KESULITAN BELAJAR MATEMATIKA: ANALISIS PENGETAHUAN AWAL [DIFFICULTY IN LEARNING MATHEMATICS: PRIOR KNOWLEDGE ANALYSIS]
DOI:
https://doi.org/10.19166/johme.v4i1.2091Trefwoorden:
learning difficulties, mathematics epistemology, prior knowledge, thinking process, constructivism, kesulitan belajar, epistemologi matematika, pengetahuan awal, konstruktivismeSamenvatting
In line with constructivism theory, prior knowledge is important in learning. Prior knowledge is the basis for a person being able to accept any new information that has been given. The background of this paper is the recognition that a number of students have difficulty learning mathematics. The results of observations when teaching grade 12 students about the matrix show that students still have difficulty in performing addition and subtraction arithmetic operations. This fact shows that there is a problem in students' prior knowledge. This paper aims to see the importance of the position of initial knowledge in student learning difficulties. This paper is a literature review. The results obtained show that initial knowledge is a source of student learning difficulties. This can be seen from the nature of mathematics and the thinking process of students in learning mathematics. From the nature of mathematics, according to constructivism, knowledge is acquired in a progressive constructive manner. Difficulties will arise when the prior knowledge is epistemologically different from the new knowledge. From the thinking process, students use their prior knowledge to construct new knowledge or respond to new information. The implication is that learning difficulties will arise when there is a conflict between prior knowledge and new knowledge.
BAHASA INDONESIA ABSTRACT: Sejalan dengan teori konstruktivisme, pengetahuan awal (prior knowledge) merupakan hal penting dalam pembelajaran. Pengetahuan awal menjadi landasan bagi seseorang untuk mampu menerima informasi baru yang telah diberikan. Hal yang melatar belakangi tulisan ini adalah banyaknya anak didik yang kesulitan belajar matematika. Hasil observasi ketika mengajar SMA kelas XII tentang matriks menunjukkan siswa masih kesulitan dalam melakukan operasi hitung penjumlahan dan pengurangan. Hal tersebut menunjukkan ada masalah dalam pengetahuan awal siswa. Tujuan penulisan adalah untuk melihat pentingnya posisi pengetahuan awal dalam kesulitan belajar siswa. Tulisan ini merupakan kajian literatur. Hasil yang diperoleh menunjukkan pengetahuan awal merupakan sumber kesulitan belajar siswa. Hal ini dilihat dari natur matematika dan proses berpikir siswa dalam belajar matematika. Dari natur matematika, menurut teori konstruktivisme, pengetahuan diperoleh secara konstruktif progresif. Implikasinya, kesulitan akan muncul ketika secara epistemology pengetahuan awal berbeda dengan pengetahuan yang akan dipelajari. Dari proses berpikir, dalam membentuk pengetahuan baru atau merespon informasi yang dihadapkan padanya, siswa menggunakan pengetahuan awalnya. Implikasinya, kesulitan belajar akan muncul ketika terjadi konflik antara pengetahuan awal dengan pengetahuan yang akan dipelajari.
Referenties
Adhi, Y., Winardi, Y., & Listiani, T. (2018). Penerapan model integrasi biblika Bryan Smith tahap 2 pada pembelajaran matematika untuk meningkatkan pemahaman Wawasan Kristen Alkitabiah (WAK) siswa kelas XI IPA-2 di suatu SMA di Toraja [The implementation of the Bryan Smith stage 2 Biblical integration model in learning mathematics to improve the understanding of a Biblical Christian Worldview (BCW) of grade 11 Science-2 students in a high school in Toraja]. JOHME: Journal of Holistic Mathematics Education, 2(1), 45-56. https://doi.org/10.19166/johme.v2i1.979
Bona, M. F. (2018). Indonesia darurat matematika. Retrieved from https://www.beritasatu.com/irawati-diah-astuti/nasional/521939/indonesia-darurat-matematika
Brousseau, G. (2011). Theory of didactical situations in mathematics: Didactique des mathematiques, 1970-1990. Dordrecht, Netherlands: Springer.
Darmayasa, J. B. (2018). Landasan, tantangan, dan inovasi berupa konteks ethnomathematics dalam pembelajaran matematika sekolah menengah pertama. JNPM (Jurnal Nasional Pendidikan Matematika), 2(1), 9-13. https://doi.org/10.33603/jnpm.v2i1.709
Ernest, P. (2016). Philosophy of mathematics education. Abingdon, England: Routledge.
Ernest, P. (2015). The philosophy of mathematics education: Stephen Lerman’s contributions. Shifts in the Field of Mathematics Education, 203-213. https://doi.org/10.1007/978-981-287-179-4_14
Firmansyah, M. A. (2017). Peran kemampuan awal matematika dan belief matematika terhadap hasil belajar. Prima: Jurnal Pendidikan Matematika, 1(1), 55-68. https://doi.org/10.31000/prima.v1i1.255
Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, Netherlands: Reidel.
Ghufron, M. N., & Risnawita, R. (2015). Kesulitan belajar pada anak: Identifikasi faktor yang berperan. Elementary: Islamic Teacher Journal, 3(2), 297-311. Retrieved from https://journal.iainkudus.ac.id/index.php/elementary/article/view/1455/1331
Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching. ZDM, 44(5), 601-612. https://doi.org/10.1007/s11858-012-0438-6
Howell, R. W., & Bradley, J. (2011). Mathematics through the eyes of faith. New York, NY: HarperOne.
Job, P., & Schneider, M. (2014). Empirical positivism, an epistemological obstacle in the learning of calculus. ZDM, 46(4), 635-646. https://doi.org/10.1007/s11858-014-0604-0
Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist, 58(9), 697-720. https://doi.org/10.1037/0003-066x.58.9.697
Kansanen, P. (1999). Teaching as teaching-studying-learning interaction. Scandinavian Journal of Educational Research, 43(1), 81-89. https://doi.org/10.1080/0031383990430105
Kemendikbud. (2016). Peraturan menteri pendidikan dan kebudayaan nomor 21 tahun 2016 tentang standar isi pendidikan dasar dan menengah. Retrieved from http://bsnp-indonesia.org/wp-content/uploads/2009/06/Permendikbud_Tahun2016_Nomor021_Lampiran.pdf
Kristiana, T. B., Winardi, Y., & Hidayat, D. (2017). Biblical integration in a mathematics classroom: A qualitative research in a senior high school. JOHME: Journal of Holistic Mathematics Education, 1(1), 1-9. https://doi.org/10.19166/johme.v1i1.709
Meletiou, M. (2003). On the formalist view of mathematics: Impact on statistics instruction and learning. Proceedings of the Third European Conference in Mathematics Education. Bellaria, Italy: European Society for Research in Mathematics Education. Retrieved from https://www.mathematik.uni-dortmund.de/~erme/CERME3/Groups/TG5/TG5_meletiou_cerme3.pdf
Meletiou-Mavrotheris, M. (2007). The formalist mathematical tradition as an obstacle to stochastical reasoning. Philosophical Dimensions in Mathematics Education, 131-155. https://doi.org/10.1007/978-0-387-71575-9_7
Nickel, J. (2001). Mathematics: Is God silent?. Vallecito, CA: Ross House Books.
Organisation for Economic Co-operation and Development. (2019). PISA 2018 results (Volume I): What students know and can do. Paris, France: OECD Publishing.
Paladang, K. K., Indriani, S., & Dirgantoro, K. P. S. (2018). Analisis kesalahan siswa kelas VIII SLH Medan dalam mengerjakan soal matematika materi fungsi ditinjau dari prosedur Newman [Analyzing students’ errors in solving mathematics problems in function topics based on Newman’s procedures in grade 8 at SLH Medan]. JOHME: Journal of Holistic Mathematics Education, 1(2), 93-103. https://doi.org/10.19166/johme.v1i2.798
Payung, L. M., Ramadhan, A., & Budiarsa, I. M. (2016). Pengaruh pengetahuan awal, kecerdasan emosional, dan motivasi belajar terhadap hasil belajar IPA siswa kelas VIII SMP Negeri 3 Parigi. e-Jurnal Mitra Sains, 4(3), 59-67. Retrieved from https://media.neliti.com/media/publications/154263-ID-pengaruh-pengetahuan-awal-kecerdasan-emo.pdf
Poythress, V. S. (1967). Foundations of Christian scholarship: Essay in the Van Til perspective. Vallecito, CA: Ross House Books.
Poythress, V. S. (2015). Redeeming mathematics: A God-centered approach. Wheaton, Illinois: Crossway.
Purwana, U. (2012). Profil pengetahuan awal (prior knowledge) siswa SMP tentang kemagnetan. Jurnal Pendidikan MIPA, 13(2), 117-124. Retrieved from http://jurnal.fkip.unila.ac.id/index.php/jpm/article/view/406/162
Putra, R. W. Y. (2015). Pembelajaran konflik kognitif untuk meningkatkan kemampuan komunikasi matematis siswa berdasarkan kategori pengetahuan awal matematis. Al-Jabar: Jurnal Pendidikan Matematika, 6(2), 155-166. Retrieved from http://ejournal.radenintan.ac.id/index.php/al-jabar/article/view/44/38
Saragih, M. J., Hidayat, D., & Tamba, K. P. (2019). Implikasi pendidikan yang berpusat pada Kristus dalam kelas matematika [The implications of Christ-center education for mathematics classes]. JOHME: Journal of Holistic Mathematics Education, 2(2), 97-107. https://doi.org/10.19166/johme.v2i2.1695
Schwarz, B. B. (2014). Psychological approaches in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Dordrecht, Netherlands: Springer. https://doi.org/10.1007/978-94-007-4978-8_167
Tamba, K. P., Saragih, M. J., & Listiani, T. (2018). Learning trajectory of quadratic inequality. JOHME: Journal of Holistic Mathematics Education, 2(1), 12-21. https://doi.org/10.19166/johme.v2i1.1202
Tamba, K. P., & Siahaan, M. M. L. (2020). Pembuat nol sebagai hambatan didaktis dalam pertidaksamaan kuadrat. JNPM (Jurnal Nasional Pendidikan Matematika), 4(2), 292-307. https://doi.org/10.33603/jnpm.v4i2.3614
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. https://doi.org/10.1007/bf00305619
Thompson, P. W. (2014). Constructivism in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Dordrecht, Netherlands: Springer. https://doi.org/10.1007/978-94-007-4978-8_31
Tsamir, P. (2007). When intuition beats logic: Prospective teachers’ awareness of their same sides - same angles solutions. Educational Studies in Mathematics, 65(3), 255-279. https://doi.org/10.1007/s10649-006-9053-1
Wati, E., & Saragih, M. J. (2018). Kesulitan belajar matematika berkaitan dengan konsep pada topik aljabar: Studi kasus pada siswa kelas VII sekolah ABC Lampung [Difficulties in learning mathematics concepts in algebra: A case study of grade VII students in ABC school Lampung]. Polyglot: Jurnal Ilmiah, 14(1), 53-64. https://doi.org/10.19166/pji.v14i1.453
Zderad, J. (2004). Creationism - A viable philosophy of mathematics. Retrieved from https://www.semanticscholar.org/paper/Creationism-%E2%80%93-A-Viable-Philosophy-of-Mathematics-Zderad/f0d46f161ed749284003b585c492830eefb4e0e7?p2df
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