Using Context to Learn Matrices Concepts Meaningfully

Yoppy Wahyu Purnomo, Nurlaela Rahmawati, Kadir Kadir


Mathematical concepts will be embedded if they can be imagined and appear in everyday life. Therefore, this study aims to develop Local Instructional Theory in context-based matrix learning. Design research is adopted to achieve these objectives. The design research has three stages, namely, preliminary experiment, teaching experiment, and retrospective analysis. The study was conducted at a high school on the outskirts of the capital, involving 39 students of class XI. The data was collected employing tests, observation, interviews, worksheets, and documentation in the form of video recordings, photos, and student journals. The results indicated that students were able to construct their concept of matrices through the context of a favorite or a hobby as a starting point in compiling and defining a matrix, and continued with the matrix multiplication concept (matrix scalar multiplication as repeated addition; terms and products of two matrices).


Design research; local instructional theory; learning trajectory; realistic mathematics education

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Andrews-Larson, C., Wawro, M., & Zandieh, M. (2017). A hypothetical learning trajectory for conceptualizing matrices as linear transformations. International Journal of Mathematical Education in Science and Technology, 48(6), 809-829.

Arsaythamby, V., & Zubainur, C. M. (2014). How a Realistic Mathematics Educational Approach Affect Students Activities in Primary School. Procedia-Social and Behavioral Science, 159, 309-313.

Aygor, N., & Burhanzade, H. (2014). The Comparative Analyzes of the Students Performance about Matrix in Student Selection Exam (ÖSS) and the Approved Lecture Books of Ministry for the National Education (MEB). Procedia - Social and Behavioral Sciences.

Cárcamo, A., Fuentealba, C., & Garzón, D. (2019). Local Instruction Theories at the University Level: An Example in a Linear Algebra Course. Eurasia Journal of Mathematics, Science and Technology Education, 15(12).

Carlson, D. (1993). Teaching Linear Algebra: Must the Fog Always Roll in? The College Mathematics Journal, 24(1), 29-40.

Gravemeijer, K. (2004). Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105-128.

Hendroanto, A., Budayasa, I. K., Galen, F. Van, & Eerde, D. Van. (2015). Supporting Students Spatial Ability in Understanding Three-Dimensional Representations. Universitas Negeri Surabaya.

Hidayat, R., & Iksan, Z. H. (2015). The Effect of Realistic Mathematic Education on Students Conceptual Understanding of Linear Progamming. Creative Education.

Horton, R. M., Wiegert, E. M., & Marshall, J. C. (2008). Squaring Matrices: Connecting Mathematics and Science. The Mathematics Teacher, 102(2), 102-106.

Kadir. (2004). Efektivitas Strategi Peta Konsep dalam Pembelajaran Sains dan Matematika (Meta-Analisis Penelitian Eksperimen Psikologi dan Pendidikan). Jurnal Pendidikan Dan Kebudayaan, 10(051), 761-781.

Kusuma, N. F., Subanti, S., & Usodo, B. (2018). Students misconception on equal sign. In Journal of Physics: Conference Series (Vol. 1008). Institute of Physics Publishing.

Lesmana, H., Yusmin, E., & Sayu, S. (2015). Pendeskripsian Pemahaman Konseptual Siswa Menyelesaikan Soal-Soal Operasi Matriks Kelas X SMKN 3 Pontianak. Jurnal Pendidikan Dan Pembelajaran, IV(12), 1-10.

Manulang, S. (2017). Matematika SMA Kelas X. (D. Agung Lukito, Ed.) (Revisi). Jakarta: Kementrian Pendidikan dan Kebudayaan.

Parta, K. F. dan I. N. (2016). Pengembangan Lembar Kerja Siswa Materi Perkalian Matriks Bercirikan Penemuan Terbimbing untuk Siswa SMK Kelas X. Jurnal Pendidikan Matematika, I(9), 1721-1729.

Prahmana, R. C. I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar). Depok: PT Rajagrafindo Perkasa.

Pramudiani, P., Oktafiani, A. F., Aziz, T. A., & Purnomo, Y. W. (2017). Enhancing Conceptual Knowledge about Shape through Realistic Mathematics Education. Jurnal Inovasi Pendidikan Dasar, 3(1), 31-38.

Purnomo, Y. W., Kowiyah, Alyani, F., & Assiti, S. S. (2014). Assessing number sense performance of Indonesian elementary school students. International Education Studies, 7(8), 74-84.

Purnomo, Y. W., Widowati, C., & Ulfah, S. (2019). Incomprehension of the Indonesian Elementary School Students on Fraction Division Problem. Infinity Journal, 8(1), 57-74.

Putrawangsa, S. (2018). Desain Pembelajaran Design Research sebagai Pendekatan Desain Pembelajaran. Mataram: CV. Reka Karya Amerta (Rekarta).

Rahmawati, N., & Purnomo, Y. W. (2020). Analysis of Student Learning Barriers in Solving Context Problems Related to the Matrix. In The 2nd International Conference of Education on Science, Technology, Engineering, and Mathematics (ICE-STEM 2020) (pp. 56-61). Jakarta: Universitas Muhammadiyah Prof. Dr. HAMKA. Retrieved from

Revina, S. (2017). Influence of Culture on the Adaptation of Realistic Mathematics Education in Indonesia. University of Hong Kong.

Suastika, John, T., & Utami, T. (2015). Penelusuran Miskonsepsi Mahasiswa tentang Matriks Menggunakan Certainty of Response Index. Prosiding Seminar Nasional Fisika SNF 2015, IV(Oktober).

Van Den Heuvel-Panhuizen, M. (2003). The Didactical Use of Models in Realistic Mathematics Education: An Example from a Longitudinal Trajectory on Percentage. Educational Studies in Mathematics, 54(1), 9-35. Retrieved from

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 521-525). Dordrecht: Springer Netherlands.

Webb, D. C., Kooij, H. Van Der, & Geist, M. R. (2011). Design Research in the Netherlands: Introducing Logarithms Using Realistic Mathematics Education. Journal of Mathematics Education at Teacher College, 2, 47-52.

Wijaya, A. (2008). Design Research in Mathematics Education: Indonesian Traditional Games as Means to Support Second Graders Learning of Linear Measurement. Universiteit Utrecht.

Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Teachers teaching practices and beliefs regarding context-based tasks and their relation with students difficulties in solving these tasks. Mathematics Education Research Journal, 27(4), 637-662.

Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning. Journal of Mathematical Behavior, 29(2), 57-75.



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International Journal on Emerging Mathematics Education
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