Students' Thinking Process in Solving Geometry Problems based on Harel Theory on Malay Traditional House Design

Resy Nirawati, Rosmaiyadi Rosmaiyadi, Buyung Buyung, Dodik Kariadi

Abstract


The thinking process is a cognitive development that occurs in the minds of students by involving new knowledge and problems that occur related to geometry concepts to solve problems or find solutions to the problems presented. This study aims to study and describe comprehensively the thinking process of students in solving geometry problems based on Harel theory in the design of Malay traditional houses. This research method is qualitative research with a case study design. Furthermore, the data collection used is observation, tests and interviews. Then for data analysis carried out is reflective analysis with data trustworthiness using the triangulation method. Thefindings in the research  of students' thinking processes in solving geometry in the design of Malay traditional houses are the core category / central phenomenon built or constructed by three themes which include mental act, ways of thinking and ways of understanding. Ageometric spec on the design components of West Kalimantan Malay traditional houses includes rectangles, triangles, squares, parallelograms, semicircles,  isosceles triangles, right triangles, rhombuses, and trapeziums. The findings in this study need to be implemented in mathematics learning design, which relates to students' experiences in everyday life that touch the realm of local cultural arts so that students become more understanding of the geometry concepts explained so that they can dig deeper into mental acts,  ways of thinking and ways of understanding in  order to foster various student thought processes in  Solve mathematics problems

Keywords


Case studies, geometry, harel theory, malay traditional house, problem solving, students, thought process

Full Text:

PDF

References


Aberdeen, T. (2013). Case study research: Design and methods (4th ed.). The Canadian Journal of Action Research, 14(1), 69–71. https://doi.org/10.33524/cjar.v14i1.73

Akkaya, A., Tatar, E., & Kağızmanlı, T. B. (2011). Using dynamic software in teaching of the symmetry in analytic geometry: The case of geogebra. Procedia - Social and Behavioral Sciences, 15, 2540–2544. https://doi.org/10.1016/j.sbspro.2011.04.141

Atiyah, M., Dijkgraaf, R., & Hitchin, N. (2010). Geometry and physics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1914), 913–926. https://doi.org/10.1098/rsta.2009.0227

Bistari, B. (2017). The local wisdom of Sambas malay ethnic assessed from character mathematical connections. JETL (Journal Of Education, Teaching and Learning), 2(2), 147. https://doi.org/10.26737/jetl.v2i2.278

Carter, N., Bryant-Lukosius, D., DiCenso, A., Blythe, J., & Neville, A. J. (2014). The use of triangulation in qualitative research. Oncology Nursing Forum, 41(5), 545–547. https://doi.org/10.1188/14.ONF.545-547

Clements, D. H. (1998). Geometric and spatial thinking in young children. In Science of Advanced Materials. https://doi.org/10.1166/sam.2014.1766

Clements, D. H., & Sarama, J. (2010). Learning trajectories in early mathematics- Sequences of acquisition and teaching. In Encyclopedia on Early Childhood Development.

Creswell, J. W., Hanson, W. E., Plano, V. L. C., & Morales, A. (2007). Qualitative research designs: Selection and implementation. The Counseling Psychologist, 35(2), 236–264. https://doi.org/10.1177/0011000006287390

Daugaard, D. (2020). Emerging new themes in environmental, social and governance investing: a systematic literature review. Accounting and Finance, 60(2), 1501–1530. https://doi.org/10.1111/acfi.12479

Dikovic, L. (2009). Implementing dynamic mathematics resources with geogebra at the college level. International Journal of Emerging Technologies in Learning (IJET), 4(3), 51–54. https://doi.org/10.3991/ijet.v4i3.784

Harel, G. (2008a). DNR perspective on mathematics curriculum and instruction. Part I: focus on proving. ZDM Mathematics Education, 40, 487–500. https://doi.org/10.1007/s11858-008-0104-1

Harel, G. (2008b). What is mathematics? A pedagogical answer to a philosophical question. Columbia University Libraries. https://doi.org/10.5948/UPO9781614445050.018

Harel, G. (2013). DNR-based curricula: The case of complex numbers [DNR-based curriculum: The case of complex numbers]. Journal of Humanistic Mathematics, 3(2), 2–61. https://doi.org/10.5642/jhummath.201302.03

Harel, G. (2020). The DNR system as a conceptual framework for curriculum development and instruction. In R. A. Lesh, E. Hamilton, & J. J. Kaput (Eds.), Foundations for the future in mathematics education (1st ed., pp. 263–280). Routledge. https://doi.org/10.4324/9781003064527-16

Harel, G., & Sowder, L. (2013a). Advanced mathematical-thinking at any age: Its nature and its development. Advanced Mathematical Thinking: A Special Issue of Mathematical Thinking and Learning, May 2014, 27–50. https://doi.org/10.4324/9781315045955

Harel, G., & Sowder, L. (2013b). Advanced Mathematical Thinking. In A. Selden & J. Selden (Eds.), Advanced mathematical-thinking at any age: Its nature and its development (1st ed.). Routledge. https://doi.org/10.4324/9781315045955

Ikhwanudin, T., Prabawanto, S., & Wahyudin, W. (2019). The error pattern of students with mathematics learning disabilities in the inclusive school on fractions learning. International Journal of Learning, Teaching and Educational Research, 18(3), 75–95. https://doi.org/10.26803/ijlter.18.3.5

Ikhwanudin, T., & Suryadi, D. (2018). How students with mathematics learning disabilities understands fraction: A case from the Indonesian inclusive school. International Journal of Instruction, 11(3), 309–326. https://doi.org/10.12973/iji.2018.11322a

Jahnke, H. N., & Hefendehl-Hebeker, L. (2019). Traditions in German-Speaking Mathematics Education Research. In H. N. Jahnke & L. Hefendehl-Hebeker (Eds.), ICME-13 Monographs. Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-11069-7

Jamilah, J., Suryadi, D., & Priatna, N. (2020). Didactic transposition from scholarly knowledge of mathematics to school mathematics on sets theory. Journal of Physics: Conference Series, 1521, Article 032093. https://doi.org/10.1088/1742-6596/1521/3/032093

Kehi, Y. J., M, Z., & Waluya, S. B. (2019). Kontribusi Etnomatematika Sebagai Masalah Kontekstual dalam Mengembangkan Literasi Matematika. Prisma, Prosiding Seminar Nasional Matematika, 2, 190–196.

Koichu, B., Harel, G., & Manaster, A. (2013). Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions. Instructional Science, 41(4), 681–698. https://doi.org/10.1007/s11251-012-9254-1

Laborde, C. (2015). Teaching and Learning Geometry. The Proceedings of the 12th International Congress on Mathematical Education, February, 431–436. https://doi.org/10.1007/978-3-319-12688-3_35

Lesh, R. (1981). Problem solving processes that enable an individual to use mathematical ideas in real situations are not necessarily the type that have been discussed by Polya ( 1957 ), Landa ( 1974 ), Wickelgren ( 1974 ), Davis ( 1973 ) or other problem solving theorist. Educational Studies in Mathematics, 12, 235–264.

Lewis, C. M. (2019). A case study of qualitative methods. In M. Clancy, M. Loui, M. Guzdial, S. Dziallas, S. Krishnamurthi, K. Fisler, & A. Ko (Eds.), The Cambridge Handbook of Computing Education Research (pp. 875–894). Cambridge University Press. https://doi.org/10.1017/9781108654555.032

Lim, K. H. (2006). Students’ mental acts of anticipating in solving problems involving algebraic inequalities and equations. UC San Diego Electronic Theses and Dissertations.

Lipman, M. (2003). Mental acts. In M. Lipman (Ed.), Thinking in education (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9780511840272.009

Mendick, H. (2005). Mathematical stories: Why do more boys than girls choose to study mathematics at AS-level in England? British Journal of Sociology of Education, 26(2), 235–251. https://doi.org/10.1080/0142569042000294192

Merriam, S. B. (1998). Qualitative research and case study applications in education (1st ed.). Jossey-Bass.

Moon, J. (2007). The pedagogy of critical thinking. In J. Moon (Ed.), Critical Thinking (1st ed., pp. 146–169). Routledge. https://doi.org/10.4324/9780203944882-21

Morin, S., & Herman, T. (2022). Systematic Literature Review : Keberagaman Cara Berpikir Siswa Dalam Pemecahan Masalah. Jurnal Pembelajaran Matematika Inovatif, 5(1), 271–286. https://doi.org/10.22460/jpmi.v5i1.271-286

Nirawati, R., Fatimah, S., & Juandi, D. (2021). Realistic Mathematics Learning on Students' Ways of Thinking. Mathematics Teaching Research Journal, 13(4), 112-130.

Ndemo, Z., & Ndemo, O. (2018). Secondary school students’ errors and misconceptions in learning algebra. Journal of Education and Learning (EduLearn), 12(4), 690–701. https://doi.org/10.11591/edulearn.v12i4.9556

Nurhasanah, H., Turmudi, & Jupri, A. (2021). Karakteristik ways of thinking (wot) dan ways of understanding (wou) siswa berdasarkan teori Harel [Characteristics of ways of thinking (wot) and ways of understanding (wou) of students based on Harel’s theory]. Journal of Authentic Research on Mathematics Education, 3(1), 105–113. https://doi.org/10.37058/jarme.v3i1.2449

Odabasi Çimer, S., & Ursavas, N. (2012). Student teachers’ ways of thinking and ways of understanding digestion and the digestive system in biology. International Education Studies, 5(3), 1–14. https://doi.org/10.5539/ies.v5n3p1

Pepin, B., Xu, B., Trouche, L., & Wang, C. (2017). Developing a deeper understanding of mathematics teaching expertise: an examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise. Educational Studies in Mathematics, 94(3), 257–274. https://doi.org/10.1007/s10649-016-9727-2

Reis, Z. A., & Ozdemir, S. (2010). Using geogebra as an information technology tool: Parabola teaching. WCLTA 2010: Procedia Social and Behavioral Sciences, 9, 565–572. https://doi.org/10.1016/j.sbspro.2010.12.198

Sadeghi, F., Adel, S. M. R., Zareian, G., & Davoudi, M. (2020). Iranian EFL teachers’ and learners’ perceptions of the principles of critical thinking: A constructivist grounded theory study. Iranian Journal of Language Teaching Research, 8(2), 63–81.

Sari, F. A., Marlissa, I., & Dahlan, J. A. (2019). Analisis ways of thinking (wot) dan ways of understanding (wou) pada buku teks pelajaran matematika SMP kelas VII materi bilangan. Jurnal Pendidikan Matematika, 10(2).

Sharp, C. A. (2003). Qualitative research and evaluation methods (3rd ed.). Evaluation Journal of Australasia, 3(2), 60–61. https://doi.org/10.1177/1035719X0300300213

Sudihartinih, E., & Wahyudin. (2019). Analysis of students’ self efficacy reviewed by geometric thinking levels and gender using rasch model. Journal of Engineering Science and Technology, 14(1), 509–519.

Tran, T., Nguyen, N.-G., Bui, M.-D., & Phan, A.-H. (2014). Discovery Learning with the Help of the GeoGebra Dynamic Geometry Software. International Journal of Learning, Teaching and Educational Research, 7(1), 44–57.

Umbara, U., Wahyudin, & Prabawanto, S. (2019). Ethnomatematics : how does cigugur traditional community use palintangan on farming. Journal of Physics: Conference Series, 1265(1). https://doi.org/10.1088/1742-6596/1265/1/012025

Willard, D. (1994). The integrity of the mental act: Husserlian reflections on a fregian problem. In L. Haaparanta (Ed.), Mind, meaning and mathematics (Vol. 237, pp. 235–262). Kluwer Academic Publisher. https://doi.org/10.1007/978-94-015-8334-3_9

Yin, R. K. (1981). The case study strategy, a serious research. Knowledge: Creation, Diffusion, Utilization, 3(1), 97–114.

Yin, R. K. (1999). Enhancing the quality of case studies in health services research. Health Services Research, 34(5 Pt 2), 1209–1224.

Zengin, Y., Furkan, H., & Kutluca, T. (2012). The effect of dynamic mathematics software geogebra on student achievement in teaching of trigonometry. Procedia - Social and Behavioral Sciences, 31(2011), 183–187. https://doi.org/10.1016/j.sbspro.2011.12.038




DOI: http://dx.doi.org/10.26737/jpmi.v9i1.5110

Refbacks

  • There are currently no refbacks.


Published by:

Institute for Managing and Publishing of Scientific Journal

STKIP Singkawang


Jl. STKIP, Kelurahan Naram, Kecamatan Singkawang Utara, Kota Singkawang, Kalimantan Barat, Indonesia

Website: https://journal.stkipsingkawang.ac.id/index.php/JPMI/index

Email: [email protected]

JPMI Indexed by:

     

Creative Commons License

JPMI (Jurnal Pendidikan Matematika Indonesia) is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.