Main Article Content


This study aims to describe the achievement of the ability of students' reflective abstraction in solving Linear Algebra problems and the relationship with prerequisite knowledge. The important of this research because the characteristic of Linear Algebra requiring reflectif abstraction skill that must be support by the prerequisite knowledge. The reflective abstraction abilities studied in this study are level, i.e.1) recognition,2) representation, 3) structural abstraction, and 4) structural awareness. These stages are adjusted to Polya's problem solving stages, namely: understanding the problem, devising a plan, carrying out the plan, and looking back. This type of research is descriptive-quantitative. The subjects of this study were students of the Mathematics Education Study Program, Faculty of Tarbiyah and Teacher Training of UIN Sunan Gunung Djati Bandung Indonesia. Collecting data through tests and interviews, data were analyzed with percentage and the pearson product-moment correlation.The results showed that the achievement level  consisiting of ) recognition,2) representation, 3) structural abstraction, and 4) structural awareness of the students’ reflective abstraction abilities on linear algebra problem solving are very good, this can be seen from the percentage achieved at stages of the recognition,the representation,the structural abstraction, and the structural awareness which is associated with Polya problem solving measures above an average of 73,31% (moderat category); there are relationship between students' reflective abstraction abilities and their prerequisite knowledge; and prerequisite knowledge influences the students’reflective abstraction abilities.


Prerequisite Knowledge Problem Solving Reflective Abstraction

Article Details


  1. Ausubel, D. P., Novak, J. D., & Hanesian, H. (1968). Educational psychology: A cognitive view. Holt, Rinehart and Winston.

  2. Bodner, G. M. (1986). Constructivism: A theory of knowledge. Journal of Chemical Education, 63(10), 873. doi:10.1021/ed063p873

  3. Cifarelli, V. V. (1990). The role of abstraction as a learning process in mathematical problem-solving. Purdue University.

  4. Dick, W., Carey, L., & Carey, J. (2006). The systematic design of instruction (6th Editio). Allyn and Bacon.

  5. Dorier, J. L. (2002). Teaching linear algebra at university. Proceedings of the International Congress of Mathematicians, August 20-28, 2002, 1, 875-884.

  6. Dorier, J. L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In The teaching and learning of mathematics at university level (pp. 255–273). Springer. doi:10.1007/0-306-47231-7_24

  7. Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86–95. doi:10.1007/BF02655883

  8. Fuady, A., & Rahardjo, S. (2019). Abstraction reflective student in problem solving of Mathematics based cognitive style. International Journal of Humanities and Innovation (IJHI), 2(4), 103–107. doi:10.33750/ijhi.v2i4.50

  9. Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra. Educational Studies in Mathematics, 36(3), 219–245. doi:10.1023/A:1003473509628

  10. Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40. doi:10.1007/BF03217454

  11. Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In On the teaching of linear algebra (pp. 191–207). Springer. doi:10.1007/0-306-47224-4_7

  12. Irfan, A., & Anzora, A. (2017). Analisis Pemahaman Konsep Aljabar Mahasiswa Calon Guru melalui Peta Konsep pada Program Studi Pendidikan Matematika Universitas Abulyatama Aceh. Jurnal Dedikasi Pendidikan, 1(1), 1–10.

  13. Kariadinata, R. (2019). Pengantar Aljabar Linear disertai Peta Konsep. Pustaka Setia.

  14. Kariadinata, R., Sugilar, H., Farlina, E., & Kurahman, O. T. (2017). The Sociomathematical Norms in Linear Algebra Lecture.

  15. Mitchelmore, M., & White, P. (2004). Abstraction in Mathematics and Mathematics Learning. International Group for the Psychology of Mathematics Education.

  16. Mufidah, A., Sulasteri, S., Majid, A. F., & Mattoliang, L. A. (2019). Analisis Pemahaman Konsep Aljabar pada Mata Kuliah Aljabar Linear Elementer. Al Asma: Journal of Islamic Education, 1(1), 42–52.

  17. Nur, M. (2000). Strategi-strategi belajar. Universitas Negeri Surabaya.

  18. Panjaitan, B. (2009). Level-Level Abstraksi Reflektif dalam Pemecahan Masalah Matematika.

  19. Polya, G. (1973). How to solve it second edition. Princeton University Press.

  20. Polya, G. (1985). How to Solve it a New Aspect of Mathematical Method (United State of America. Pricenton University Press.

  21. Riyanto, H. Y. (2014). Paradigma Baru pembelajaran: Sebagai referensi bagi pendidik dalam Implementasi Pembelajaran yang Efektif dan berkualitas. Prenada Media.

  22. Schwarz, B. B., Hershkowitz, R., & Prusak, N. (2010). Argumentation and mathematics. Educational Dialogues: Understanding and Promoting Productive Interaction, 115, 141.

  23. Stewart, S., & Thomas, M. O. (2010). Student learning of basis, span and linear independence in linear algebra. International Journal of Mathematical Education in Science and Technology, 41(2), 173–188. doi:10.1080/00207390903399620

  24. Sugilar, H., Kariadinata, R., & Sobarningsih, N. (2019). Spektrum Symbol dan Structure Sense Matematika Siswa Madrasah Tsanawiyah. Kalamatika: Jurnal Pendidikan Matematika, 4(1), 37–48. doi:10.22236/KALAMATIKA.vol4no1.2019pp37-48

  25. Suryaningsih, Y. (2017). Korelasi Hasil Belajar Mata Kuliah Aljabar Linear Elementer Mahasiswa Program Studi Pendidikan Matematika FKIP Universitas Lambung Mangkurat Berdasarkan Mata Kuliah Prasyarat. EDU-MAT: Jurnal Pendidikan Matematika, 4(2), 118-125. doi:10.20527/edumat.v4i2.2569

  26. Tall, D. (1991). Advanced mathematical thinking (Vol. 11). Springer Science & Business Media.

  27. Tall, D. (1994). A versatile theory of visualisation and symbolisation in mathematics. Invited plenary lecture at the CIAEM Conference, 1, 15-26.

  28. Welder, R. M. (2006). Prerequisite knowledge for the learning of algebra. Conference on Statistics, Mathematics and Related Fields, Honolulu, Hawaii, 1-26.

  29. Wiryanto, W. (2014). Level-level Abstraksi Dalam Pemecahan Masalah Matematika. Jurnal Pendidikan Teknik Elektro, 3(3), 569–578.