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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

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

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