan masalah statistika yang bersifat kontekstual dalam kehidupan sehari-hari. Untuk mengatasi masalah tersebut, penelitian ini bertujuan untuk menguji pengaruh model pembelajaran STEM-PBL (Science, Thechnology, Engineering, Mathematics – Problem Based Learning) dalam meningkatkan kemampuan berpikir kritis siswa. Metode penelitian yang digunakan adalah pendekatan eksperimen dengan pretest posttest control group design. Sampel dalam penelitian ini terdiri dari siswa kelas X-1 ECP sebagai kelas eksperimen dan kelas X-2 ECP sebagai kelas kontrol, yang dipilih menggunakan teknik cluster random sampling dari populasi seluruh siswa kelas X SMA Negeri 7 Kediri. Data yang diperoleh kemudian dianalisis menggunakan uji t untuk mengetahui pengaruh model pembelajaran STEM-PBL terhadap kemampuan berpikir kritis siswa dan uji N-gain untuk mengukur peningkatan kemampuan berpikir kritis siswa. Hasil dari penelitian ini menunjukkan bahwa penggunaan model pembelajaran STEM-PBL memberikan pengaruh positif dan signifikan dalam meningkatkan kemampuan berpikir kritis siswa, yang terlihat dari perbedaan hasil yang signifikan antara kelas eksperimen dan kontrol serta nilai N-gain yang diperoleh.
PENGEMBANGAN MEDIA PEMBELAJARAN INTERAKTIF “SUSI: SUSUN SISI” PADA PEMBELAJARAN BANGUN DATAR Kiky Ardhianti; Axcelleosa Gloria Setiawan; Ina Febrianti; Ika Santia
Afore : Jurnal Pendidikan Matematika Vol 4 No 2 (2025): Afore : Jurnal Pendidikan Matematika
Publisher : Universitas Nias Raya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.57094/afore.v4i2.2912

Abstract

This study was motivated by the low level of understanding among elementary school students, particularly those in fifth grade, regarding the topic of plane figures in mathematics. This condition highlights the need for innovative learning media that can enhance students’ active participation in the learning process. The primary objective of this research is to develop an interactive learning medium called SUSI (Susun Sisi), specifically designed to facilitate students’ comprehension of plane figure concepts in an engaging and accessible manner. The research adopts a Research and Development (R&D) approach using the ADDIE model, which includes five systematic phases: analysis, design, development, implementation, and evaluation. The study involved one instructional media expert and 30 fifth-grade students as research subjects. The instruments employed consisted of expert validation sheets and student response questionnaires. Data were collected through expert validation and limited trials with students, then analyzed quantitatively. The results indicate that the SUSI learning media was rated valid by experts with a score of 84%, and was perceived as highly practical by students, achieving a practicality rate of 93.14%. Therefore, the SUSI media is deemed suitable for use in mathematics instruction and is recommended for classroom implementation by educators.
Model Pembelajaran Project Based Learning untuk Meningkatkan Ketuntasan Hasil Belajar Numerasi Siswa Kelas 1 SDN 2 Ngrawan Irdani, Laili Rahma; Santia, Ika
EDUKASIA Jurnal Pendidikan dan Pembelajaran Vol. 4 No. 2 (2023): Edukasia: Jurnal Pendidikan dan Pembelajaran
Publisher : LP. Ma'arif Janggan Magetan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62775/edukasia.v4i2.658

Abstract

This research was motivated by the low level of complete learning outcomes for grade 1 students at SD Negeri 2 Ngrawan regarding numeracy. The aim of this research is to improve the completeness of student learning outcomes. This type of research is classroom action research. Classroom action research was carried out in two cycles. The subjects of this research were class 1 students consisting of 12 students. Techniques for collecting data are tests, observation and documentation. The results of the research show that carrying out learning activities by applying the project based learning model can improve the completeness of students' numeracy learning outcomes. This is indicated by an increase in test results from each cycle. In cycle I, the percentage of student success reached 25%. Meanwhile, in cycle II, the percentage of student success reached 83%. The research can be said to be successful because the percentage of success reaches ≥80%. The conclusion of this research is that the project based learning model can improve the completeness of students' numeracy learning outcomes.
Co-Authors Aan Nurfahrudianto Ahmad Choirul Anam Akbar Sutawidjadja Am Ayu Kusuma Dewi Anam, Ahmad Choirul Anggraini, Novia Afriana Anjayani, Ririn Annisa Nur Kamilah Aprilia Dwi Handayani Aprilia Dwi Handayani Aprilia Dwi Handayani, Aprilia Dwi Aprillia Dwi Handayani Aprillia Dwi Handayani Ardiana Ardiana, Ardiana Arifah, Khusnul Axcelleosa Gloria Setiawan Bambang Agus Sulistyono Bambang Agus Sulistyono Candraningtyas, Tsatsabilla Diannira Darsono Darsono Darsono Darsono Darsono Darsono Dewi, Am Ayu Kusuma Dewi, Lusi Noviana Dian Devita Yohanie Yohanie Encil Puspitoningrum, Encil Fiantika, Feny Rita Hanny Cindy Prastica Hermawan, Tanto Hersiyati Palayukan Hima, Lina Ruhatul I Ketut Suada Ilham, Slamet Muhammad Imam Rofiki Ina Febrianti Irdani, Laili Rahma Jatmiko Jatmiko Jatmiko Jatmiko Jatmiko Jatmiko Jatmiko Jatmiko Kamilah, Assa'adatul Kariam, Betseba Khasanah, Hanizyah Quswatul Kiky Ardhianti Kristianti, Lina Laili Rahma Irdani Lina Rihatul Hilma lina Rihatul Hima Lina Rihatul Hima Lina Rihatul Hima, Lina Rihatul Lisa Deepsea Yofita Sani Mohammad, Nanda Nacaska Oktihsani Mulia, Parindra Mahardika Nanda Nacaska Oktihsani Mohammad Nuricahyati, Wendy Febia Pai’pinan, Matius Pangestu, Yorda Aditya Prasetyani, Tamara Jasmine Prastaningtyas, Efa wahyu Purnama, Sephia Rahayu Purwanto Purwanto Purwanto Purwanto Purwanto Putri Eka Sari PUTRI EKA SARI, PUTRI EKA Putri, Like Rizky Rochana, Siti Romadhoni, Alifvia Novita Putri Samidjo Samidjo, Samidjo Samijo, Samijo Setyaningrum, Dita Siti Rochana Slamet Muhammad Ilham Subanji Subanji Subanji Sudirman Sulistyo, Bagus Suryo Widodo Sutawidjadja, Akbar Tamara Jasmine Prasetyani Vivi Kusumaningrum Wahyu Henky Irawan Wida, Ovilia Nur Widyawati, Irma Yulian, Felix Yudha Yuni Katminingsih Yuni Katminingsih Zayyadi, Moh