Proof -Based Learning Design Using APOS Theory on Triangle Inequality Theorem Material
DOI:
https://doi.org/10.37303/jelmar.v4i2.163Keywords:
learning trajectory, proof, triangle inequality theorem, APOS theoryAbstract
This research aims to produce a series of activities that can support evidence-based learning on the material of the Triangle Inequality Theorem. The research method used was design research type validation study and involved 22 4th semester students of the Mathematics Education study program at PGRI University Palembang. The research was conducted through 3 stages, namely preliminary design, design experiment and restropective analysis. Data collection was carried out using observation techniques, documentation and activity sheets. The research data were analyzed qualitatively, namely comparing the results of observations during the learning process with the HLT that had been designed. The results showed that the designed activities can support evidence-based learning for Triangle Inequality Theorem material.
Downloads
References
Arnawa, I. M., Nita, S., Yanita, Ginting, B., & Yerizon. (2020). Improvement of a positive attitude toward abstract algebra through the APOS theory approach. Journal of Physics: Conference Series, 1503, Article 012008. https://doi.org/10.1088/1742-6596/1503/1/012008
Arnawa, I. M., Yerizon, & Nita, S. (2019). Improvement of students' level of proof ability in abstract algebra through APOS theory approach. International Journal of Scientific & Technology Research, 8(7), 128–131.
Borji, V., Alamolhodaei, H., & Radmehr, F. (2018). Application of the APOS-ACE theory to improve students' graphical understanding of derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(7), 2947–2967.
Darari, M. B., Panjaitan, M., Febrian, D., & Harahap, F. (2021). Efektivitas penerapan laboratorium virtual pada mata kuliah matematika dasar di Fakultas Matematika dan Ilmu Pengetahuan Alam Unimed. AXIOM: Jurnal Pendidikan dan Matematika, 10(2), 210–220. https://doi.org/10.30821/axiom.v10i2.10437
Darmadi. (2009). Spektrum hasil belajar analisis real mahasiswa Program Studi Pendidikan Matematika IKIP PGRI Madiun. Dalam Prosiding Seminar Nasional Matematika dan Pendidikan Matematika (hlm. 247–251). Universitas Negeri Yogyakarta.
Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. Dalam D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 275–282). Springer.
Eerde, D. van. (2013). Design research: Looking into the heart of mathematics education. Dalam Proceedings of the 1st SEA-DR Conference (hlm. 1–11). Sriwijaya University.
Erawati, N. K. (2018a). Kualitas pengajaran dosen dan motivasi belajar mahasiswa dengan siklus ACE APOS. EMASAINS, 7(2).
Erawati, N. K. (2018b). Penerapan siklus ACE APOS pada mata kuliah analisis riil. EMASAINS, 7(1), 22–28.
Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.
Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. Dalam J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 17–51). Routledge.
Gunawan, H. (2009). Pengantar analisis real. ITB Press.
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5–23.
Hartati, S. J. (2014). Design of learning model of logic and algorithms based on APOS theory. International Journal of Evaluation and Research in Education (IJERE), 3(2), 109–118.
Haswati, D., Bilda, W., & Nopitasari. (2019). Pengembangan lembar aktivitas geometri analitik datar berbasis pendekatan saintifik. Dalam Prosiding Diskusi Panel Nasional Pendidikan Matematika (hlm. 113–118). Universitas Indraprasta PGRI.
Hidayat, W., & Aripin, U. (2020). Identifikasi kesalahan jawaban mahasiswa pada mata kuliah trigonometri berdasarkan dimensi pengetahuan Krathwohl. JNPM (Jurnal Nasional Pendidikan Matematika), 4(1), 142–153. https://doi.org/10.33603/jnpm.v4i1.3316
Isnani, Waluya, S. B., Rochmad, Dwijanto, & Asih, T. (2021). Analisis miskonsepsi mahasiswa pada mata kuliah analisis real. Dalam PRISMA: Prosiding Seminar Nasional Matematika (hlm. 235–238). Universitas Negeri Semarang.
Kartika, E. D., & Yazidah, N. I. (2019). Analisis kemampuan pembuktian matematis pada mata kuliah analisis real berdasarkan adversity quotient. PRIMA: Jurnal Pendidikan Matematika, 3(2), 152–157.
Kholifa, I., Suswanti, & Nuryadi. (2019). Pengembangan laboratorium matematika virtual dengan software Appy Pie untuk meningkatkan kemampuan komunikasi dan adaptive e-learning. Jurnal Mercumatika: Jurnal Penelitian Matematika dan Pendidikan Matematika, 3(2), 104–113. https://doi.org/10.26486/jm.v3i2.876
Kocijancic, S., & O'Sullivan, C. (2004). Real or virtual laboratories in science teaching: Is this actually a dilemma? Informatics in Education, 3(2), 239–250. https://doi.org/10.15388/infedu.2004.17
Laamena, C. M., Nusantara, T., & Muksar, M. (2018). International Electronic Journal of Mathematics Education, 13(3), 185–198.
Melhuish, K., Fukawa-Connelly, T., Dawkins, P. C., Woods, C., & Weber, K. (2022). Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn. Journal of Mathematical Behavior, 67, Article 100986. https://doi.org/10.1016/j.jmathb.2022.100986
Narain, P., & Stylianides, A. J. (2020). Demystifying proofs through structured interaction: A case study. https://doi.org/10.17863/CAM.54180
Ningsih, Y. L., Darmawijoyo, & Hartono, Y. (2015). Pengembangan lembar aktivitas mahasiswa topik turunan berdasarkan teori APOS. Jurnal Pendidikan Matematika dan Sains, 3(1), 10–22.
Nurizzati, Y. (2016). Efektivitas pembelajaran statistika dasar dengan metode praktikum berbasis pendidikan karakter Islami di Jurusan Tadris Ilmu Pengetahuan Sosial IAIN Syekh Nurjati Cirebon. Holistik: Journal for Islamic Social Sciences, 1(1), 36–48.
Nurrahmah, A., Kartono, Zaenuri, & Isnarto. (2022). Tinjauan pustaka sistematis: Abstraksi matematis mahasiswa pada pembelajaran matematika berdasarkan teori APOS. Dalam Prosiding Seminar Nasional Pascasarjana Universitas Negeri Semarang (hlm. 120–129).
Plomp, T. (2013). Educational design research: An introduction. Dalam T. Plomp & N. Nieveen (Eds.), Educational design research. SLO.
Prahmana, R. C. I. (2017). Design research: Teori dan implementasinya. Rajawali Pers.
Prastowo, A. (2015). Panduan kreatif membuat bahan ajar inovatif. Diva Press.
Rangkuti, A. N., & Siregar, A. I. (2019). Lintasan belajar teorema Pythagoras dengan pendekatan pendidikan matematika realistik. Logaritma: Jurnal Ilmu-ilmu Pendidikan dan Sains, 7(2), 149–162.
Reid, D. (2001). Proof, proofs, proving and probing: Research related to proof. Dalam Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education.
Risnanosanti, Prasetiyo, A. A., & Syofiana, M. (2023). Hypothetical learning trajectory penalaran matematis pada materi statistika SMP. Indiktika: Jurnal Inovasi Pendidikan Matematika, 5(2), 201–210. https://doi.org/10.31851/indiktika.v5i2.11743
Saftari, M., & Sariman. (2021). Lembar aktivitas mahasiswa materi integral jumlah Riemann berdasarkan teori aksi, proses, objek, skema (APOS). Inomatika, 3(2), 152–163. https://doi.org/10.35438/inomatika.v3i2.200
Sagala, S. (2014). Konsep dan makna pembelajaran. Alfabeta.
Septiati, E. (2021). Kemampuan mahasiswa dalam mengonstruksi bukti matematis pada mata kuliah analisis real. Indiktika: Jurnal Inovasi Pendidikan Matematika, 4(1), 64–72. https://doi.org/10.31851/indiktika.v4i1.6761
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.
Slavin, R. E. (2008). Psikologi pendidikan: Teori dan praktik (8th ed.). PT Indeks.
Supriadi, A. (2021). Pemahaman mahasiswa tentang integral lipat dua berdasarkan teori APOS. Indiktika: Jurnal Inovasi Pendidikan Matematika, 4(1), 55–63. https://doi.org/10.31851/indiktika.v4i1.6606
Syamsuri, & Marethi, I. (2018). APOS analysis on cognitive process in mathematical proving activities. International Journal on Teaching and Learning Mathematics, 1–12.
Wijaya, A., Elmaini, & Doorman, M. (2021). A learning trajectory for probability: A case of game-based learning. Journal on Mathematics Education, 12(1), 1–16.
Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2007). Didactic effectiveness of mathematical definitions: The case of the absolute value. International Electronic Journal of Mathematics Education, 2(2), 72–90.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
