Strategies to Minimize Students Learning Obstacle in Fractions A Grounded Theory
Abstract
Abstract: Fractions are a fundamental mathematical concept that is quite important for life. However, the existing facts prove that fraction concepts in mathematics are a problem that has become a learning obstacle for students in schools. Therefore, this study aims to find alternative strategies to minimize the learning obstacle. The researcher then used a grounded theory design to find this strategy. Researchers also combined research design with phenomenology to find the core categories. Researchers used systematic analysis (open, axial, and selective), combined with thematic analysis with NVivo-12. The analysis results revealed that ontogenic in the form of participants were unable to simplify, determine equivalent fractions, and carelessness was the most significant learning obstacle. The strategy obtained was the use of a didactic design based on a didactical situation in collaboration with didactical design research, which would minimize student learning barriers on fractions.
Keywords: fractions, learning obstacle, grounded theory, phenomenology, didactical situation.
Abstrak: Pecahan merupakan konsep matematika dasar yang cukup penting bagi kehidupan. Namun, fakta yang ada membuktikan bahwa konsep pecahan dalam matematika merupakan masalah yang menjadi hambatan belajar siswa di sekolah. Oleh karena itu, penelitian ini bertujuan untuk mencari alternatif strategi untuk meminimalkan hambatan belajar. Peneliti kemudian menggunakan desain grounded theory untuk menemukan strategi tersebut. Peneliti juga menggabungkan desain penelitian dengan fenomenologi untuk menemukan kategori inti. Peneliti menggunakan analisis sistematis (terbuka, aksial, dan selektif), dikombinasikan dengan analisis tematik dengan NVivo 12. Hasil analisis menunjukkan bahwa siswa mengalami hambatan ontogenik, seperti siswa tidak dapat menyederhanakan, menentukan pecahan senilai, dan kecerobohan merupakan hambatan belajar yang paling signifikan. Strategi yang diperoleh adalah penggunaan desain didaktis berdasarkan situasi didaktis yang dikombinasikan dengan penelitian desain didaktis, yang akan meminimalkan hambatan belajar siswa dalam pembelajaran pecahan.
Kata kunci: pecahan, hambatan belajar, grounded theory, fenomenologi, situasi didaktis.
Full Text:
PDFReferences
Aebi, M. F., & Linde, A. (2015). The Epistemological Obstacles in Comparative Criminology: A Special Issue Introduction. European Journal of Criminology, 12(4), 381–385. https://doi.org/10.1177/1477370815595311
Ballard, C. L., & Johnson, M. F. (2004). Basic Math Skills and Performance in an Introductory Economics Class. Journal of Economic Education, 35(1), 3–23. https://doi.org/10.3200/JECE.35.1.3-23
Bertschy, F., Künzli, C., & Lehmann, M. (2013). Teachers’ Competencies for the Implementation of Educational Offers in the Field of Education for Sustainable Development. Sustainability (Switzerland), 5(12), 5067–5080. https://doi.org/10.3390/su5125067
Bosch, M., Chevallard, Y., & Gascon, J. (2005). Science or Magic? The Use of Models and Theories in Didactics of Mathematics. CERME 4, (December), 1254–1263. https://bit.ly/3JFcwiP
Boyd, P., & Ash, A. (2018). Mastery Mathematics: Changing Teacher Beliefs Around in-Class Grouping and Mindset. Teaching and Teacher Education, 75, 214–223. https://doi.org/10.1016/j.tate.2018.06.016
Brezavšček, A., Jerebic, J., Rus, G., & Žnidaršič, A. (2020). Factors Influencing Mathematics Achievement of University Students of Social Sciences. Mathematics, 8(12), 1–24. https://doi.org/10.3390/math8122134
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. New York: Kluwer Academic Publishers. https://id.id1lib.org/book/2245294/b37452
Chacón, A. A. M. (2005). Difficulties Found by the Students During the Study of Substraction of Integer Numbers. CERME, 4, 629–721. http://erme.site/cerme-conferences/cerme-4/
Çiltaş, 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. Retrieved from www.iojes.net
Clabaugh, G. K. (2010). The Educational Theory of Lev Vygotsky: A Multi-Dimensional Analysis. NewFoundations. https://bit.ly/3sOGom3
Clements, D. H., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thinking and Learning, 6(2), 81–89. https://bit.ly/3gVVRuR
Clinton, V., & Walkington, C. (2019). Interest-Enhancing Approaches to Mathematics Curriculum Design: Illustrations and Personalization. Journal of Educational Research, 112(4), 495–511. https://doi.org/10.1080/00220671.2019.1568958
Coetzee, J., & Mammen, K. J. (2017). Science and Engineering Students’ Difficulties with Fractions at Entry-Level to University. IEJME, 12(3), 281–310. https://doi.org/10.29333/iejme/614
Cortina, José Luis, Višnovská, J., & Zúñiga, C. (2015). An Alternative Starting Point for Fraction Instruction. International Journal for Mathematics Teaching and Learning, 1–28. https://bit.ly/3oWOTKB
Cortina, Jose Luis, Zuniga, C., & Visnovska, J. (2014). Equipartition as a Didactical Obstacle in Fraction Instruction. Acta Didactica Universitatis Comenianae Mathematics, 14, 1–18. https://bit.ly/3JGfC69
Creswel, J. W. (2017). Research Design: Pendekatan Metode Kualitatif, Kuantitatif, dan Campuran. Yogyakarta: Pustaka Pelajar.
Creswell, J. W. (2012). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. In Educational Research (6th ed.). https://doi.org/10.1017/CBO9781107415324.004
Duzenli-Gokalp, N., & Sharma, M. D. (2010). A Study on Addition and Subtraction of Fractions: The Use of Pirie and Kieren Model and Hands-On Activities. Procedia - Social and Behavioral Sciences, 2(2), 5168–5171. https://doi.org/10.1016/j.sbspro.2010.03.840
Fauzi, I., & Suryadi, D. (2020). Learning Obstacle the Addition and Subtraction of Fraction in Grade 5 Elementary Schools. MUDARRISA: Jurnal Kajian Pendidikan Islam, 12(1), 51–68. https://doi.org/10.18326/mdr.v12i1.51-68
Fitriani, H. N., Turmudi, T., & Prabawanto, S. (2018). Analysis of Students Error in Mathematical Problem Solving Based on Newman’s Error Analysis. International Conference on Mathematics and Science Education, 3, 791–796. https://bit.ly/3LKNMHK
Frudenthal, H. (2002). Didactical Phenomenology of Mathematical Structurs. New York: Kluwer Academic Publishers. http://dx.doi.org/10.1007/0-306-47235-X
Gagani, R. F. M., & Jr, F. M. D. (2019). Characterizing the Difficulty in Fraction Operation. International Journal of Advanced Research and Publications, 3(6), 168–174. https://bit.ly/3v3xGTw
Galante, D. (2014). The Use of the History of Mathematics in the Teaching of Preservice Teachers. Redimat, 3(2), 110–120. https://doi.org/10.4471/redimat.2014.45
Greenberg, D. (1996). Funny & Fabulous Fraction Stories: 30 Reproducible Math Tales and Problems to Reinforce Important Fraction Skills. New York: Scholastic Professional Books. https://id.id1lib.org/book/1272430/47bb75
Gunawan, M. S., Putri, R. I. I., & Zulkardi. (2017). Learning Fractions through Swimming Context for Elementary School Students. Advances in Social Science, Education and Humanities Research, 100, 61–65. https://doi.org/10.2991/seadric-17.2017.14
Harel, G. (2008). What is Mathematics? A Pedagogical Answer to a Philosophical Question. In Bonnie Gold & R. A. Simons (Eds.), Proof and Other Dilemmas: Mathematics and Philosophy (pp. 265–290). Washington: The Mathematical Association of America, Inc. https://bit.ly/3JzT6vr
Iulia, & Gugoiu, T. (2006). The Book of Fractions. Mississauga: La Citadelle. https://studylib.net/doc/7955385/the-book-of-fractions
Johnson, M., & Kuennen, E. (2006). Basic Math Skills and Performance in an Introductory Statistics Course. Journal of Statistics Education, 14(2), 1–15. https://doi.org/10.1080/10691898.2006.11910581
Joutsenlahti, J., & Perkkila, P. (2019). Sustainability Development in Mathematics Education-A Case Study of What Kind of Meanings Do Prospective Class Teachers Find for the Mathematical Symbol “2/3”? Sustainability, 11(457), 1–15. https://doi.org/10.3390/su11020457
Kennedy, L. M., Tipps, S., & Johnson, A. (2008). Guiding Children’s Learning of Mathematics (11th.). Belmont: Thomson Wadsworth. https://bit.ly/3v0uGHA
Kilic, C. (2015). Analyzing pre-service primary teachers’ fraction knowledge structures through problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1603–1619. https://doi.org/10.12973/eurasia.2015.1425a
Ku, H. B., & Yuen-Tsang, A. W. K. (2018). Capacity Building. The SAGE Handbook of Governance, (April), 1–12. https://doi.org/10.4135/9781446200964.n30
Lestari, I. (2014). Pengaruh Waktu Belajar dan Minat Belajar terhadap Hasil Belajar Matematika. Jurnal Formatif, 3(2), 115–125. http://dx.doi.org/10.30998/formatif.v3i2.118
Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers : The case of fraction division Knowledge and confidence of pre-service mathematics teachers : the case of fraction division. ZDM, 40, 833–843. https://doi.org/10.1007/s11858-008-0148-2
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Fraction and Decimal Arithmetic. Development Review, 38, 201–221. https://doi.org/10.1016/j.dr.2015.07.008
Malone, A. S., & Fuchs, L. S. (2017). Error Patterns in Ordering Fractions among At-Risk Fourth-Grade Students. Journal of Learning Disabilities, 176(5), 139–148. https://doi.org/10.1016/j.physbeh.2017.03.040
Marmur, O., Yan, X., & Zazkis, R. (2019). Research in Mathematics Education Fraction Images: The Sase of Six and a Half. Research in Mathematics Education, 1–26. https://doi.org/10.1080/14794802.2019.1627239
Morais, C., & Serrazina, L. (2017). Decimal Numbers: A Potential Bridge between Rational Numbers Representations. Journal of Mathematics Education, 10(1). https://doi.org/10.26711/007577152790004
Moru, E. K. (2007). Talking with the Literature on Epistemological Obstacles. For the Learning Mathematics, 27(3), 34–37. http://www.jstor.org/stable/40248586
Nessipbayeva, O. (2012). The Competencies of the Modern Teacher. International Perspectives on Education, 148–154. Retrieved from http://bit.ly/2fRwNoY
Nguyen, P. L., Duong, H. T., & Phan, T. C. (2017). Identifying the Concept Fraction of Primary School Students: The Investigation in Vietnam. Educational Research and Reviews, 12(8), 531–539. https://doi.org/10.5897/err2017.3220
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic Analysis: Striving to Meet the Trustworthiness Criteria. International Journal of Qualitative Methods, 16, 1–13. https://doi.org/10.1177/1609406917733847
Ojose, B. (2015). Students’ Misconceptions in Mathematics: Analysis of Remedies and What Research Says. Ohio Journal of School Mathematics, 72, 30–34. https://bit.ly/3oZitPv
Petit, M. M., Laird, R. E., & Marsden, E. L. (2010). A Focus on Fractions: Bringing Research to the Classroom. New York: Routledge. https://id.id1lib.org/book/2871316/32f937
Quessada, M. P., & Clément, P. (2007). An Epistemological Approach to French Syllabi on Human Origins During the 19th and 20th Centuries. Science and Education, 16(9–10), 991–1006. https://doi.org/10.1007/s11191-006-9051-9
Rizkianto, I., Zulkardi, & Darmawijaya. (2013). Constructing geometric properties of rectangle, square, and triangle in the third grade of Indonesian primary schools. Journal on Mathematics Education, 4(2), 160–171. https://doi.org/10.22342/jme.4.2.414.160-171
Rodriguez, M. (2012). The Importance Teaching of Listening and Speaking Skill. Madrid: Universitas Complvtensis Matritensis. http://data.conferenceworld.in/SRNM/49.pdf
Roni, A., Zulkardi, Z., & Putri, R. I. I. (2017). Learning Divisions of Fractions through Sprint Running Pictures. Journal of Education and Learning, 11(4), 381. https://doi.org/10.11591/edulearn.v11i4.5982
Roy, J. R., & Roy, G. (2008). Holiday Fractions (Math All Around). New York: Marshal Cavendish Benchmark. https://id.id1lib.org/book/1223222/3ab74f
Salkind, G. M., & Hjalmarson, M. (2007). Mathematical Representations. Virginia: George Mason University. https://bit.ly/3rZFXpE
Simon, M. A., Placa, N., Kara, M., & Avitzur, A. (2018). Empirically-Based Hypothetical Learning Trajectories for Fraction Concepts: Products of the Learning through Activity Research Program. Journal of Mathematical Behavior, (August), 1–13. https://doi.org/10.1016/j.jmathb.2018.03.003
Smaniego, A. H. F., & Barrera, S. V. (1999). Brousseau in Action: Didactical Situation for Learning How to Graph Functions. ATCM, 1–9. https://atcm.mathandtech.org/EP/1999/ATCMP020/PAPER/paper.pdf
Sollervall, H., & Iglesia, D. G. de la. (2016). Designing a Didactical Situation with Mobile and Web Technologies. CERME9, 2410–2417. Prague: Charles University in Prague. https://hal.archives-ouvertes.fr/hal-01289292
Suryadi, D. (2019a). Landasan Filosofis Penelitian Desain Didaktis (DDR). Bandung: Pusat Pengembangan DDR Indonesia.
Suryadi, D. (2019b). Penelitian Desain Didaktis (DDR) dan Implementasinya. Bandung: Gapura Press.
Tall, D. (2004). Building theories: The three worlds of mathematics. For the Learning of Mathematics, 24(1), 29–32. http://www.jstor.org/stable/40248444
Tall, D. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitive, 11, 195-215. https://bit.ly/3eMk3yA
Tall, D. (2008). The Transition to Formal Thinking in Mathematics. Mathematics Education Research Journal, 20(2), 5–24. http://dx.doi.org/10.1007/BF03217474
Tian, J., & Siegler, R. S. (2016). Fractions Learning in Children with Mathematics Difficulties. Journal of Learning Disabilities, 1–24. https://doi.org/10.1177/0022219416662032
Tokan, M. K., & Imakulata, M. M. (2019). The Effect of Motivation and Learning Behaviour on Student Achievement. South African Journal of Education, 39(1), 1–8. https://doi.org/10.15700/saje.v39n1a1510
Topciu, M., & Myftiu, J. (2015). Vygotsky Theory on Social Interaction and its Influence on the Development of Pre-School. European Journal of Social Science Education and Research, 2(3), 172–179. http://dx.doi.org/10.26417/ejser.v4i1.p172-179
Turmudi, T., Kusumah, Y., Juandi, D., & Mulyana, E. (2014). Development of Didactical Design of Mathematics Pedagogy Through Professional Program of Mathematics Teacher Education. Jurnal Pendidikan dan Pembelajaran Universitas Negeri Malang, 21(1), 10–23. https://bit.ly/3Bzexu6
Ubah, I. J. A., & Bansilal, S. (2018). Pre-Service Primary Mathematics Teachers’ Understanding of Fractions: An Action-Process-Object-Schema Perspective. South African Journal of Childhood Education, 8(2), 1–12. http://dx.doi.org/10.4102/sajce.v8i2.539
Verenikina, I. (2003). Vygotsky’s Socio-Cultural Theory and the Zone of Proximal Development. In E. H. Hasan, E. Gould, & I. Verenikina (Eds.), Information Systems and Activity Theory: Expanding the Horizon (pp. 1–8). Wollongong: University of Wollongong Press. https://bit.ly/3IcEWA4
Vollstedt, M., & Rezat, S. (2019). An Introduction to Grounded Theory with a Special Focus on Axial Coding and the Coding Paradigm. https://doi.org/10.1007/978-3-030-15636-7_4
Westenskow, A., & Moyer-packenham, P. (2013). Using an Iceberg Intervention Model to Understand Equivalent Fraction Learning When Students with Mathematical Learning Difficulties Use Different Manipulatives. International Journal of Technology in Mathematics Education, 23(2), 45–62. https://doi.org/10.1564/tme
Wijaya, A., Retnawati, H., Setyaningrum, W., Aoyama, K., & Sugiman. (2019). Diagnosing students’ learning difficulties in the eyes of Indonesian mathematics teachers. Journal on Mathematics Education, 10(3), 357–364. https://doi.org/10.22342/jme.10.3.7798.357-364
Yulianingsih, A., Febrian, & Dwinata, A. (2018). Analisis Kesalahan Konsep Pecahan pada Siswa Kelas VII A SMP Negeri 13 Satu Atap Tanjungpinang. Mosharafa: Jurnal Pendidikan Matematika, 7(2), 199–206. http://dx.doi.org/10.31980/mosharafa.v7i2.22
Refbacks
- There are currently no refbacks.
Copyright (c) 2022 Jurnal Pendidikan MIPA
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The copyright is reserved to The Jurnal Pendidikan MIPA that is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.