Desain Didaktis Penjumlahan dan Pengurangan Pecahan Campuran di Sekolah Dasar


  • Irfan Fauzi Sekolah Dasar Negeri 093 Tunas Harapan Cijerah, Bandung, Jawa Barat, Indonesia
  • Ririn Arini Sekolah Dasar Negeri Panunggulan 2, Serang, Banten, Indonesia



This research was motivated by the students' learning obstacle in understanding the addition and subtraction of mixed fractions. So this research aims to develop a didactic design on the addition and subtraction of mixed fractions in grade 5 elementary schools based on student learning trajectories and can improve students' learning obstacles on addition and subtraction of mixed fractions. This research used the Didactical Design Research (DDR) method in one of the elementary schools in Bandung, with the subjects being 30 students in grade 5 and 29 students in grade 6. The data collection techniques used tests, interview, document analysis, focus group discussion (FGD), and observation. The results of this research indicated that the Didactic Design has a positive impact on student understanding and reduces the students' learning obstacles which are ontogenic, epistemological and didactical on the addition and subtraction of mixed fractions. Then, the average score of the students after the didactic design implementation was 75.3. This research is expected to be a reference for teachers in developing didactic designs for learning mathematics, especially fraction material in elementary schools using Didactical Design Research (DDR).


Aamaas, Å., Duesund, K., & Lauritzen, S. M. (2017). Placements Abroad and Scaffolding Structures. Studies in Higher Education, 1–15.

Ahmad, S., Hussain, A., Batool, A., Sittar, K., & Malik, M. (2016). Play and Cognitive Development: Formal Operational Perspective of Piaget’s Theory. Journal of Education and Practice, 7(28), 72-79.

Alajmi, A. (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.

Asminingsih. (2016). Menggunakan Jigsaw untuk Meningkatkan Kompetensi Operasi Hitung Berbagai Bentuk Bilangan Pecahan di Kelas III SDN Baujeng 1 Ta 2012-2013. Jurnal Ilmiah Edukasi & Sosial, 7(2), 142-145.

Barahmand, A. (2020). Equivalent Fractions and Natural Number Bias. For the Learning of Mathematics, 40(3), 20-22.

Baxter, J.A., &Williams, S. (2010). Social and Analytic Scaffolding in Middle School Mathematics: Managing The Dilemma of Telling. Journal of Mathematics Teacher Education, 13(1), 7-26.

Bishop, A. (1998). Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Dordrecht, Boston, London: Kluwer Academic Publisher.

Brosseaou, G. (2002). Theory of Didactical Situation in Mathematics. New York, Boston, Dordrecht, London, Moscow: Kluwer Academic Publishers.

Demiri, L. (2013). Researching Teachers and Pre-Service Teachers’knowledge of Students’ Misconceptions about Fractions. Thesis, Marmara University Institute of Educational Sciences, Istanbul, Turkey.

Deringol, Y. (2018). Primary School Students’ Mathematics Motivation and Anxieties. Cypriot Journal of Educational Sciences, 13(4), 537–548.

Fathurrohman, M., Rahayu, I., & Nindiasari, H. (2009). Pengembangan Media Pembelajaran Untuk Menghindari Mind in Chaos. Jurnal Ilmu Pendidikan, 16(2), 106–111.

Fauzi, I. (2020). Desain Didaktis Penjumlahan dan Pengurangan Pecahan di Kelas 5 Sekolah Dasar. Thesis, Universitas Pendidikan Indonesia.

Fauzi, I., & Suryadi, D. (2020a). 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), 33–45.

Fauzi, I., & Suryadi, D. (2020b). Learning Obstacle the Addition and Subtraction of Fraction in Grade 5 Elementary Schools. Mudarrisa: Jurnal Kajian Pendidikan Islam, 12(1), 50-67.

Fitri, N. L., & Prahmana, R. C. I. (2019). Misconception in Fraction for Seventh-Grade Students. Journal of Physics: Conference Series, 1188 012031, 1-8.

Fitriani, C., Murniati, A. R., & Usman, N. (2017). Kompetensi Profesional Guru dalam Pengelolaan Pembelajaran di MTs Muhammadiyah Banda Aceh. Jurnal Administrasi Pendidikan, 5(2), 88-95.

Fortes, E. C., & Andrade, R. R. (2019). Mathematical Creativity in Solving Non-Routine Problems. The Normal Lights, 13(1), 108-135.

Freudenthal, H. (1971). Geometry between the Devil and The Deep Sea. Educational Studies in Mathematics, 3, 413–435.

Fuchs, L. S., Malone, A. S., Schumacher, R. F., Namkung, J., Wang, A. (2016). Fraction Intervention for Students with Mathematics Difficulties: Lessons Learned from Five Randomized Controlled Trials. Journal of Learning Disabilities, 50(6) 631–639.

Gabriel, F., Coché, F., Szűcs, D., Carette, V., Rey, B., & Content, A. (2013). A Componential View of Children’s Difficulties in Learning Fractions. Developmental Psychology, 715(4), 1-12.

Gall, M. D., Gall, J. P., & Borg, W. R. (1999). Applying Educational Research: How to Read, Do, and Use Research (6th ed.). New York: Pearson.

Gerard, V. (1998). A Comprehensive Theory of Representation for Mathematics Education. The Journal of Mathematical Behavior, 17(2), 167-181.

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What Mathematics Education May Prepare Students for the Society of the Future? International Journal of Science and Mathematics Education, 15, 105–123.

Guantar, D. A. (2017). Textbooks Analysis: Analyzing English as a Foreign Language (EFL) Textbooks from the Perspective of Indonesian Culture. Language Circle: Journal of Language and Literature, 7(2), 173-182.

Hadi, S., Retnawati, H., Munadi, S., Apino, E., & Wulandari, N. F. (2018).The Difficulties of High School Students in Solving Higher-Order Thinking Skills Problems. Problems of Education in The 21st Century, 76(4), 520-532.

Hansen, A., Mavrikis, M., & Geraniou, E. (2016). Supporting Teachers’ Technological Pedagogical Content Knowledge of Fractions Through Codesigning a Virtual Manipulative. Journal of Mathematics Teacher Education, 19(2), 205-226.

Harel, G. (2008). What is Mathematics? A Pedagogical Answer to a Philosophical Question. In Gold, B & Simons, R. (Eds.), Proof and Another Dilemmas. Mathematics and Philosophy (pp. 265-290). Washington: The Mathematical Association of America, Inc.

Hoch, S., Reinhold, F., Werner, B, Richter-Gebert, J & Reiss, K. (2018). Design and Research Potential of Interactive Textbooks: The Case of Fractions. ZDM Matehematics Education, 50(5), 839-848.

Ionescu, T., & Vasc, D. (2014). Embodied Cognition: Challenges for Psychology and Education. Procedia-Social and Behavioral Sciences, 128, 275–280.

Iulia & Gugoiu, T. (2006). The Book of Fraction. Mississauga, Ontario, Canada: Albina Way.

Jäder, J., Sidenvall, J., & Sumpter, L. (2016). Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving. International Journal of Science and Mathematics Education, 15(4), 759–776. doi:10.1007/s10763-016-9712-3.

Kamil, M. (2010). Landasan Teori dalam Pengembangan Model Pembelajaran. Bandung: Universitas Pendidikan Indonesia.

Khiat, H. (2010). A Grounded Theory Approach: Conceptions of Understanding in Engineering Mathematics Learning. The Qualitative Report, 15(6), 1459-1488.

Klymchuk, S. (2014). Provocative Mathematics Questions: Drawing Attention to a Lack of Attention. Teaching Mathematics and Its Applications, 34(2), 63–70. doi:10.1093/teamat/hru022.

Lee, G., Kwon, J., Park, S. S., Kim., J. W., Kwon, H. G., & Park, C. K. (2013). Development of an Instrument for Measuring Cognitive Conflict in Secondary‐Level Science Classes. Journal of Research in Science Teaching, 40(6), 585-603.

Lin, T., Hsu, Y., Lin, S., Changlai, M., Yang, K., & Lai, T. (2012). A Review of Empirical Evidence on Scaffolding for Science Education. International Journal of Science and Mathematics Education, 10, 437-455.

Loc, N. P., Tong, D. H., & Chau, P. T. (2017). Identifying the Concept "Fraction" of Primary School Students: The Investigation in Vietnam. Educational Research and Reviews, 12(8), 531-539.

Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why Is Learning Fraction and Decimal Arithmetic So Difficult?. Developmental Review, 38, 201-221.

Lovatt, D., & Hedges, H. (2014). Children’s Working Theories: Invoking Disequilibrium. Early Child Development and Care, 185(6), 909–925.

Mabilangan, R. A. (2011). Problem Solving Strategies of High School Students on Non-routine Problems: An Exploratory Study. Thesis, Philippine Normal University.

Mahlios, J. (1988). Word Problems: Do I Add or Subtract?. Arithmetic Teacher, 25(2), 16–20.

Mayasari, D. (2020). Program Perencanaan Pembelajaran Matematika. Sleman: CV Budi Utama.

Mufarizuddin. (2018). Analisis Kesulitan Pembelajaran Matematika Siswa Kelas 5 SD Negeri 012 Bangkinang Kota. Journal on Education, 1(2), 40-47.

Müller, Eycke & Baker. (2015). Piaget’s Theory of Intelligence in Goldstein, S., Princiotta, D., & Naglieri, J. A. (Eds.). Handbook of Intelligence.

Mulligan, J. (2011). Towards Understanding the Origins of Children’s Difficulties in Mathematics Learning. Australian Journal of Learning Difficulties, 16(1), 19–39.

Namkung, J., & Fuchs, L. (2019). Remediating Difficulty with Fractions for Students with Mathematics Learning Difficulties. Learning Disabilities: A Multidisciplinary Journal, 24(2), 36-48.

Novriany, M. R., Surya, E. (2017). Analysis of Student Difficulties in Mathematics Problem Solving Ability at MTs SWASTA IRA Medan. International Journal of Sciences: Basic and Applied Research (IJSBAR), 33(3), 63-75.

Nurjanah, D., & Leonard. (2016). Pengembangan Desain Pembelajaran Matematika Kelas V Sekolah Dasar. Prosiding Seminar Nasional Pendidikan Matematika FTMIPA Unindra, 2, 525-534.

Özcan, Z. C., İmamoğlu, Y., & Bayraklı, V. K. (2017). Analysis of Sixth Grade Students’ Think-Aloud Processes While Solving a Non-routine Mathematical Problem. Educational Science: Theory & Practice, 17(1), 129-144.

Rellensmann, J., & Schukajlow, S. (2020). Does Students’ Interest in a Mathematical Problem Depend on the Problem’s Connection to Reality? An Analysis of Students’ Interest and Pre‑service Teachers’ Judgments of Students’ Interest in Problems with and without a Connection to Reality. ZDM, 49(3), 367–378.

Rismawati., Suhendri, H., & Zulakrnain, I. (2019). Pengembangan Desain Pembelajaran Matematika Kelas V SD Berbasis Etnomatematika. Journal of Mathematics Education, Science and Tecnology, 4(2), 230-250.

Sari, N., Wibowo, T., & Kurniawan, H. (2019). Identifikasi Kesulitan Numerik Siswa dalam Mengaplikasikan Operasi Hitung Bilangan Pecahan. Seminar Nasional Matematika ke-11 Universitas Gadjah Mada, 60-72.

Şiap, İ, & Duru, A. (2004). The Ability to Use Geometrical Models in Fractions. Kastamonu Education Journal, 12(1), 89-96.

Siniguian, M. T. (2017). Students Difficulty in Solving Mathematical Problems. International Journal of Advanced Research in Engineering and Applied Sciences, 6(2), 1-12.

Suratno, T. (2016). Didaktik dan Didactical Design Research. In Suryadi, D., Mulyana, E., Suratno, T., Dewi, D. A. K., & Maudy. S.Y. (Eds.), Monograph Didactical Design Research. Bandung: Rizqi Press.

Suryadi, D. (2018). Landasan Filosofis Penelitian Desain Didaktis (DDR). Bandung: Departemen Pendidikan Matematika UPI.

Tian, J., Siegler, R. S. (2016). Fractions Learning in Children With Mathematics Difficulties. Journal of Learning Disabilities, 50(6), 614- 10.1177/0022219416662032.

Warsito, Nuraini & Sukirwan (2019). Desain Pembelajaran Pecahan melalui Pendekatan Realistik di Kelas V. Mosharafa: Jurnal Pendidikan Matematika, 8(1), 25-36.

Yusri, Y., & Arifin, S. (2018). Desain Pembelajaran Kooperatif Berbasis Teori Bruner Untuk Meningkatkan Kualitas Pembelajaran Matematika. HISTOGRAM: Jurnal Pendidikan Matematika, 2(2), 147-155.

Zengin, Y. (2017). International Forum of Educational Technology & Society Investigating the Use of the Khan Academy and Mathematics Software with a Flipped Classroom Approach in Mathematics Teaching Published by International Forum of Educational Technology & Society Inv. Journal of Educational Technology & Society, 20(2), 89–100.

Zhang, L., Yu, S., Li, B., & Wang, J. (2017). Can Students Identify the Relevant Information to Solve a Problem?. Educational Technology & Society, 20(4), 288-299.



How to Cite

Fauzi, I., & Arini, R. (2021). Desain Didaktis Penjumlahan dan Pengurangan Pecahan Campuran di Sekolah Dasar. Jurnal Didaktika Pendidikan Dasar, 5(1), 1-30.