Epistemological Obstacles on The Quadratic Inequality

https://doi.org/10.24042/ajpm.v11i2.6858

Kimura Patar Tamba, Melda Jaya Saragih

Abstract


Students often experience difficulties and errors in solving quadratic inequality problems. These difficulties and errors are not only caused by students’ ignorance or misconceptions, but also caused by epistemological obstacles. This study aimed to determine the epistemological obstacles faced by the junior high school students in quadratic inequality. This research was a qualitative research that involved 105 ninth-grade students at one of the junior high schools in Bandung, Indonesia. The data were collected through open-ended tasks and task-based interviews. The data were analyzed using the inductive coding process to classify students’ errors.  The descriptive analysis was carried out to reveal students’ ways of understanding and ways of thinking behind each error to be compared with historical analysis. Based on the description of ways of understanding and ways of thinking and comparison with this historical phenomenon, the epistemological obstacles had be confirmed. The results showed that there were epistemological obstacles in quadratic inequalities. The epistemological obstacles consisted of students' quadratic equation knowledge acts and students' arithmetic knowledge acts. However, no epistemological obstacles were found in the development history of quadratic inequality. Students' epistemological obstacles were parallel to the historical phenomena of quadratic inequality.

 

 


Keywords


Epistemological obstacles; Quadratic inequality; Ways of thinking; Ways of understanding.

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References


Bicer, A., Capraro, R. M., & Capraro, M. M. (2014). Pre-service teacher’s linear and quadratic inequality understanding. International Online Journal of Educational Science, 3(3), 221–229.

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 and Technology Education, 3(3), 221–229. https://doi.org/10.12973/ejmste/75401

Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. In Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2

Brown, S. A. (2008). Exploring epistemological obstacles to the development of mathematics induction. The 11th Conference for Research on Undergraduate Mathematics Education, 1–19.

Cohen, L., Manion, L., & Morrison, K. (2018). Research Methods in Education (8th ed.). Routledge.

Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: Choosing among five approaches. In SAGE (4th ed.). SAGE.

Fuadiah, N. F. (2015). Epistemological Obstacles on Mathematic’S Learning in Junior High School Students: a Study on the Operations of Integer Material. May, 17–19. https://eprints.uny.ac.id/23197/1/ME - 43.pdf

Peraturan Menteri Pendidikan Dan Kebudayaan Nomor 21 Tahun 2016 Tentang Standar Isi Pendidikan Dasar Dan Menengah, 3345 (2016).

Lockwood, E., & Weber, E. (2015). Ways of Thinking and Mathematical Practices. The Mathematics Teacher, 108(6), 461. https://doi.org/10.5951/mathteacher.108.6.0461

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. https://doi.org/10.5901/mjss.2014.v5n27p634

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. https://doi.org/10.5901/mjss.2014.v5n27p716

Mananggel, M. B. (2020). Diagnosing Students’ Difficulties in Solving Mathematical Word Problem. JUPITEK: Jurnal Pendidikan Matematika, 2(2), 61–68. https://doi.org/10.30598/jupitekvol2iss2pp61-68

NCTM. (2000). Principles and Standard for School Mathematics. he National Council of Mathematics of Teacher of Mathematics Inc.

Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020). Epistemological Obstacles: An Overview of Thinking Process on Derivative Concepts by APOS Theory and Clinical Interview. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032028

Schneider, M. (2014). Epistemological Obstacles in Mathematics Education (S. Lerman (ed.); Vol. 52, Issue 1). Springer. https://doi.org/10.1007/s11858-020-01130-4

Sierpińska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18(4), 371–397. https://doi.org/10.1007/BF00240986

Subroto, T., & Suryadi, D. (2018). Epistemological obstacles in mathematical abstraction on abstract algebra. Journal of Physics: Conference Series, 1132(1). https://doi.org/10.1088/1742-6596/1132/1/012032

Sunariah, L., & Mulyana, E. (2020). The didactical and epistemological obstacles on the topic of geometry transformation. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032089

Tamba, K. P. (2015). Pengembangan Desain Didaktis Pertidaksamaan Kuadrat pada Sekolah Menengah Atas. Universitas Pendidikan Indonesia.

Tamba, K. P., Saragih, M. J., & Listiani, T. (2018). Learning Trajectory of Quadratic Inequality. JOHME: Journal of Holistic Mathematics Education, 2(1), 12. 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. https://doi.org/10.33603/jnpm.v4i2.3614




DOI: https://doi.org/10.24042/ajpm.v11i2.6858

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Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.