Mathematics Learning with Concrete Manipulatives among Second-Grade Students at SDN Tridadi: A Perspective on the Concrete Operational Stage

Eviska Loviandari; Banun Havifah Cahyo Khosiyono; Akbar Al Masjid; Ana Fitrotun Nisa; Titik Muti'ah

doi:10.62159/isej.v7i3.2647

Eviska Loviandari Sarjanawiyata Tamansiswa University
Banun Havifah Cahyo Khosiyono Sarjanawiyata Tamansiswa University
Akbar Al Masjid Sarjanawiyata Tamansiswa University
Ana Fitrotun Nisa Sarjanawiyata Tamansiswa University
Titik Muti'ah Sarjanawiyata Tamansiswa University

DOI: https://doi.org/10.62159/isej.v7i3.2647

Keywords: Cognitive Development, Concrete Manipulatives, Concrete Operational Stage, Mathematics Learning, Second-Grade Students

Abstract

Mathematics learning in elementary schools needs to consider students’ cognitive development, particularly among second-grade students who are beginning to develop logical thinking while still relying on concrete experiences. Although Jean Piaget’s theory of cognitive development has been widely discussed in relation to elementary mathematics education, empirical evidence of how characteristics of the concrete operational stage are manifested in actual classroom learning remains limited. This study aims to examine the characteristics of the concrete operational stage in mathematics learning among second-grade students and to explore the role of concrete manipulatives in supporting their understanding of mathematical concepts. A descriptive qualitative approach was employed involving 15 second-grade students at SDN Tridadi selected through purposive sampling. Data were collected through structured classroom observations and clinical interviews, while source and method triangulation were used to strengthen the credibility of the findings. The data were analyzed using an interactive qualitative analysis model consisting of data reduction, descriptive data presentation, and conclusion drawing. The findings indicate that the students demonstrated characteristics of the early concrete operational stage. Classification and number conservation were observed during mathematics learning, while reversibility was still developing and required support through concrete objects. The use of concrete manipulatives provided opportunities for students to directly manipulate, compare, and represent mathematical quantities when solving addition and subtraction problems. Clinical interviews further showed that students’ reasoning was closely related to their ability to visualize and manipulate concrete quantities. The study concludes that empirical observation of second-grade students provides important insight into the manifestation of the concrete operational stage in actual mathematics learning. Mathematics instruction that considers students’ cognitive developmental characteristics and incorporates concrete manipulatives can provide learning experiences that connect mathematical concepts with concrete and observable experiences.

Downloads

Download data is not yet available.

References

Agustina, N. S., Yulianto, S., Semarang, U. N., Tujuan, A., Sumowono, S. D. N., Semarang, K., Sumowono, S. D. N., Statistics, I. B. M. S., Moments, P. P., Kunci, K., Konkret, M., Operasi, K., Dasar, H., Belajar, M., & Matematika, P. (2026). Pengaruh Penggunaan Media Konkret terhadap Kemampuan Operasi Hitung Dasar dan Motivasi Belajar Matematika Siswa Kelas IV SD. 21(1), 563–572. https://doi.org/10.31603/paedagogie.v21i1.16196

Anditiasari, N., & Dewi, N. R. (2021). Analisis Teori Perkembangan Kognitif Piaget Pada Anak Usia 11 Tahun Di Brebes Piaget ’ s Theory of Cognitive Development Analysis in 11 Year Olds in Brebes. 6(1), 97–108.

Apriyanti, E., & Fauzi, A. (2023). Model Pembelajaran Realistic Mathematics Education Dalam Meningkatkan Pemahaman Konsep Matematika Siswa Sekolah Dasar. 9(4), 1978–1986. https://doi.org/10.31949/educatio.v9i4.5940

Ayuni, R., & Puspita, R. D. (n.d.). IMPLEMENTASI TEORI BELAJAR KOGNITIF MELALUI MEDIA.

Diana, F., Udin, T., Maufur, S., Syekh, I., & Cirebon, N. (2022). PERAN TEORI BELAJAR KOGNITIF TERHADAP PEMAHAMAN BELAJAR SISWA MI / SD A . PENDAHULUAN Karakteristik kognitif siswa SD sangat penting untuk dipahami. 03(03), 279–299.

Dwijantie, J. S., & Nurishlah, L. (2025). Strategi Perencanaan Pembelajaran untuk Menumbuhkan Epistemic Curiosity Anak Usia Dini. 8(2), 898–908. https://doi.org/10.31004/aulad.v8i2.1298

Fadila, A. R., Sunan, U. I. N., & Surabaya, A. (2026). Urgensi Pemahaman Karakteristik Belajar Peserta Didik dalam Mewujudkan Pembelajaran yang Efektif. 4(3), 515–528.

Firma, A., & Putri, H. (2024). Analisis Metakognisi Peserta Didik Kelas V Sekolah Dasar dalam Memecahkan Masalah Matematika Bangun Ruang dalam Perspektif Teori Perkembangan Kognitif Jean Piaget. 33(01), 26–39.

Hadi, S., Sa, L., Yani, J., & Wulandari, A. M. (2025). Rekayasa Jean Piaget : Teori Perkembangan Kognitif dalam Konsepsi Anak di Usia Sekolah Dasar. 9(1), 158–168.

Jusniani, N., Setiawan, E., Terbuka, U., Suryakancana, U., & Pendahuluan, A. (2023). PEMBELAJARAN MATEMATIKA BERBASIS STEAM. 11, 590–605.

Kartika, K., Darmayanti, H., Islam, U., Raden, N., Palembang, F., & Palembang, K. (2023). Proses Pembelajaran dan Perkembangan Kognisi Menurut Perspektif Jean Piaget. 1(1), 39–54.

Magister, P., Dasar, P., & Surakarta, U. M. (2021). Implementasi Teori Perkembangan Kognitif Jean Piaget dalam Pembelajaran Matematika di Sekolah Dasar. 3(2), 153–162.

Muslimah, A., Wahyuni, T., & Agusdianita, N. (2025). Strategi Pembelajaran Keliling Balok Menggunakan Media Konkret di Sekolah Dasar Negeri 54 Lebong Bengkulu. 04(01), 1873–1883.

Nabilah, A., Amalia, F., Angreini, H. S., Rahmi, M., Zulkarnain, I., Fajriah, N., Mangkurat, U. L., Logis, B., & Kreatif, B. (2024). Pendekatan dalam pembelajaran matematika yang dapat mengembangkan kemampuan berpikir logis dan kreatif pada siswa sekolah dasar. 2.

Nafila, V. (2026). Enhancing Numeracy Literacy of Deaf Students : Developing Problem-Based Learning with Realistic Mathematics Education Assisted By E-Comic. 18(20), 984–1000. https://doi.org/10.35445/alishlah.v18i1.9093

Nurjihan, D. S., & Bunawan, W. (2025). Jurnal Pendidikan MIPA. 15(September), 1120–1127.

Pendidikan, J., Digital, P., Belajar, T., Jean, K., Tahap, P., Konkret, O., Kelas, S., Sanjaya, I. G. A., Suarni, N. K., & Margunayasa, I. G. (2024). Meningkatkan Hasil Belajar Siswa SD Melalui Penggunaan Media. 5(1).

Pendidikan, J., & Vol, M. (2026). HIPOTENUSA : Jurnal Pendidikan Matematika Vol. 1, No. 2, Mei 2026 ISSN 3124-825X https://sfa-alfatih-press.com/HIPOTENUSA. 1(2).

Prameswari, T. I., Jupisa, R., & Iryani, E. (2025). Penerapan Teori Kognitivisme dalam Meningkatkan Efektivitas Proses Pembelajaran di Sekolah. 4(2), 14160–14168.

Qonita, A. (2025). Penggunaan Media Konkret dalam Meningkatkan Hasil Belajar Siswa Kelas II Pada Materi Pecahan di SDIT Al Qonita. 9, 3–7.

Rahmadani, A., Ulkhaira, N., Syafitri, N., & Azhari, Y. (2025). Implikasi Perkembangan Peserta Didik dalam Pembelajaran di Kelas V Sekolah Dasar. 5.

Rahmadewi, S. (2025). DIAGNOSTIC ASSESSMENT AS THE FOUNDATION FOR ADAPTIVE AND DIFFERENTIATED LEARNING TRANSITION TO THE. 24(2). https://doi.org/10.20414/tsaqafah.v24i2.14168

Rizqiyati, I., Wardani, A., & Rizqi, Z. (2023). Penelitian Teori Perkembangan Piaget Tahap Operasional Konkret Pada Usia 11-12 Tahun Terhadap Hukum Kekekalan Volume. 6, 634–638.

Rukayah, S., & Fuady, A. (2026). Rekontruksi Makna Belajar Transformasi Geometri Berbasis Perspektif Fenomenologi Siswa. 8(3), 114–131.

Rusdiana (2025). (2025). DIMENSI KOGNITIF DAN SOSIAL EMOSIONAL DALAM PSIKOLOGI PERKEMBANGAN ANAK ( USIA 0-7 TAHUN ): DIMENSI KOGNITIF DAN SOSIAL EMOSIONAL DALAM PSIKOLOGI PERKEMBANGAN ANAK ( USIA 0-7 TAHUN ): 3(6).

Sagita, D. K., Ermawati, D., & Riswari, L. A. (2023). Kemampuan Pemecahan Masalah Matematis Siswa Sekolah Dasar. 9(2), 431–439. https://doi.org/10.31949/educatio.v9i2.4609

Saputra, A., & Suryandi, L. (n.d.). Perkembangan kognitif anak usia dini dalam perspektif vygotsky dan implikasinya dalam pembelajaran. 3(2).

Saputra, H. (2024). Perkembangan Berpikir Matematis Pada Anak Usia Sekolah Dasar. 6(2), 53–64.

Siregar, A. (2023). Penjumlahan , Pengurangan , Pembagian , Perkalian Pada Operasi Bilangan Bulat. 3, 6248–6259.

Yulia, P., Lova, F. F., Studi, P., Matematika, T., Islam, U., Imam, N., Padang, B., Matematika, J. T., Peraga, A., & Konsep, P. (2025). META-ANALISIS PENGARUH PENGGUNAAN ALAT. 8, 1077–1085.