ABSTRAKSI REFLEKTIF SISWA SEKOLAH MENENGAH PERTAMA PADA MATERI SEGIEMPAT DAN SEGITIGA

Keywords: Reflective Abstraction, Concept Understanding, Squares and triangles, APOS Theory

Abstract

The purpose of this study is to determine a person's ability to perform mental activities mechanically in associating new information received with previously owned information (reconstruction) which is a reflective abstraction. The process of reconstructing the concepts of quadrilaterals and triangles by students uses the mental mechanism approach of APOS theory (interiorization, encapsulation, de-encapsulation, coordination). The process can be known by observing students and analyzing the results of student work, starting with determining 1 class to be given a mathematical ability test. 29 students were present when the math ability test was given. The results of the mathematical ability test were analyzed and then found 2 students of different sexes with moderate ability. The first student is male and the second student is female, hereinafter referred to as the research subject, then the research subject is given the task of quadrilateral and triangle. The results showed that female students had done all stages of reflective abstraction in APOS theory. So, that these students were at the level of relational understanding. Meanwhile, male students only did several stages in the reflective abstraction stage on the APOS theory so that these students were included in the level of instrumental understanding.

References

Anam, A. C., Juniati, D., & Wijayanti, P. (2019). Understanding the Quadrilateral Concepts of Junior High School Students Based on APOS Theory in Terms of Differences in Cognitive Styles. In Mathematics, Informatics, Science, and Education International Conference (MISEIC 2019). (pp. 75–78). Atlantis Press.

Arnawa, I. M. (2009). Mengembangkan kemampuan mahasiswa dalam memvalidasi bukti pada aljabar abstrak melalui pembelajaran berdasarkan teori APOS. Jurnal Matematika Dan Sains, 14(2).

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). Apos theory: A framework for research and curriculum development in mathematics education. Apos Theory: A Framework for Research and Curriculum Development in Mathematics Education. https://doi.org/10.1007/9781461479666

Badraeni, N., Pamungkas, R. A., Hidayat, W., Rohaeti, E. E., & Wijaya, T. T. (2020). Analisis Kesulitan Siswa Berdasarkan Kemampuan Pemahaman Matematik Dalam Mengerjakan Soal Pada Materi Bangun Ruang Sisi Datar. Jurnal Cendekia : Jurnal Pendidikan Matematika, 4(1), 247–253.

Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2007). How can we assess mathematical understanding? In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2).

Haylock, D., & Cockburn, A. D. (2008). Understanding mathematics for young children: A guide for foundation stage and lower primary teachers. United Kingdom: United Kingdom: SAGE Publication.

Helwig, R., Anderson, L., & Tindal, G. (2001). Influence of elementary student gender on teachers’ perceptions of mathematics achievement. Journal of Educational Research, 95(2). https://doi.org/10.1080/00220670109596577

Jafar. (2013). Membangun Pemahaman yang Lengkap (Completely Understanding) dalam Pembelajaran Konsep Grup. In Konferensi Nasional Pendidikan Matematika (KNPM) V, Himpunan Matematika Indonesia (pp. 87–95).

Khoiri, M. (2014). Pemahaman Siswa Pada Konsep Segiempat Berdasarkan Teori van Hiele. Prosiding Seminar Nasional Matematika.

Mardiyah, U. R. A., & Budiarto, M. T. (2019). Abstraksi Reflektif dalam Mengonstruk Bangun Segiempat. MATHEdunesa, 8(3), 517–523.

Martínez-Planell, R., & Cruz Delgado, A. (2016). The unit circle approach to the construction of the sine and cosine functions and their inverses: An application of APOS theory. Journal of Mathematical Behavior, 43. https://doi.org/10.1016/j.jmathb.2016.06.002

Piaget, J. (2014). Studies in Reflecting Abstraction. London: London: Psychology Press. https://doi.org/10.4324/9781315800509

Rofiki, I., Anam, A. C., Sari, P. E., Irawan, W. H., & Santia, I. (2020). Students’ Mental Construction in Cube and Cuboid Concept Based on Mathematics Ability Differences. Al-Jabar: Jurnal Pendidikan Matematika, 11(1), 133–144.

Skemp, R. R. (2012). The Psychology of learning mathematics: Expanded American edition. The Psychology of Learning Mathematics: Expanded American Edition. https://doi.org/10.4324/9780203396391

Sutrisna, N., Pramuditya, S. A., Raharjo, J. F., & Setiyani, S. (2021). Kemampuan Abstraksi Reflektif Matematis Siswa pada Materi Bangun Ruang. Journal of Didactic Mathematics, 2(1), 26–32.

Weyer, R. S. (2010). APOS theory as a conceptualization for understanding mathematical learning. Summation: Mathematics and Computer Science Scholarship at Ripon, 3, 9–15.

Wijaya, T. T., Ying, Z., & Suan, L. (2020). Using Geogebra in Teaching Plane Vector. Journal of Innovative Mathematics Learning, 3(1), 15–23.

Wijaya, T. T., Dewi, N. S. S., Fauziah, I. R., & Afrilianto, M. (2018). Analisis Kemampuan Pemahaman Matematis Siswa Kelas IX Pada Materi Bangun Ruang. UNION: Jurnal Ilmiah Pendidikan Matematika, 6(1), 19–28. https://doi.org/10.30738/.v6i1.2076

Wulandari, E. D., Hidayanto, E., & Rahardi, R. (2019). Mathematical Representation of Cerebral Palsy Students in Constructing the Concept of Plane Geometry Based on APOS Theory. Ournal of Physics: Conference Series, 1227(1), 012018.

Published
2021-09-03
How to Cite
Anam, A. C. (2021). ABSTRAKSI REFLEKTIF SISWA SEKOLAH MENENGAH PERTAMA PADA MATERI SEGIEMPAT DAN SEGITIGA. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 3(2), 107-121. https://doi.org/10.35316/alifmatika.2021.v3i2.107-121
Abstract viewed = 65 times
FULL TEXT PDF downloaded = 50 times