Transpotition Didactic Design in Mathematics Learning: A Hermeneutic Phenomenology

Authors

  • Ahmad Muzaki UNDIKMA
  • Masjudin Masjudin Universitas Pendidikan Mandalika
  • Pujilestari Pujilestari Universitas Pendidikan Mandalika
  • Ita Chairun Nissa Universitas Pendidikan Mandalika
  • Sri Yuliyanti , Universitas Pendidikan Mandalika

DOI:

https://doi.org/10.31980/mosharafa.v13i4.1951

Keywords:

transposisi didaktis, kesulitan belajar siswa, fenomena heurmeneutik, transpotition didactic, learning obstacles, hermeneutic phenomenology

Abstract

Abstrak

Meskipun banyak penelitian telah mengeksplorasi pentingnya pecahan dalam kurikulum sekolah dasar, penelitian mengenai topik ini di tingkat sekolah menengah pertama masih terbatas, terutama dalam mengidentifikasi faktor-faktor penyebab kesulitan belajar siswa dan merancang pendekatan alternatif untuk mengatasi tantangan tersebut. Oleh karena itu, penelitian ini bertujuan untuk menyelidiki kedua aspek tersebut. Metode yang digunakan dalam penelitian ini adalah fenomenologi hermeneutik. Partisipan dalam penelitian ini adalah siswa SMPN 1 Narmada Lombok Barat yang terdiri dari 29 siswa kelas VIII. Peneliti berperan sebagai instrumen utama yang didukung dengan beberapa alat seperti tes operasi pecahan, pedoman wawancara mendalam. Temuan penelitian mengungkapkan bahwa rendahnya kemampuan siswa dalam mengoperasikan bilangan bulat, khususnya perkalian dan pembagian, merupakan faktor utama kesulitan belajar. Rancangan didaktis terdiri dari 3 tahap. Tahap pertama meliputi beberapa kegiatan yaitu Ayo Tebak dan Ayo Baca. Tahap kedua meliputi kegiatan-kegiatan seperti Mari Mencari, Mari Berdiskusi, dan Mari Menyimpulkan. Tahap ketiga terdiri dari kegiatan Ayo Latihan dan Refleksi Diri. Tahapan ini dikembangkan untuk memperkuat pemahaman terhadap prasyarat tersebut melalui kegiatan yang melibatkan penentuan kelipatan persekutuan terkecil dan faktor persekutuan terbesar. Sebagai rekomendasi, penelitian ini menyarankan agar guru matematika mengadopsi berbagai situasi didaktik berbasis masalah dalam pembelajaran pecahan.

Abstract

Although numerous studies have explored the role of fractions in the elementary school curriculum, research at the junior high school level remains limited, especially in identifying factors contributing to students' learning difficulties and developing alternative instructional approaches to address these challenges. This study aimed to examine both aspects. A hermeneutic phenomenology method was employed, with participants consisting of 29 eighth-grade students from SMPN 1 Narmada in West Lombok. The researcher acted as the primary instrument, supported by tools such as fraction operation tests and in-depth interview guidelines. The findings indicated that students’ difficulties stemmed primarily from their weak understanding of integer operations, particularly multiplication and division. To address this, a three-stage didactic design was implemented. The first stage included activities like "Let’s Guess" and "Let’s Read." The second stage incorporated "Let’s Search," "Let’s Discuss," and "Let’s Conclude." The final stage consisted of "Let’s Practice" and "Self-Reflection." These stages were designed to strengthen prerequisite knowledge through exercises on determining the least common multiple and greatest common factor. The study recommends that mathematics teachers integrate problem-based didactic strategies into fraction instruction.

References

Ahmad, C. V. (2021). Causes of students’ reluctance to participate in classroom discussions. ASEAN Journal of Science and Engineering Education, 1(1), 47–62, DOI: 10.xxxxx/AJSEE.v1i1

Alkhateeb, M. A. (2019). Common errors in fractions and the thinking strategies that accompany them. International Journal of Instruction, 12(2), pp. 399–416.DOI: 10.29333/iji.2019.12226a

Aylward, R. (2012). The three phases of learning. In International Proceedings of Economics Development and Research, Tshwane: Tshwane University of Technology, South Africa, 32–36. DOI: 10.7763/IPEDR

Brousseau, G. (2002). Theory of didactical situations in mathematics. New York: Kluwer Academic Publishers.

Brown, A., & Danaher, P. A. (2017). CHE principles: Facilitating authentic and dialogical semi-structured interviews in educational research structured interviews in educational research. International Journal of Research & Method in Education, 42(1), 76–90, doi: 10.1080/1743727X.2017.1379987

Chorlay, R., Clark, K. M., & Tzanakis, C. (2022). History of mathematics in mathematics education: Recent developments in the field. ZDM-Mathematics Education, 54(7), 1407–1420. DOI: 10.1007/s11858-022-01442-7

Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research, 6th ed. New York: SAGE Publishing. DOI: 10.1017/CBO9781107415324.004

Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches, 5th ed. Thousand Oaks, California: Sage Publication, Inc.

Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: Results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107(3), 525–545. DOI: 10.1007/s10649-021-10033-4

Dangal, M. R., & Joshi, R. (2020). Hermeneutic phenomenology: Essence in educational research. Open Journal for Studies in Philosophy, 4(1), 25–42. DOI: https://doi.org/10.32591/coas.ojsp.0401.03025d

Diputra, K. S., Suryadi, D., Herman, T., & Jupri, A. (2022). Teacher’s knowledge of fraction in the perspective of didactic-mathematical knowledge. Journal of Engineering Science and Technology Special Issue on ICMScE2022, 136–143

Deeken, C., Neumann, I. & Heinze, A. (2020). Mathematical prerequisites for STEM programs: What do university instructors expect from new STEM undergraduates?. International Journal of Research in Undergraduate Mathematics Education, 6(1), 23–41. Doi: 10.1007/s40753-019-00098-1

Dhlamini, Z. B., & Kibirige, I. (2014). Grade 9 learners’ errors and misconceptions in addition of fractions. Mediterr J Soc Sci, 5(8), 236–244. DOI: 10.5901/mjss.2014.v5n8p236

Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Özel, Z. E. Y. (2016). Students’ mathematical work on absolute value: Focusing on conceptions, errors and obstacles. ZDM-Mathematics Education, 48(6), 895–907. DOI: 10.1007/s11858-016-0780-1

Ghorbanpour, E., Abbasian, G. R., & Mohseni, A. (2021). Assessment alternatives in developing L2 listening ability: Assessment for, of, as learning or integration? Assessment x̄ approach,” International Journal of Language Testing, 11(1).

Hoffmann, A., & Even, R. (2023). The mutual contribution between mathematics and other fields: Mathematicians’ and teachers’ views. ZDM-Mathematics Education, May, doi: 10.1007/s11858-023-01496-1

Husband, G. (2020). Ethical data collection and recognizing the impact of semi-structured interviews on research respondents. Educ Sci (Basel), 10(8), 1–12. DOI: 10.3390/educsci10080206

Isnawan, M. G., Azis, A., & Almazroei, E. E. (2023). Parents’ perspectives on distance learning mathematics during the Covid-19 pandemic: A phenomenological study in Indonesia. European Journal of Educational Research, 12(1), 567–581. DOI: 10.12973/eu-jer.12.1.567

Isnawan, M. G., Suryadi, D., & Turmudi, T. (2022). How do secondary students develop the meaning of fractions? A hermeneutic phenomenological study. Beta: Jurnal, 15(1), 1–19. DOI: 10.20414/betajtm.v15i1.496

Isnawan, M. G., Alsulami, N. M., Rusmayadi, M., & Yanuarto, W. N. (2023). Analysis of student learning barriers in fractional multiplication: A hermeneutics phenomenology study in higher education. Edumatica: Jurnal Pendidikan Matematika, 13(1), 11–22. DOI: https://doi.org/10.22437/edumatica.v13i01.24190

Jaworski, B., & Huang, R. (2014). Teachers and didacticians: Key stakeholders in the processes of developing mathematics teaching. ZDM-Mathematics Education, 46(2), 173–188. DOI: 10.1007/s11858-014-0574-2

Keshavarz, H. (2020). Hermeneutic phenomenology in supporting research and information services: Contributions to information science. Journal of Information Science Theory and Practice, 8(4), 29–39, DOI: https://doi.org/10.1633/JISTaP.2020.8.4.3

Koskinen, R., & Pitkäniemi, H. (2022). Meaningful learning in mathematics: A research synthesis of teaching approaches. International Electronic Journal of Mathematics Education, 17(2), p. em0679. DOI: 10.29333/iejme/11715

Laverty, S. M. (2003). Hermeneutic phenomenology and phenomenology: A comparison of historical and methodological considerations. Int J Qual Methods, 2, 1–29.

Lawshe, C. H. (1975). A quantitative approach to content validity. Personel Psychology, 28, 563–575, DOI: 10.1111/J.1744-6570.1975.TB01393.X

Lestiana, H., Rejeki, S., & Setyawan, F. (2016). Identifying students’ errors on fractions. Journal of Research and Advances in Mathematics Education, 1(2), 131–139, DOI: 10.23917/jramathedu.v1i2.3396

Lin, Y. W., Tseng, C. L., & Chiang, P. J. (2017). The effect of blended learning in mathematics course. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 741–770. DOI: 10.12973/eurasia.2017.00641a

Maass, K., Geiger, V., Ariza, M. R., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM-Mathematics Education, 51(6), 869–884. DOI: 10.1007/s11858-019-01100-5

Makhubele, Y. E. (2021). The analysis of grade 8 fractions errors displayed by learners due to deficient mastery of prerequisite concepts. International Electronic Journal of Mathematics Education, 16(3), p. em0645, DOI: 10.29333/iejme/11004

Makonye, J. P., & Khanyile, D. W. (2015). Probing grade 10 students about their mathematical errors on simplifying algebraic fractions. Research in Education, 94(1), 55–70, DOI: 10.7227/RIE.0022

Man-Keung, S. (2022). The role of M (mathematical worlds) in HPM (history and pedagogy of Mathematics) and in STEM (science, technology, engineering, mathematics). ZDM-Mathematics Education, 54(7), 1643–1655. DOI: 10.1007/s11858-022-01375-1

Marfuah, M., Suryadi, D., Turmudi, T., & Isnawan, M. G. (2022). Providing online learning situations for in-service mathematics teachers’ external transposition knowledge during Covid-19 pandemic: Case of Indonesia. Electronic Journal of e-Learning, 20(1), 69–84, DOI: 10.34190/ejel.20.1.2388

Mohamed, R., Ghazali, M., & Samsudin, M. A. (2021). A systematic review on teaching fraction for understanding through representation on Web of Science database using PRISMA. LUMAT, 9(1), 100–125, DOI: 10.31129/LUMAT.9.1.1449

Namkung, J., & Fuchs, L. (2019). Remediating difficulty with fractions for students with mathematics learning difficulties,” Learning Disabilities: A Multidisciplinary Journal, 24(2), 36–48. DOI: 10.18666/ldmj-2019-v24-i2-9902

Purnomo, Y. W., Pasri, Aziz, T. A., Shahrill, M., & Prananto, I. W. (2022). Students’ failure to understand fraction multiplication as part of a quantity. Journal on Mathematics Education, 13(4), 681–702. DOI: 10.22342/jme.v13i4.pp681-702

Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning obstacles in the making of lesson plans by prospective mathematics teacher students. Educ Res Int, 2022(Sep), 1–15. doi: 10.1155/2022/2896860.

Sandefur, J., Lockwood, E., Hart, E., & Greefrath, G. (2022). Teaching and learning discrete mathematics,” ZDM-Mathematics Education, 54(4), 753–775. DOI: 10.1007/s11858-022-01399-7

Sjöblom, M., Valero, P., & Olander, C. (2022). Teachers’ noticing to promote students’ mathematical dialogue in group work. Journal of Mathematics Teacher Education, DOI: 10.1007/s10857-022-09540-9

Stolz, S. A. (2013). Phenomenology and physical education. Educational Philosophy and Theory, 45(9), 949–962. DOI: 10.1080/00131857.2013.785355

Suryadi, D. (2019). Landasan filosofis penelitian desain didaktis (DDR). Bandung: Pusat Pengembangan DDR Indonesia.

Suryadi, D. (2019). Penelitian desain didaktis (DDR) dan implementasinya. Bandung: Gapura Press.

Trivena, V., Ningsih, A. R., & Jupri, A. (2017). Misconception on addition and subtraction of fraction at primary school students in fifth-grade. J Phys Conf Ser, 895(1), 0–7. DOI: 10.1088/1742-6596/895/1/012139

Yang, L. P., & Xin, T. (2022). Changing educational assessments in the post-Covid-19 Era: From assessment of learning (AoL) to assessment as learning (AaL),” Educational Measurement: Issues and Practice, 41(1), 54–60. DOI: 10.1111/emip.12492

Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China. ZDM-Mathematics Education, 52(2), 281–294. DOI: 10.1007/s11858-020-01145-x.

Yolcu, A., & Popkewitz, T. S. (2019). Making the able body: School mathematics as a cultural practice. ZDM-Mathematics Education, 51(2), 251–261. doi: 10.1007/s11858-018-1003-8

Zhang, X., Clements, M. A. K., & Ellerton, N. F. (2014). Conceptual mis(understandings) of fractions: From area models to multiple embodiments. Mathematics Education Research Journal, 27(2), 233–261. DOI: 10.1007/s13394-014-0133-8

Zuhri, R. S., Wilujeng, I., & Haryanto. (2023). Multiple representation approach in elementary school science learning: A systematic literature review. International Journal of Learning, Teaching and Educational Research, 22(3), 51–73, DOI: 10.26803/ijlter.22.3.4

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Published

2024-10-30

How to Cite

Muzaki, A., Masjudin, M., Pujilestari, P., Nissa, I. C., & Yuliyanti, S. (2024). Transpotition Didactic Design in Mathematics Learning: A Hermeneutic Phenomenology. Mosharafa: Jurnal Pendidikan Matematika, 13(4), 963–974. https://doi.org/10.31980/mosharafa.v13i4.1951

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