Pembuat Nol sebagai Hambatan Didaktis dalam Pertidaksamaan Kuadrat
DOI:
https://doi.org/10.33603/jnpm.v4i2.3614Abstract
Abstrak. Penelitian ini bertujuan untuk menganalisis hambatan didaktis pada pertidaksamaan kuadrat. Pilihan didaktis sering didasarkan pada intuisi guru akan kompleksitas dan ketidaklengkapan informasi akan sebuah pendekatan. Melalui analisis didactical obstacles, guru dapat menghindari atau setidaknya berhati-hati pada suatu pendekatan yang terlihat sederhana dan mudah, tetapi menuntun pada terjadinya hambatan belajar. Penelitian menggunakan pendekatan kualitatif dengan paradigma interpretif dalam kerangka penelitian desain didaktis. Penelitian dilakukan pada 105 siswa kelas IX dan satu orang guru pada salah satu Sekolah Menengah Atas di Bandung. Pengumpulan data dilakukan melalui soal tes pertidaksamaan kuadrat, analisis buku pegangan guru, wawancara siswa dan guru. Hasil pekerjaan siswa atas soal pertidaksamaan kuadrat dianalisis untuk melihat cara mengetahui siswa dan pemahaman siswa. Cara mengetahui ini akan dibandingkan dengan pilihan didaktis yang digunakan guru. Hasil penelitian menunjukkan terdapat didactical obstacles dalam pertidaksamaan kuadrat. Hambatan didaktis tersebut adalah penggunaan metafora pembuat nol sebagai konsep utama dalam penyelesaian pertidaksamaan kuadrat. Pembuat nol ini merupakan implikasi dari penggunaan pendekatan sign chart. Untuk itu guru perlu berhati-hati menggunakan pendekatan garis bilangan dan metafora pembuat nol sebagai pilihan pendekatan didaktis. Penggunaan pendekatan dengan lintasan belajar yang dimulai dari pendekatan fungsi, dapat dipertimbangkan guru dalam pembelajaran pertidaksamaan kudarat.
Kata Kunci: Pembuat Nol, Hambatan Didaktis, Pertidaksamaan Kuadrat.
References
Abramovich, S. (2005). Spreadsheet modeling as a didactical framework for inequality-based reduction. International Journal of Mathematical Education in Science and Technology, 37 (5), 527–541.
Almog, N., & Ilany, B.S. (2012). Absolute value inequalities: high school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364.
Bazzini, L. dan Tsamir, P. (2001). Research-based instruction: widening students’ perspective when dealing with inequality. Proceedings of the 12th ICMI Study The Future of Teaching and Learning of Algebra, 61-68. The University of Melbourne, Melbourne.
Bicer, A., Capraro, R.M., & Capraro, M. M. (2014). Pre-service teacher’s linear and quadratic inequality understanding. International Journal for Mathematics Teaching and Learning, 15(1), 1-10.
Bingolbali, E., Akkoç, H., Ozmantar, M. F., & Demir, S. (2011). Pre-service and in-service teachers’ views of the sources of students’ mathematical difficulties. International Electronic Journal of Mathematics Education, 6(1), 40-59.
Blanco, L. J., & Garrote, M. (2007). Difficulties in learning inequalities in students of the first year of pre-university education in Spain. Eurasia Journal of Mathematics, Science & Technology Education, 3(3), 221-229.
Brown, S., A. (2008). Exploring epistemological obstacles to the development of mathematics induction. Proceedings of the 11th Conference for Research on Undergraduate Mathematics Education, 1–19.
Brousseau, G. (2002). Theory of Didactical Situation in Mathematics. Dordrecht: Kluwer Academic Publishers.
Çilta?, A. & Tatar, E. (2011). Diagnosing Learning Difficulties Related to the Equation and Inequality that Contain Terms with Absolute Value. International Online Journal of Educational Sciences, 3(2), 461-473.
Cohen, L., Manion, L., & Morrison, K. (2011). Research methods in education. London: Routledge Falmer.
Cornu B. (2002). Limits. In: Tall D. (Eds.), Advanced Mathematical Thinking. Mathematics Education Library, 11 (153-166) . Springer, Dordrecht.
Cortina, J. L., Visnovska, J., & Zúñiga, C. (2013). Equipartition is a didactical obstacle in fraction instruction. Acta Didactica Universitatis Comenianae Mathematics, 14(1), 1–18.
Dobbs, D., & Peterson, J. (1991). The sign-chart method for solving inequalities. The Mathematics Teacher, 84(8), 657-664.
Kemendikbud. (2016). Peraturan menteri pendidikan dan kebudayaan nomor 21 tahun 2016 tentang standar isi pendidikan dasar dan menengah. Jakarta: Kemendikbud.
Kieran, C. (2004). The equation/inequality connection in constructing meaning for inequality situations. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 143–127. Bergen, Norway: Bergen University College.
Linchevski, L., & Sfard, A. (1991). Rules without reasons as processes without objects – the case of equations and inequalities. Proceedings of PME15, 2, 317-324, Assisi, Italy.
Mahmood, M., & Al-Mirbati, R. (2017). An algebraic approach for solving quadratic inequalities. Australian Senior Mathematics Journal, 31(2), 31-41.
Makonye, J., & Shingirayi, M. (2014). The obstacles faced by the learners in the learning of quadratic inequalities. Mediterranean Journal of Social Sciences, 5(27), 716-725.
Makonye, J., & Nhlanhla, S. (2014). Exploring “non-science” grade 11 learners’ errors in solving quadratic equations. Mediterranean Journal of Social Sciences, 5(27), 634-644.
Mananggel, M. (2020). Diagnosis of students difficulties in solving word problem related to the quadratic innequalities using mapping mathematics. JUPITEK: Jurnal Pendidikan Matematika, 2(2), 61-68.
Manno, G. (2005). Embodiment and a-didactical situation in the teaching-learning of the perpendicular straight lines concept. Unpublished Thesis. Palermo: Unipa.
McLaurin, S. (1985). A unified way to teach the solution of inequalities. The Mathematics Teacher, 78(2), 91-95.
Moru, E. (2007). Talking with the literature on epistemological obstacles. For the Learning of Mathematics, 27(3), 34-37.
NCTM. (2000). Principles and Standard for School Mathematics. Reston Virginia: The National Council of Mathematics of Teacher of Mathematics, Inc.
Nyikahadzoyi, M. R., Mapuwei, T., & Chinyoka, M. (2013). Some cognitive obstacles faced by ‘a’ level mathematics students in understanding inequalities: a case study of bindura urban high schools. International Journal of Academic Research in Progressive Education and Development, 2(2), 2226–6348.
Sackur, K. (2004). Problems related to the use of graphs in solving inequalities. Proceedings of the 28th Conference of the International Group of Psychology of Mathematics Education, Bergen, Norway, 1, 148-152.
Suryadi, D. (2013). Didactical Design Research (DDR) dalam pengembangan pembelajaran matematika. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. Bandung, Indonesia: STKIP Siliwangi.
Tamba, K. P., Saragih, M. J., & Listiani, T. (2018). Learning trajectory of quadratic inequality. JOHME: Journal of Holistic Mathematics Education, 2(1), 12-21. DOI:10.19166/johme.v2i1.1202
Tsamir, P., & Almog, N. (2001). Students' strategies and difficulties: the case of algebraic inequalities. International Journal Of Mathematical Education In Science And Technology, 32(4), 513-524.
Tsamir, P., & Bazzini, L. (2004). Consistencies and inconsistencies in students' solutions to algebraic ‘single-value’ inequalities. International Journal of Mathematical Education in Science and Technology, 35(6), 793-812.
Tsamir, P., & Reshef, M. (2006). Students' preferences when solving quadratic inequalities. Focus on Learning Problems in Mathematics, 28(1), 37-50.
Ureyen, M., Mahir, N., & Cetin, N. (2006). The mistakes made by the students taking a calculus course in solving inequalities. Electronic International Journal for Mathematics Teaching and Learning, 7(1), 1-6.
Yin, L.Y. (2005). Understanding student?s quadratic inequality misconception through an in-depth interview. Third International Qualitative Research Convention 2005. Qualitative Research Experience Across Discipline, Universiti Teknologi Malaysia & Qualitative Research Association of Malaysia, Johor, Malaysia.
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