Analysis of the Elementary School Students' Learning Obstacles: A Case Study on the Concept of Fractions
(1) Universitas Pendidikan Indonesia
(2) Universitas Pendidikan Indonesia
(3) Universitas Pendidikan Indonesia
(4) Universitas Pendidikan Indonesia
(*) Corresponding Author
Abstract
Abstract
The research aimed to conduct an in-depth investigation of the learning obstacles faced by elementary students in the concept of fractions. Employing a qualitative method, this study involved the fourth and fifth graders of elementary schools as the participants. The data were collected both quantitatively and qualitatively. The quantitative data were collected through a test on the concept of fractions developed by the research team. Meanwhile, the qualitative data were collected via interviews. The data were then analyzed using quantitative and qualitative methods. The results of the quantitative data analysis indicated that the average number of students who answered the overall test questions correctly was 13.33%. Through qualitative analysis, it was found that the students experienced three types of learning obstacles including epistemological, didactical, and ontogenical obstacles. Epistemological obstacles were faced by the students in the construction of fractions as parts of a whole in the visualization of the model area. Didactical obstacles occurred in the construction of fractions as parts of a whole in the visualization of discrete models and improper fractions. Ontogenical obstacles occurred in the construct of fractions as measures, especially placing fractions on the number line. The findings of this study can be used as a basis for educators to develop learning designs on the concept of fractions in elementary schools.
Keywords: concept of fractions, learning obstacles, elementary school students.
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Abstrak
Penelitian ini bertujuan untuk melakukan investigasi mendalam tentang hambatan belajar yang dialami siswa sekolah dasar pada konsep pecahan. Dengan menggunakan metode kualitatif, penelitian ini melibatkan siswa kelas IV dan V sekolah dasar sebagai partisipan penelitian. Data dikumpulkan secara kuantitatif maupun kualitatif. Data kuantitatif dikumpulkan melalui tes konsep pecahan yang disusun dan dikembangkan tim peneliti. Sementara itu, data kualitatif diperoleh melalui wawancara. Data yang telah diperoleh kemudian dianalisis menggunakan metode kuantitatif dan kualitatif. Hasil analisis data kuantitatif menunjukkan bahwa banyaknya siswa yang berhasil menjawab keseluruhan pertanyaan tes dengan benar adalah 13.33%. Melalui analisis kualitatif, ditemukan bahwa siswa mengalami tiga jenis hambatan belajar yaitu hambatan epistimologis, didaktis, dan ontogenis. Hambatan epistimologis dialami siswa pada konstruk pecahan sebagai bagian dari keseluruhan dalam visualisai model area. Hambatan didaktis terjadi pada konstruk pecahan sebagai bagian dari keseluruhan dalam visualisasi model diskrit serta pecahan campuran. Hambatan ontogenis terjadi pada konstruk pecahan sebagai ukuran khususnya menempatkan pecahan pada garis bilangan. Temuan pada penelitian dapat digunakan sebagai dasar bagi pendidik dalam mengembangkan desain pembelajaran pada konsep pecahan di sekolah dasar.
Kata kunci: konsep pecahan, hambatan belajar, siswa sekolah dasar.
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Alajmi, A. H. (2012). How do Elementary Textbooks Address Fractions? A Review of Mathematics Textbooks in the Usa, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239–261. https://doi.org/10.1007/s10649-011-9342-1
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education. New York: Springer. https://doi.org/10.1007/978-1-4614-7966-6
Aydın, U., Tunç-Pekkan, Z., Taylan, R. D., Birgili, B., & Özcan, M. (2018). Impacts of a University–School Partnership on Middle School Students’ Fractional Knowledge: A Quasiexperimental Study. Journal of Educational Research, 111(2), 151–162. https://doi.org/10.1080/00220671.2016.1220358
Azid, N., Hasan, R., Mohamad Nazarudin, N. F., & Md-Ali, R. (2020). Embracing Industrial Revolution 4.0: The Effect of Using Web 2.0 Tools on Primary Schools Students’ Mathematics Achievement (Fraction). International Journal of Instruction, 13(3), 711–728. https://doi.org/10.29333/iji.2020.13348a
Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with Fractions Predicts Gains in Mathematics Achievement. Journal of Experimental Child Psychology, 113(3), 447–455. https://doi.org/10.1016/j.jecp.2012.06.004
Bailey, D. H., Zhou, X., Zhang, Y., Cui, J., Fuchs, L. S., Jordan, N. C., Gersten, R., & Siegler, R. S. (2015). Development of Fraction Concepts and Procedures in U.S. and Chinese Children. Journal of Experimental Child Psychology, 129, 68–83. https://doi.org/10.1016/j.jecp.2014.08.006
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. New York: Kluwer Academic Publisher. https://doi.org/10.1007/0-306-47211-2
Čadež, T. H., & Kolar, V. M. (2018). How Fifth-Grade Pupils Reason About Fractions: A Reliance on Part-Whole Subconstructs. Educational Studies in Mathematics, 99(3), 335–357. https://doi.org/10.1007/s10649-018-9838-z
Carvalho, G. S., Silva, R., Lima, N., Coquet, E., & Clément, P. (2004). Portuguese Primary School Children’s Conceptions About Digestion: Identification of Learning Obstacles. International Journal of Science Education, 26(9), 1111–1130. https://doi.org/10.1080/0950069042000177235
Charalambous, C. Y., & Hill, H. C. (2012). Teacher Knowledge, Curriculum Materials, and Quality of Instruction: Unpacking a Complex Relationship. Journal of Curriculum Studies, 44(4), 443–466. https://doi.org/10.1080/00220272.2011.650215
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a Theoretical Model to Study Students’ Understandings of Fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2
Ciosek, M., & Samborska, M. (2016). A False Belief About Fractions - What is Its Source? Journal of Mathematical Behavior, 42, 20–32. https://doi.org/10.1016/j.jmathb.2016.02.001
Clément, P. (2003). Situated Conceptions and Obstacles. The Example of Digestion / Excretion. In D. Psillos, P. Karioyoglou, V. Tselfes, E. Hatzikraniotis, G. Fassoulopoulos, & M. Kallery (Eds.). Science Education Research in the Knowledge-Based Society (pp. 89–97). Dordrecht: Springer. https://doi.org/10.1007/978-94-017-0165-5_10
Dewi, D. A. K., Suryadi, D., Suratno, T., Mulyana, E., & Kurniawan, H. (2017). Meaning of Fractions. Journal of Physics: Conference Series 812 012115, 1–6. https://doi.org/10.1088/1742-6596/755/1/011001
Diputra, K. S., Suryadi, D., Herman, T., & Jupri, A. (2022). Teacher’s Knowledge of Fractions in the Perspective of Didactic-Mathematical Knowledge. Journal of Engineering Science and Technology Special Issue on ICMScE, 136–143.
Empson, S. B., Levi, L., & Carpenter, T. P. (2011). The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School. Early Algebraization, 1, 409–428. https://doi.org/10.1007/978-3-642-17735-4_22
English, L. D. (2013). Mathematical Reasoning: Analogies, Metaphors, and Images. New York: Routledge
Fauzi, I., & Suryadi, D. (2020). The Analysis of Students’ Learning Obstacles on the Fraction Addition Material for Five Graders of Elementary Schools. Al Ibtida: Jurnal Pendidikan Guru MI, 7(1), 33. https://doi.org/10.24235/al.ibtida.snj.v7i1.6020
Gall, J. P., Gall, M. D., & Borg, W. R. (2014). Applying Educational Research: How to Read, Do, and Use Research to Solve Problems of Practice (6th ed.). United States: Pearson Education, Inc.
Geller, E. H., Son, J. Y., & Stigler, J. W. (2017). Conceptual Explanations and Understanding Fraction Comparisons. Learning and Instruction, 52, 122–129. https://doi.org/10.1016/j.learninstruc.2017.05.006
Getenet, S., & Callingham, R. (2019). Teaching Interrelated Concepts of Fraction for Understanding and Teacher’s Pedagogical Content Knowledge. Mathematics Education Research Journal, 33, 201–221. https://doi.org/10.1007/s13394-019-00275-0
Gunderson, E. A., Hamdan, N., Hildebrand, L., & Bartek, V. (2019). Number Line Unidimensionality is a Critical Feature for Promoting Fraction Magnitude Concepts. Journal of Experimental Child Psychology, 187, 104657. https://doi.org/10.1016/j.jecp.2019.06.010
Hackenberg, A. J., & Lee, M. Y. (2015). Relationships Between Students’ Fractional Knowledge and Equation Writing. Journal for Research in Mathematics Education, 46(2), 196–243. https://doi.org/https://doi.org/10.5951/jresematheduc.46.2.0196
Harvey, R. (2012). Stretching Student Teachers’ Understanding of Fractions. Mathematics Education Research Journal, 24(4), 493–511. https://doi.org/10.1007/s13394-012-0050-7
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement. American Educational Research Journal, 42(2), 371–406.
Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the Relational Structure of Fractions Seriously: Relational Reasoning Predicts Fraction Knowledge in Elementary School Children. Contemporary Educational Psychology, 62(July), 101896. https://doi.org/10.1016/j.cedpsych.2020.101896
Kazemi, F., & Rafiepour, A. (2018). Developing a Scale to Measure Content Knowledge and Pedagogy Content Knowledge of In-Service Elementary Teachers on Fractions. International Journal of Science and Mathematics Education, 16(4), 737–757. https://doi.org/10.1007/s10763-016-9792-0
Kieren, T. (1976). On the Mathematical, Cognitive, and Instructional Foundations of Rational Numbers. In R. Lesh & D. A. Bradbard (Eds.), Number and measurement: papers from a research workshop (pp. 101–144). Columbus: ERIC Information Analysis Center for Science, Mathematics, and Environmental Education. https://eric.ed.gov/?id=ED120027
Kolar, V. M., Čadež, T. H., & Vula, E. (2018). Primary Teacher Students’ Understanding of Fraction Representational Knowledge in Slovenia and Kosovo. Center for Educational Policy Studies Journal, 8(2), 71–96. https://doi.org/10.26529/cepsj.342
Lamon, S. J. (2020). Teaching Fractions and Ratios for Understanding. New York: Routledge. https://doi.org/10.4324/9781003008057
Lee, M. Y., & Lee, J. E. (2021). Pre-service Teachers’ Selection, Interpretation, and Sequence of Fraction Examples. International Journal of Science and Mathematics Education, 19, 539–558. https://doi.org/10.1007/s10763-020-10062-0
Lin, C. Y., Becker, J., Ko, Y. Y., & Byun, M. R. (2013). Enhancing Pre-Service Teachers’ Fraction Knowledge Through Open Approach Instruction. Journal of Mathematical Behavior, 32(3), 309–330. https://doi.org/10.1016/j.jmathb.2013.03.004
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is Learning Fraction and Decimal Arithmetic So Difficult? Developmental Review, 38, 201–221. https://doi.org/10.1016/j.dr.2015.07.008
Mertens, D. M. (2015). Research and Evaluation in Education and Psychology : Integrating Diversity with Quantitative, Qualitative, and Mixed Methods (4th ed.). United States: SAGE Publications, Inc.
Misquitta, R. (2011). The Division for Learning Disabilities of the Council for Exceptional Children A Review of the Literature: Fraction Instruction for Struggling Learners in Mathematics. Learning Disabilities Research & Practice, 26(2), 109–119. https://doi.org/https://doi.org/10.1111/j.1540-5826.2011.00330.x
Musser, G. L., Peterson, B. E., & Burger, W. F. (2007). Mathematics for Elementary Teachers: A Contemporary Approach. United States: John Wiley & Sons.
Pantziara, M., & Philippou, G. (2012). Levels of Students’ “Conception†of Fractions. Educational Studies in Mathematics, 79(1), 61–83. https://doi.org/10.1007/s10649-011-9338-x
Rahmadani, Nurlaelah, E., Herman, T., & Anaguna, N. (2019). Exploration of Primary School Teacher Students’ Understanding in Fraction Concept. Journal of Physics: Conference Series 1211 012060. https://doi.org/10.1088/1742-6596/1211/1/012060
Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning Fractions with and without Educational Technology: What Matters for High-Achieving and Low-Achieving Students? Learning and Instruction, 65(September 2019), 101264. https://doi.org/10.1016/j.learninstruc.2019.101264
Richardson, L., & st. Pierre, E. A. (2018). Writing: A Method of Inquiry. In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (5th ed., pp. 1410–1444). California: SAGE Publications, Inc. https://doi.org/10.1007/s11229-017-1319-x
Roesslein, R. I., & Codding, R. S. (2019). Fraction Interventions for Struggling Elementary Math Learners: A Review of the Literature. Psychology in the Schools, 56(3), 413–432. https://doi.org/10.1002/pits.22196
Shahbari, J. A., & Peled, I. (2017). Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions. International Journal of Science and Mathematics Education, 15(2), 371–391. https://doi.org/10.1007/s10763-015-9702-x
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early Predictors of High School Mathematics Achievement. Psychological Science, 23(7), 691–697. https://doi.org/10.1177/0956797612440101
Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a Concept of Fraction-as-Measure: A Study of the Learning Through Activity Research Program. Journal of Mathematical Behavior, 52, 122–133. https://doi.org/10.1016/j.jmathb.2018.03.004
Suryadi, D. (2019). Penelitian Desain Didaktis (DDR) dan Implementasinya. Bandung: Gapura Press.
Tunç-Pekkan, Z. (2015). An Analysis of Elementary School Children’s Fractional Knowledge Depicted with Circle, Rectangle, and Number Line Representations. Educational Studies in Mathematics, 89(3), 419–441. https://doi.org/10.1007/s10649-015-9606-2
van Steenbrugge, H., Lesage, E., Valcke, M., & Desoete, a. (2014). Preservice Elementary School Teachers’ Knowledge of Fractions: A Mirror of Students’ Knowledge? Journal of Curriculum Studies, 46(1), 138–161. https://doi.org/10.1080/00220272.2013.839003
Vula, E., & Kingji-Kastrati, J. (2016). Pre-service Teacher Procedural and Conceptual Knowledge of Fractions. In G. J. Stylianides & K. Hino (Eds.), Research Advances in the Mathematical Education of Preservice Elementary Teachers: An International Perspective (pp. 111–123). New York: Routledge Taylor & Francis Group. https://doi.org/10.1007/978-3-319-68342-3
Walle, J. A. Van de, Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and Middle School Mathematics: Teaching Developmentally (8th ed.). New York: Pearson Education, Inc.
Wilkie, K. J., & Roche, A. (2022). Primary Teachers’ Preferred Fraction Models and Manipulatives for Solving Fraction Tasks and for Teaching. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09542-7
Yilmaz, G. K., Ertem, E., & Çepni, S. (2010). The Effect of the Material Based on the 7E Model on the Fourth Grade Students’ Comprehension Skill About Fraction Concepts. Procedia - Social and Behavioral Sciences, 2(2), 1405–1409. https://doi.org/10.1016/j.sbspro.2010.03.209
Zhang, X., Clements, M. A. (Ken), & Ellerton, N. F. (2015). Enriching Student Concept Images: Teaching and Learning Fractions Through a Multiple-Embodiment Approach. Mathematics Education Research Journal, 27(2), 201–231. https://doi.org/10.1007/s13394-014-0137-4
DOI: 10.24235/al.ibtida.snj.v10i1.13078
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