Memperkasakan Kemahiran Pedagogi dalam Kalangan Guru Matematik: Aplikasi Kaedah Fuzzy Delphi (Enhancing Pedagogical Skills Among Mathematics Teachers: Application of the Fuzzy Delphi Method)

Abstract

Kemahiran pedagogi penting untuk memastikan keberkesanan pengajaran matematik masa kini. Guru yang berkemahiran tinggi dapat menyesuaikan pengajaran untuk memenuhi keperluan individu murid, termasuk mereka yang berkeperluan khas atau berlatar belakang sosioekonomi berbeza. Namun begitu, penguasaan kemahiran ini sering terhalang oleh pelbagai cabaran seperti kekurangan latihan, beban tugas pentadbiran yang tinggi serta kekangan sumber sokongan. Kajian sistematik yang meneliti aspek kemahiran pedagogi dalam konteks pengajaran matematik masih terhad dan memerlukan penyelidikan yang lebih mendalam. Oleh itu, kajian ini dijalankan bagi mengenal pasti dan mengesahkan elemen-elemen penting dalam kemahiran pedagogi yang diperlukan dalam pengajaran matematik yang berkesan. Kajian ini menggunakan tinjauan literatur dan kaedah Fuzzy Delphi bagi memperoleh pandangan serta konsensus pakar berkaitan elemen-elemen yang relevan. Seramai 13 orang pakar dalam bidang matematik dan kurikulum telah terlibat dalam kajian ini. Dapatan menunjukkan tahap kesepakatan tinggi terhadap tiga konstruk utama iaitu kemahiran komunikasi, kemahiran mengajar dan kemahiran visualisasi. Setiap konstruk merangkumi elemen-elemen spesifik yang menyumbang kepada keberkesanan pedagogi guru. Implikasi kajian menunjukkan keberkesanan kaedah Fuzzy Delphi dalam mencapai konsensus pakar serta menyediakan pendekatan sistematik dalam pembangunan model kemahiran pedagogi. Kajian lanjutan dicadangkan bagi menilai kebolehgunaan model dalam konteks bilik darjah sebenar serta memperluas elemen model mengikut keperluan pengajaran semasa. Kata kunci: : Kemahiran Pedagogi; pengajaran; Guru Matematik; kaedah Fuzzy Delphi; konsensus pakarAbstract: Pedagogical skills play a vital role in ensuring the effectiveness of mathematics teaching. Teachers who possess high pedagogical competence can adapt their instructional approaches to meet the diverse needs of students, including those with special educational needs and varying socioeconomic backgrounds. However, the mastery of these skills is often hindered by challenges such as limited training opportunities, administrative workload, and insufficient support resources. Systematic research on pedagogical skills in mathematics is scarce and requires further comprehensive investigation. Therefore, this study aimed to identify and validate the key elements of pedagogical skills essential for effective mathematics instruction. A literature review and the Fuzzy Delphi Method were employed to obtain expert insights and consensus on relevant pedagogical skill elements. A total of 13 experts in mathematics and curriculum participated in the study. The findings revealed a high level of agreement on three primary constructs: communication skills, teaching skills, and visualisation skills. Each construct comprises specific elements that enhance teaching effectiveness. The study demonstrates that the Fuzzy Delphi Method effectively achieves expert consensus and offers a systematic framework for developing a pedagogical skills model. Future research should assess the models’ practical application in real classroom settings and explore additional elements to meet evolving instructional needs.Keywords: Pedagogical skills; teaching; Mathematics teachers; Fuzzy Delphi Method; expert consensusReferencesAbang Adam, A. D. (2018). Pembangunan Model Standard Kompetensi Guru Kanan Mata Pelajaran Di Malaysia.  National University Of Malaysia.Abdullah, A. H., Hamzah, M. H., Hussin, R. H. S. R., Kohar, U. H. A., Rahman, S. N. S. A., & Junaidi, J. (2017). Teachers’ readiness in implementing science, technology, engineering and mathematics (STEM) education from the cognitive, affective and behavioural aspects. 2017 IEEE 6th International Conference on Teaching, Assessment, and Learning for Engineering (TALE), December, 6–12. https://doi.org/10.1109/TALE.2017.8252295Akbari, R., & Yazdanmehr, E. (2014). A critical analysis of the selection criteria of expert teachers in ELT. Theory and Practice in Language Studies, 4(8), 1653–1658. https://doi.org/10.4304/tpls.4.8.1653-1658Al-Rikabi, Y. K., & Montazer, G. A. (2024). Designing an e-learning readiness assessment model for Iraqi Universities employing fuzzy delphi method. In Education and Information Technologies (Vol. 29, Issue 2). Springer US. https://doi.org/10.1007/s10639-023-11889-0Alkhaldi, I. A. Rahaman, Talib, O., Kamarudin, N., Abduljalil, H., & Sabitu, A. (2021). The application of fuzzy delphi method (FDM) in the development of fun-driven mobile learning (FDML) model for teaching of arithmetic in Saudi Schools. Malaysian Journal of Social Sciences and Humanities (MJSSH), 6(12), 223–232. https://doi.org/10.47405/mjssh.v6i12.1205Ambusaidi, A. K., & Al-Maqbali, F. Y. (2022). Exploring pedagogical decision making from the lens of science teachers in response to different pedagogical issues. Social Sciences & Humanities Open, 5(1), 100236. https://doi.org/10.1016/j.ssaho.2021.100236Aminah, J., & Crispina, G. K. H. (2020). Pengaruh pengalaman mengajar dalam pengetahuan, motivasi dan pelaksanaan pengajaran dan pembelajaran STEM. Jurnal Pendidikan Sains & Matematik Malaysia, 10(2), 45–56.Aziz, N. F. A., & Maat, S. M. (2021). Kesediaan dan efikasi guru matematik sekolah rendah dalam pengintegrasian teknologi semasa pandemik COVID-19. Malaysian Journal of Social Sciences and Humanities (MJSSH), 6(8), 93–108. https://doi.org/10.47405/mjssh.v6i8.949Bakti, G. (2014). Penerapan teori belajar vygotsky dalam pembelajaran. Academia, 1(3), 1–13.Brown, R. (2020). Re-conceptualising the development of agency in the school mathematics classroom. Theory into Practice, 59(2), 139–149. https://doi.org/10.1080/00405841.2019.1702394Cavalli-Sforza, V., & Ortolano, L. (1984). Delphi forecasts of land use: Transportation interactions. Journal of Transportation Engineering, 110(3), 324–339. https://doi.org/10.1061/(ASCE)0733-947X(1984)110:3(324)Chen, S., Geesa, R., Izci, B., & Song, H. (2021). Investigating preservice teachers’ science and mathematics teaching efficacy, challenges, and support. Teacher Educator, 0(0), 1–21. https://doi.org/10.1080/08878730.2021.2007560Ching, N. C., & Nurfaradilla Mohamad, N. (2021). Penggunaan kaedah visualisasi dalam pengajaran dan pembelajaran perbendaharaan kata Bahasa Inggeris ( Using Method Visualization in the Teaching and Learning of English Vocabulary ). Jurnal Dunia Pendidikan, 3(3), 444–449.Chua, C., Kosnin, A. M., & Yeo, K. J. (2024). Fuzzy delphi method for A-level mathematics technological pedagogical and content knowledge module. International Journal of Evaluation and Research in Education (IJERE), 13(1), 441. https://doi.org/10.11591/ijere.v13i1.25982Costley, K. C. (2012). An overview of the life, central concepts, including classroom applications of Lev Vygotsky. In Online Submission.De Freitas, G., & Spangenberg, E. D. (2019). Mathematics teachers’ levels of technological pedagogical content knowledge and information and communication technology integration barriers. Pythagoras, 40(1), 1–13. https://doi.org/10.4102/PYTHAGORAS.V40I1.431Demir, K., & Qureshi, A. M. (2019). Pakistani science teachers’ experiences of professional development: a phenomenological case study. Journal of Science Teacher Education, 30(8), 838–855. https://doi.org/10.1080/1046560X.2019.1607707Doabler, C. T., Clarke, B., Firestone, A. R., Turtura, J. E., Jungjohann, K. J., Brafford, T. L., Sutherland, M., Nelson, N. J., & Fien, H. (2019). Applying the curriculum research framework in the design and development of a technology-based tier 2 mathematics intervention. Journal of Special Education Technology, 34(3), 176–189. https://doi.org/10.1177/0162643418812051Ha, H. T. L., Pham, A. T. K., Nguyen, H. T., & Duong, H. T. T. (2021). Training pedagogical skills: Evaluation of lecturers and teacher training students at educational universities in Vietnam. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2054. https://doi.org/10.29333/ejmste/11418Hasim, M. A., Jabar, J., Sufian, A., Ibrahim, N. F., & Khalid, F. A. (2023a). Employing fuzzy delphi techniques to validate the components and contents of e-learning antecedents and usage behavior towards e-learning performance. European Journal of Educational Research, 12(1), 467–480. https://doi.org/10.12973/eu-jer.12.1.467Ioannidi, V., & Gogaki, I. (2021). Pedagogical skills and e-Teaching - The example of mathematics and reading. European Journal of Open Education and E-Learning Studies, 6(1). https://doi.org/10.46827/ejoe.v6i1.3530Jamelaa Bibi, A., & Siti Ilyana, M. Y. (2018). A fuzzy delphi method-developing high-performance leadership standard for malaysian school leaders. Journal of Education and Social Sciences, 9(2), 1–10.Khairu Nuzul, H. (2020). Reka Bentuk Dan Pembangunan Model Pengajaran “e-TVET” Bagi Program Mekanikal Dan Pembuatan Di Kolej Vokasional Zon Utara. Universiti Pendidikan Sultan Idris.Kuzina, N. A. (2020). Integration of pedagogical approaches and their use in the educational process. Education and Science: Current Trends, 2022(c), 4–6. https://doi.org/10.31483/r-75004Lawrie, G. A. (2018). Personal journeys of teachers : an investigation of the development of teacher professional knowledge and skill by expert tertiary chemistry teachers. Chemistry Education Research Practice. https://doi.org/10.1039/c8rp00187aLeonard, J., C. Burrows, A., & Kitchen, R. (2019). Recruiting, preparing, and retaining STEM teachers for a global generation. In Recruiting, Preparing, and Retaining STEM Teachers for a Global Generation. BRILL. https://doi.org/10.1163/9789004399990Mabrouk, N. Ben. (2020). Green supplier selection using fuzzy delphi method for developing sustainable supply chain. Decision Science Letters, 10(1), 63–70. https://doi.org/10.5267/j.dsl.2020.10.003Mangwende, E., & Maharaj, A. (2019). Barriers to mathematics teachers’ use of their knowledge of students’ learning styles in mathematics teaching: A case of secondary schools in Zimbabwe. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1–15. https://doi.org/10.29333/ejmste/109198Martynenko, O., Chkana, Y., Shyshenko, I., & Rysina, M. (2019). Formation of intellectual skills for future mathematics teachers. TEM Journal, 8(3), 1084–1093. https://doi.org/10.18421/TEM83-55Meyer, A., Kleinknecht, M., & Richter, D. (2023). What makes online professional development effective? The effect of quality characteristics on teachers’ satisfaction and changes in their professional practices. Computers and Education, 200(November 2022). https://doi.org/10.1016/j.compedu.2023.104805Mohamad Ikram, Z. (2021). Pembangunan Dan Penilaian Model Pengajaran M-PBM Bagi Guru-Guru Matematik Sekolah Rendah. National University of Malaysia.Mohamad Tarmizi, A. H. (2020). Pengaruh Tret Personaliti, Pengetahuan Pedagogi, Kefahaman Kurikulum Dan Kemahiran Guru Ke Atas Perkembangan Bahasa Kanak-Kanak Prasekolah. National University of Malaysia.Mohd Ridhuan, M. J., & Nurulrabihah, M. N. (2020). Kepelbagaian Metodologi Dalam Penyelidikan Reka Bentuk Dan Pembangunan (I. Noh (ed.)). Qaisar Prestige Resources.Muhammad Hayat, K., Ahmad Zabidi, A. R., & Husaina Banu, K. (2021). Professional learning community, trust, and teacher professional development in malaysian secondary schools. Jurnal Pendidikan Malaysia, 46(01), 25–37. https://doi.org/10.17576/jpen-2021-46.01-04Mustaffa, Z., Hussin, Z., & Sulaiman, A. M. (2021). Pedagogi terbeza untuk pengajaran guru terhadap kepelbagaian murid. Malaysian Journal of Social Sciences and Humanities (MJSSH), 6(9), 202–214. https://doi.org/10.47405/mjssh.v6i9.997Nair, R., Aggarwal, R., & Khanna, D. (2011). Methods of formal consensus in classification/diagnostic criteria and guideline development. Seminars in Arthritis and Rheumatism, 41(2), 95–105. https://doi.org/10.1016/j.semarthrit.2010.12.001Nurulrabihah, M. N., Saedah, S., Siti Hajar, H., Mohd Ridhuan, M. J., & Zaharah, H. (2019). Aplikasi teknik fuzzy delphi terhadap berasaskan pemikiran reka bentuk. Asia Pacific Journal of Educators and Education, 34. https://doi.org/https://doi.org/10.21315/apjee2019.34.7Osborne, J., Ratcliffe, M., Collins, S., Millar, R., & Duschl, R. A. (2001). What should we teach about science? A delphi study. Evidence-Based Practice in Science Education (EPSE) Research Network, January, 93.Pamuda, D., & Mahmud, M. S. (2022). Kompetensi guru dalam pengajaran konsep matematik: kajian literatur bersistematik. Malaysian Journal of Social Sciences and Humanities (MJSSH), 7(10), e001850. https://doi.org/10.47405/mjssh.v7i10.1850Pourdavood, R. G., & Song, X. (2021). Engaging pre-service and in-service teachers in online mathematics teaching and learning: Problems and possibilities. International Journal of Learning, Teaching and Educational Research, 20(11), 96–114. https://doi.org/10.26803/ijlter.20.11.6Pournara, C., & Adler, J. (2021). Revisiting school mathematics in pre-service secondary teacher education: Purposes, opportunities and challenges. International Journal of Science and Mathematics Education, 20(2), 391–410. https://doi.org/10.1007/s10763-021-10150-9Ramlan, M., & Ghazali, D. (2018). Aplikasi Kaedah: Fuzzy Delphi Dalam Penyelidikan Sains Sosial. Universiti Malaya. https://doi.org/10.14425/9789831009505Reid, M., Lee, A., Leslie, K., Feldman, L. S., Hameed, S. M., Kirkpatrick, R., Lovrics, P. J., MacDonald, P. H., Pace, D., Shaw, J. M., Swallow, C. J., Pagliarello, G., Bigam, D. L., Porter, G., Mathieson, A., McFadden, N., Lapointe, R., MacLean, T., Kuziemsky, C., & Balaa, F. (2022). A framework for role allocation in education, research and leadership services in Canadian academic divisions of general surgery: a modified Delphi consensus. Canadian Journal of Surgery, 65(1), E73–E81. https://doi.org/10.1503/CJS.021120Roth, W. M. (2018). Elaborating the later Vygotsky’s radical initiative on the nature and function of language: Implications for mathematics education. ZDM - Mathematics Education, 50(6), 975–986. https://doi.org/10.1007/s11858-018-0912-xSaffie, N. A. M., Shukor, N. A. M., & Rasmani, K. A. (2016). Fuzzy delphi method: Issues and challenges. 2016 International Conference on Logistics, Informatics and Service Sciences, LISS 2016. https://doi.org/10.1109/LISS.2016.7854490Saidi, S. M., Teoh, S. H., Singh, P. S. A., & Retnawati, H. (2024). The relationship between teachers’ personalities and students’ attitudes. Jurnal Pendidikan Sains Dan Matematik Malaysia, 14(1), 61–70. https://doi.org/10.37134/jpsmm.vol14.1.6.2024Sanura, J., Rozniza, Z., & Muhammad Nidzam, Y. (2022). Development of technology tools in next generation learning spaces ( NGLS ) framework : A fuzzy delphi analysis. International Journal Of Special Education, 37(3).Saraceno, L. M. (2019). Disciplinary Literacy Pedagogical Content Knowledge ( DLPCK ) Today : An Exploration of Disciplinary Literacy Pedagogical Content Knowledge of Middle and High School Science, Social Studies, and English Language Arts: Vol. Dissertati. Rowan University.Shvarts, A., & Abrahamson, D. (2019). Dual-eye-tracking Vygotsky: A microgenetic account of a teaching/learning collaboration in an embodied-interaction technological tutorial for mathematics. Learning, Culture and Social Interaction, 22(May), 100316. https://doi.org/10.1016/j.lcsi.2019.05.003Talib, S., Alias, B. S., & Mohd Matore, M. E. (2024). Principal competency, teacher readiness, and teacher commitment in STEM education implementation: A qualitative study. E-Bangi Journal of Social Science and Humanities, 20(4). https://doi.org/10.17576/ebangi.2024.2104.30Ulusoy, F. (2020). Prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Teaching and Teacher Education, 94, 103103. https://doi.org/10.1016/j.tate.2020.103103Yousuf, M. I. (2007). Using experts’ opinions through delphi technique. Practical Assessment, Research and Evaluation, 12(4).Zakaria, R. A., Hamzah, M. I., & Abdul Razak, K. (2022). Analysis of self-hisbah factors on moral appreciation among muslim secondary school students in Malaysia: Fuzzy delphi method application. E-Bangi Journal of Social Science and Humanities, 19(2), 16–34. https://doi.org/10.17576/ebangi.2022.1902.02Zelenicky, L., Horvathova, D., & Rakovska, M. (2019). Forming the professional skills of a future physics teacher. AIP Conference Proceedings, 2152(September). https://doi.org/10.1063/1.5124784Zulkifli, H., Ismail, A. M., Muhamad, N. A. F., Hussin, N. H., & Mahdi Yusuf, S. A. (2024). Reliability and validity of the fuzzy delphi instrument of Islamic cognitive domains running head: Reliability and validity of Islamic cognitive domains. International Journal of Academic Research in Progressive Education and Development, 13(2), 943–956. https://doi.org/10.6007/ijarped/v13-i2/21201