Using Context to Learn Matrices Concepts Meaningfully
DOI:
https://doi.org/10.12928/ijeme.v5i2.19456Keywords:
Design research, local instructional theory, learning trajectory, realistic mathematics educationAbstract
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).
References
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. https://doi.org/10.1080/0020739X.2016.1276225
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. https://doi.org/10.1016/j.sbspro.2014.12.378
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. https://doi.org/10.1016/j.sbspro.2014.05.342
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). https://doi.org/10.29333/ejmste/108648
Carlson, D. (1993). Teaching Linear Algebra: Must the Fog Always Roll in? The College Mathematics Journal, 24(1), 29-40. https://doi.org/10.1080/07468342.1993.11973503
Gravemeijer, K. (2004). Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105-128. https://doi.org/10.1207/s15327833mtl0602_3
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. https://doi.org/10.4236/ce.2015.622251
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. https://doi.org/10.1088/1742-6596/1008/1/012058
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. https://doi.org/10.5539/ies.v7n8p74
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. https://doi.org/10.22460/infinity.v8i1.p57-74
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 https://proceedings.uhamka.ac.id/index.php/ie/article/view/249/227
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 http://www.jstor.org/stable/3483213
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. https://doi.org/10.1007/978-94-007-4978-8_170
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. https://doi.org/10.1007/s13394-015-0157-8
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. https://doi.org/10.1016/j.jmathb.2010.01.001
Downloads
Published
How to Cite
Issue
Section
License
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read the International Journal on Emerging Mathematics Education (IJEME) Author Guidelines at http://journal.uad.ac.id/index.php/IJEME/about/submissions#authorGuidelines
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities, tacitly or explicitly, of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with the International Journal on Emerging Mathematics Education (IJEME) agree to the following terms:
- Authors retain copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi-BerbagiSerupa 4.0 Internasional.
