Content of School Mathematics Textbook: A Praxeological Analysis on Indefinite Integral
Abstract
Indefinite integrals are a fundamental concept in calculus. This qualitative study aims to describe the content of school mathematics textbooks on indefinite integrals. The analysis used the concept of praxeology, which includes theory, technology, and techniques, based on the Reference Epistemological Model. The primary instrument in this research was the researcher, who used data from school mathematics textbooks, including two electronic textbooks used in Indonesia, one textbook from Singapore, and one from the Cambridge curriculum. The study results included a Reference Epistemological Model for indefinite integrals, used to compare textbook content and praxeological components. Praxeological analysis shows that the theoretical and technological components of Indonesian school mathematics textbooks are more complex than those from Singapore and the Cambridge curriculum. These differences are attributed to variations in the mathematics curricula of the three regions. Therefore, the Reference Epistemological Model can guide the development of instructional materials on indefinite integrals, taking into account the complexity differences among the textbooks.
Materi integral adalah salah satu konsep fundamental dalam kalkulus. Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk mendeskripsikan muatan pada buku teks matematika sekolah pada materi integral tak tentu. Analisis menggunakan konsep prakseologi yang meliputi teori, teknologi, dan teknik berdasarkan Referensi Model Epistemologi. Instrumen utama dalam penelitian ini adalah peneliti sendiri dengan menggunakan sumber data berupa buku teks matematika sekolah yaitu dua buku sekolah elektronik yang digunakan di Indonesia, satu buku teks matematika yang digunakan di Singapura, dan satu buku teks kurikulum Cambridge. Hasil penelitian berupa Referensi Model Epistemologi pada materi integral tak tentu yang digunakan untuk perbandingan buku dan organisasi prakseologi. Analisis prakseologi menunjukkan bahwa komponen teori, teknologi, dan teknik pada buku teks matematika sekolah dari Indonesia lebih kompleks dibandingkan dengan buku dari Singapura dan kurikulum Cambridge. Adanya perbedaan tersebut didasarkan pada muatan kurikulum yang berbeda diantara ketiganya. Dengan demikian, Referensi Model Epistemologi yang dihasilkan dapat dijadikan salah satu acuan dalam mengembangkan pembelajaran pada materi integral tak tentu, termasuk perbedaan kompleksitas antar kedua buku dapat menjadi referensi untuk digunakan sebagai sumber pembelajaran.
Keywords
Full Text:
PDFReferences
Amelia, S., & Yadrika, G. (2019). Analisis Kesalahan Siswa SMA dalam Menyelesaikan Soal Integral. Jurnal Ilmiah Dikdaya, 9(1), 124–131. https://doi.org/10.33087/dikdaya.v9i1.132
Aminah, & Kurniawati, K. R. A. (2018). Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Cerita Matematika Topik Pecahan Ditinjau Dari Gender. JTAM (Jurnal Teori Dan Aplikasi Matematika), 2(2), 118–122. https://doi.org/10.31764/jtam.v2i2.713
Blank, A. A. (1960). Remarks on the teaching of calculus in the secondary school. The Mathematics Teacher, 53(7), 537–539.
Bosch, M., & Gascon, J. (2006). Twenty-Five Years of Didactic Transposition. ICMI Bulletin, 58, 51–65.
Carlson, M., Oehrtman, M., & Engelke, N. (2010). The Precalculus Conecepts Assessment: A Tool for Assesing Students’ Reasoning Abilities and Understandings. Journal Cognition and Instruction, 28(2), 113–145. https://doi.org/10.1080/07370001003676587
Cheshier, S. R. (2006). The Field of Engineering Technology Studying Engineering Technology: A Blueprint for Success.
Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. In D. R & M. A (Eds.), Research in Didactique of Mathematics (pp. 131–167).
Confrey, J. (1981). Concepts, Processes and Mathematics Instruction. For the Learning of Mathematics, 2(1), 8–12.
Daimah, U. S., & Suparni. (2023). Pembelajaran Matematika pada Kurikulum Merdeka dalam Mempersiapkan Peserta Didik di Era Society 5.0. SEPREN: Journal of Mathematics Education and Applied, 4(2), 131–139. https://doi.org/10.36655/sepren.v4i1
Fadillah, A., Firmansyah, M. A., Syarifah, L. L., Rahardjo, S., & Erliani, T. P. (2019). Analisis Learning Obstacle pada Materi Integral. Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 1(6), 243–251. https://doi.org/10.26877/imajiner.v1i6.4802
Hong, D. S. (2024). How do students learn definite integrals? Exploring students’ learning opportunities. School Science and Mathematics, 124(1), 32–47. https://doi.org/10.1111/ssm.12605
Hoong, L. Y., Kin, H. W., & Pien, C. L. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1–18. http://math.nie.edu.sg/ame/matheduc/tme/tmeV16_1/TME16_1.pdf
Lisarani, V., Parta, I. N., & Chandra, T. D. (2018). A Comparative Analysis of the Tasks From the Selected Mathematics Textbooks of Singapore and Indonesia. Jurnal Pendidikan Sains Universitas Negeri Malang, 6(4), 94–99.
Mahayukti, G. A., & Dewi, P. K. (2021). Validity and Practicality of Problem-Based Integral Calculus Teaching Materials Assisted with Mathematical Software. In I. G. N. A. Suryaputra, G. Indrawan, & N. P. A. Pratiwi (Eds.), Proceedings of the 4th International Conference on Innovative Research Across Disciplines (ICIRAD 2021) (pp. 13–20). Atlantis Press SARL. https://doi.org/10.2991/assehr.k.211222.003
Malihatuddarojah, D., & Prahmana, R. C. I. (2019). ANALISIS KESALAHAN SISWA DALAM MENYELESAIKAN PERMASALAHAN OPERASI BENTUK ALJABAR. Jurnal Pendidikan Matematika, 13(1), 1–8. https://doi.org/10.22342/jpm.13.1.6668.1-8
Miles, M. B., & Huberman, A. M. (1994). Qualitative Data Analysis: An Expanded Sourcebook. Sage Publications Inc.
Muniarti, S., Roza, Y., & Maimunah. (2021). Analisis Keseuaian Materi Himpunan Buku Teks Siswa Matematika Kelas VII terhadap Kurikulum 2013. Mosharafa: Jurnal Pendidikan Matematika, 10(2), 177–188. https://doi.org/10.31980/mosharafa.v10i2.944
Novitasari, D. (2016). Pengaruh Penggunaan Multimedia Interaktif terhadap Kemampuan Pemahaman Konsep Matematis Siswa. Fibonacci: Jurnal Pendidikan Matematika Dan Matematika, 2(2), 8–18. https://doi.org/10.24853/fbc.2.2.8-18
Nurhikmah, S., & Febrian. (2016). Analisis Kesalahan Siswa dalam Menyelesaikan Permasalahan Integral Tak Tentu. Jurnal Tatsqif, 14(2), 218–237. https://doi.org/10.20414/jtq.v14i2.30
Oktaviyanti, R., & Supriani, Y. (2015). Utilizing Microsoft Mathematics in Teaching and Learning Calculus. Journal on Mathematics Education, 6(1), 63–76. https://doi.org/10.22342/jme.6.1.1902.63-76
Orton, A. (1985). When should we teach calculus? Mathematics in School, 14(2), 11–15.
Pramuditya, S. A., Sulaiman, H., & Wahyudin. (2019). Development of instructional media game education on integral and differential calculus. J. Phys.: Conf. Ser. 1280 042049. https://doi.org/10.1088/1742-6596/1280/4/042049
Putra, Z. H., & Witri, G. (2017). Anthropological Theory of the Didactic (ATD) A New Research Perspective on Didactic Mathematics in Indonesia. Jurnal Pigur, 2(1), 221–227.
Radmehr, F., & Drake, M. (2020). Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus. Education Sciences, 10(3), 55. https://doi.org/10.3390/educsci10030055
Rahmi, A., Hairi, A. P., Lukman, A., & Nasution, A. (2020). Analisis Kemampuan Bernalar Siswa SMA dalam Memaknai Permasalahan Integral Berbasis Konteks. Fibonacci: Jurnal Pendidikan Matematika Dan Matematika, 1(2), 1–9. https://doi.org/10.24114/jfi.v1i2.21910
Ramda, A. H., Kurnila, V. S., & Jundu, R. (2018). Implementasi Kurikulum 2013 pada Standar Isi Buku Teks Matematika Kelas VIII. Jurnal Eksakta Pendidikan (JEP), 2(2), 162–169. https://doi.org/10.24036/jep/vol2-iss2/231
Ramelan, M., & Wijaya, A. (2019). A Comparative Analysis of Indonesian and Singaporean Mathematics Textbooks from the Perspective of Mathematical Creativity: A Case Statistics and Probability. Journal of Physics: Conference Series, 1320(1), 012037. https://doi.org/10.1088/1742-6596/1320/1/012037
Rizqi, M. M., Wijayanti, D., & Basir, M. A. (2021). Analisis Buku Teks Matematika Materi Himpunan Menggunakan Model Prakseologi. Delta: Jurnal Ilmiah Pendidikan Matematika, 9(1), 57–76. https://doi.org/10.31941/delta.v9i1.1226
Robinson, W. B. (1970). The effects of two semesters of secondary school calculus on students’ first and second quarter calculus grades at the University of Utah. Journal for Research in Mathematics Education, 1(1), 57–60.
Takeuchi, H., & Shinno, Y. (2020). Comparing the Lower Secondary Textbooks of Japan and England: a Praxeological Analysis of Symmetry and Transformations in Geometry. International Journal of Science and Mathematics Education, 18(2), 791–810. https://doi.org/10.1007/s10763-019-09982-3
Tall, D. (1997). Functions and Calculus. In A. J. Bishop, K. Clements, C. Keitel, & J. Kilpatrick (Eds.), International Handbook of Mathematics Education (pp. 289–325). Kluwer.
Tall, D., & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity. Educational Studies in Matematics, 12, 151–169.
Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2017). Mathematics instruction, problems, challenges and opportunities: A case study in Manokwari Regency, Indonesia. World Transactions on Engineering and Technology Education, 15(3), 287–291.
Tasman, F., Hertog, J. Den, Zulkardi, Z., & Hartono, Y. (2011). Helping Students Acquainted with Multiplication in Rectangular Model. Journal on Mathematics Education, 2(2), 185–198. https://doi.org/10.22342/jme.2.2.747.185-198
Thompson, P. W., & Harel, G. (2021). Ideas foundational to calculus learning and their links to students’ difficulties. ZDM – Mathematics Education, 53(3), 507–519. https://doi.org/10.1007/s11858-021-01270-1
Usman, Hasbi, M., Bambang, R. M., & Mahathir. (2019). Deskripsi Kinerja dan Eksplorasi Kesulitan Belajar Siswa SMA dalam Menyelesaikan Masalah Kalkulus. Numeracy, 6(2), 218–228. https://doi.org/10.46244/numeracy.v6i2.478
Wijaya, A. (2019). The Relationships between Indonesian Fourth Graders’ Difficulties in Fractions and the Opportunity to Learn Fractions: A Snapshot of TIMSS Results. International Journal of Instruction, 10(4), 221–236. https://doi.org/10.12973/iji.2017.10413a
Wijayanti, D., & Winslow, C. (2017). Mathematical practice in texbooks analysis: Praxeological refence models, the case of proportion. REDIMAT, 6(3), 307–330. https://doi.org/10.17583/redimat.2017.2078
Woolcott, G. (2013). Mathematics Networks and Curriculum Concepts. In V. Steinle, L. Ball, & C. Bardini (Eds.), Procceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia. MERGA.
Yang, D.-C., & Sianturi, I. A. (2017). An Analysis of Singaporean versus Indonesian Textbooks Based on Trigonometry Content. EURASIA Journal of Mathematics, Science and Technology Education, 13(7), 3829–3848. https://doi.org/10.12973/eurasia.2017.00760a
Yuniarti, S., Hariyati Nur Indah Sari, T., & Khotimah, H. (2018). Utilizing GeoGebra in Application of Integral Module for High School Students in Balikpapan, East Borneo Indonesia. In Haviluddin, A. P. Wibawa, A. Pranolo, P. P. Widagdo, H. J. Setyadi, & M. Taruk (Eds.), Proceedings of the 2017 International Conference on Education and Technology (2017 ICEduTech) (Vol. 144, pp. 252–256). Atlantis Press. https://doi.org/10.2991/icedutech-17.2018.50
Zakaria, E., & Salleh, T. S. (2015). Using Technology in Learning Integral Calculus. Mediterranean Journal of Social Sciences, 6(5), 144–148. https://doi.org/10.5901/mjss.2015.v6n5s1p144
DOI: http://dx.doi.org/10.21043/jpmk.v7i1.25746
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Editorial and Administration Office:
Jurnal Pendidikan Matematika (Kudus)
Tadris Matematika, Tarbiyah Faculty, Institut Agama Islam Negeri Kudus
Jl. Conge Ngembalrejo Po Box 51, Kudus, Jawa Tengah, Indonesia, Kode Pos: 59322
Email: jpm@iainkudus.ac.id