Keywords
Generalization, mathematical generalization ability, realistic mathematics approach
Document Type
Article
Abstract
Generalization ability need to be encouraged in learning mathematics, students with generalization abilities can expand and transfer knowledge to practical knowledge. This research aims to develop learning material based on realistic mathematisc approach that oriented to generalization ability. The learning materials'developed is lesson plans and student worksheets. This is research and development with an ADDIE model. The instruments used in this study were the evaluation sheets, response questionnaire for teachers and students and tests of mathematical generalization ability. The data analysis technique used was descriptive qualitative and quantitative. The design of the learning materials focuses on aspects of the mathematical generalization ability of high school students by presenting real problems. Student activities are designed to solve real issues related to pattern analysis, focus on student contributions to find conjectures, and design interactions so students can proceed to the abstraction stage using concept linkages. So students can make conclusions regarding the given concept in response to such issues. The results show that the validity qualifications of lesson plans and student worksheets are good and very good, the practical qulifications are very good. The learning materials comply with effective based on completeness tests of generalization ability of 82.26 with good qualifications
Page Range
191-200
Issue
2
Volume
9
Digital Object Identifier (DOI)
10.21831/jrpm.v9i2.52197
Source
https://journal.uny.ac.id/index.php/jrpm/article/view/52197
Recommended Citation
Hayuningrat, S., & Rosnawati, R. (2022). Development of learning tools based on realistic mathematics approach that oriented to high school students' mathematical generalization ability. Jurnal Riset Pendidikan Matematika, 9(2), 191-200. https://doi.org/10.21831/jrpm.v9i2.52197
References
Akker, J. Van Den, Bannan, B., Kelly, A. E., Nieveen, N., & Plomp, T. (2013). Educational Design
Research. (T. Plomp & N. Nieveen, Ed.) (1 ed.). Enschede: SLO.
Aprilita, P., Ade Mirza, and Asep Nursangaji. (2016). “Analisis Kemampuan
Generalisasi Matematis Siswa Di Kelas VII Sekolah Menengah Pertama.”
Journal Pendidikan Dan Pebelajaran Khatulistiwa 5(10):3.
Astawa, I. W. Puja. (2015). Development of Analytical Geometry Learning Devices in the Field of Open Mathematics-Oriented Problems to Form Intact Professional Competencies for Prospective Mathematics Teachers. Proceedings of the 2015 National Seminar on FMIPA UNDIKSHA V
Branch, R. M. (2009). Instructional Design : The ADDIE Approach. Springer New York Dordrecht
Heidelberg London. https://doi.org/DOI 10.1007/978-0-387-09506-6
Dahar, R. W. (2006). Teori-Teori Belajar dan Pembelajaran. Bandung: Erlangga.
De Ley, L. (2016). A Scientific Learning Whitepaper Generalization: Making Learning More than a
“Classroom Exercise.” 1–7. www.SciLEARN.com
Dumitrascu, G. (2017). Understanding the Process of Generalization in Mathematics through Activity
Theory. International Journal of Learning, Teaching and Educational Research, 16(12), 46–69. https://doi.org/10.26803/ijlter.16.12.4
El Mouhayar, R. (2022). The Role of Languages in the Process of Objectification in Pattern Generalization in a Multilingual Mathematics Classroom. International Journal of Science and Mathematics Education, 20(5), 999–1020. https://doi.org/10.1007/s10763-021-10174-1
Ellis, A., Tillema, E., Lockwood, E., & Moore, K. (2017). Generalization across Domains The Relating-Forming-Extending Generalization Framework. Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education., 677–684.
Gravemeijer. (1994). Developing Realistic Mathematics Education. Utrecht: Freudenthal Institute. Güler, H. K. (2018). Activities Written by Prospective Primary Teachers on Realistic Mathematics
Education. International Journal of Evaluation and Research in Education (IJERE), 7(3), 229. https://doi.org/10.11591/ijere.v7i3.14267
Hadi, Sutarto. (2017). Pendidikan Matematika Realistik : Teori Pengembangan dan Implementasinya.
PT Raja Grafindo Persada.
Hashemi, N., Salleh, M., Kashefi, H., & Rahimi, K. (2013). Generalization in the Learning of
Mathematics. International Seminar on Quality and Affordable Education (ISQAE 2013), 2(2),
–215.
Iordache, O. (2019). Assimilation and Accommodation. 28(2), 91–111. https://doi.org/10.1007/978-3-
-01243-4_5
Isoda, M., & Katagiri, S. (2012). Introductory Chapter: Problem Solving Approach to Develop
Mathematical Thinking. Mathematical Thinking, 1(2012), 1–28. https://doi.org/10.1142/9789814350853_0001
Lingefjärd, T., & Hatami, R. (2020). The beauty of abstraction in mathematics. Policy Futures in
Education, 18(4), 467–482. https://doi.org/10.1177/1478210319895104
Marlina, M. (2013). Development of Junior High School Geometry Learning Tools with Collaborative
Learning Strategies. Journal of Mathematics Education, 8(2)
Mason, J. (1996). Exspressing Generality and Roots of Algebra. Kluwer Academic Publishers, 65–86.
https://doi.org/10.1007/978-94-009-1732-3_5
Mullis, I.V.S., Martin, M.O., & E. (2013). TIMSS 2015 Assessment Frameworks. Chestnut Hill MA: TIMSS & PIRLS International Study Center, Boston Collage.
National Council of Teacher Mathematics. (2000). Principles and Standards for School Mathematics Overview. In The Arithmetic Teacher (Vol. 29, Issue 5). The National Council of Teachers of Mathematics, Inc. https://doi.org/10.5951/at.29.5.0059
Nguyen, T. T., Trinh, T. P. T., Ngo, H. T. V., Hoang, N. A., Tran, T., Pham, H. H., & Bui, V. N.
(2020). Realistic mathematics education in Vietnam: Recent policies and practices. International
Journal of Education and Practice, 8(1), 57–71.
Nieveen, N. (1999). Prototyping to Reach Product Quality. Design Approaches and Tools in
Education and Training, 125–135. https://doi.org/10.1007/978-94-011-4255-7_10
Nirawati, R., Darhim, Fatimah, S., & Juandi, D. (2021). Realistic Mathematics Learning on Students’
Ways of Thinking. Mathematics Teaching-Research Journal, 13(4), 112–130.
Nugraheni, L. P., & Marsigit, M. (2021). Realistic mathematics education: An approach to improve
problem solving ability in primary school. Journal of Education and Learning (EduLearn),
(4), 511–518. https://doi.org/10.11591/edulearn.v15i4.19354
Nugraheni, E. A. & Sugiman (2013). Pengaruh Pendekatan PMRI terhadap Aktivitas dan Pemahaman
Konsep Matematika Siswa SMP. PYTHAGORAS: Jurnal Pendidikan Matematika, 8(1), 101–
https://doi.org/10.21831/jrpm.v3i1.10407
Nurhasanah, H. S., Hidayat, E., & Mulyani, E. (2019). Analisis Kemampuan Sintesis Peserta Didik
dengan Menggunakan Model Problem Based Learning Ditinjau Dari Self Esteem. Journal
Authentic Research on Mathematics Education (JARME), 1(1).
Putri, S. K., Hasratuddin, H., & Syahputra, E. (2019). Development of Learning Devices Based on Realistic Mathematics Education to Improve Students’ Spatial Ability and Motivation. International Electronic Journal of Mathematics Education, 14(2), 393–400. https://doi.org/10.29333/iejme/5729
Shadiq, F., & Mustajab, N. A. (2010). Pembelajaran Metematika dengan Pendekatan Realistik di
SMP. Daud, A., & Suharjana, A. (2010). Modul Matematika SMP Program Bermutu (Kajian Kritis Dalam Pembelajaran Matematika Di SMP). Yogyakarta. PPPPTK Matematik.
Sitorus, Y. I., & Sutirna, S. (2021). Analisis Kemampuan Generalisasi Siswa SMP Negeri 08
Karawang Pada Materi Segitiga. JIPMat, 6(1), 60–75. https://doi.org/10.26877/jipmat.v6i1.8019
Sosa Moguel, L. E., Aparicio Landa, E., & Cabañas-Sánchez, G. (2019). Characterization of Inductive Reasoning in Middle School Mathematics Teachers in a Generalization Task. International Electronic Journal of Mathematics Education, 14(3), 563–581. https://doi.org/10.29333/iejme/5769
Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in
Mathematics, 20(2), 147–164. https://doi.org/10.1007/BF00579460
Tall, David (1991). Advanced Mathematical Thinking. London: Kluwer Academic Publisher.
Tiro, C., Jamal, M. A., & Mastuang. (2015). Development of Learning Devices Using the Guided Discovery Learning Model on the Principal Material of Light. Periodic Scientific Physical Education, 3(2).
Ulandari, L., Amry, Z., & Saragih, S. (2019). Development of Learning Materials Based on Realistic
Mathematics Education Approach to Improve Students’ Mathematical Problem Solving Ability and Self-Efficacy. International Electronic Journal of Mathematics Education, 14(2), 375–383. https://doi.org/10.29333/iejme/5721
Weinberg, P. (2019). Generalizing and proving in an elementary mathematics teacher education program: Moving beyond logic. Eurasia Journal of Mathematics, Science and Technology Education, 15(9). https://doi.org/10.29333/ejmste/108450
Widoyoko S. (2009). Evaluasi Program Pembelajaran.Yogyakarta: Pustaka Belajar
Yao, X., & Elia, J. (2021). Connections between Empirical and Structural Reasoning in Technology- Aided Generalization Activities. International Electronic Journal of Mathematics Education,
(2), em0628. https://doi.org/10.29333/iejme/9770