Desain Lintasan Pembelajaran untuk Meningkatkan Estimasi dalam Kemampuan Number Sense Siswa Sekolah Dasar

Authors

Anna Fauziah Universitas PGRI Silampari
Viktor Pandra Universitas PGRI Silampari

DOI:

Keywords:

lintasan pembelajaran, number sense, estimasi, PMRI

Abstract

This design research aims to develop a learning trajectory design within the Indonesian Realistic Mathematics Education (PMRI) framework to improve elementary school students' number sense, particularly in estimation skills. This research was conducted in three stages: preliminary, design experiment, and retrospective analysis. This study involved 25 elementary school students in Lubuklinggau. Data were collected through worksheets, classroom documentation (photos and videos), and student interviews, and analyzed qualitatively and descriptively. The learning trajectory emphasized estimation by rounding prices to the nearest thousand and ten thousand, using the context of Hypermart shopping. The retrospective analysis focused on instructional elements, including task types, number operations, contextual relevance, problem openness, number selection, question types, and classroom culture. The findings indicate that a real and familiar context significantly improves students' estimation skills and learning engagement. This study concludes that a context-based learning trajectory is effective in supporting students' number sense development.

Keywords: Estimation, Learning Trajectory, Number Sense, Estimation, PMRI

References

Adamuz-Povedano, N., Fernández-Ahumada, E., García-Pérez, M. T., & Montejo-Gámez, J. (2021). Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education. Mathematics, 9(5), 518. https://doi.org/10.3390/math9050518

Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the Effects of Different Multiple Representational Systems in Learning Primary Mathematics. Journal of the Learning Sciences,. Journal of the Learning Sciences, 11(1), 25–61. https://doi.org/https://doi.org/10.1207/S15327809JLS1101_2

Andrews, P., Sunde, P. B., Nosrati, M., Petersson, J., Rosenqvist, E., Sayers, J., & Xenofontos, C. (2021). Computational Estimation and Mathematics Education: A Narrative Literature Review. Journal of Mathematics Education, 14(1), 6–27. https://doi.org/10.26711/007577152790061

Balkist, P. S., & Jupri, A. (2025). Number Sense of Junior High School Students Based on Learning Speed: Slow, Average, and Fast Learners. Journal on Mathematics Education, 16(1), 23–50. https://doi.org/10.22342/jme.v16i1.pp23-50

Birgin, O., & Peker, E. (2025). Development and Validation of A Two‐Tier Number Sense Test for Sixth‐Grade Students in Fractions and Decimals. Psychology in the Schools, 62(1), 219–236. https://doi.org/10.1002/pits.23321

Coppersmith, J. G., & Star, J. R. (2022). A Complicated Relationship: Examining The Relationship Between Flexible Strategy Use and Accuracy. Journal of Numerical Cognition, 8(3), 382–397. https://doi.org/10.5964/jnc.7601

Corso, L. ., Corso, H. V, & de Salles, J. F. (2024). Intervention in Mathematical Skills: Number Sense. In Neuropsychological Interventions for Children - Volume 1 (pp. 169–180). Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-53586-4_12

Dolfi, S., Decarli, G., Lunardon, M., De Filippo De Grazia, M., Gerola, S., Lanfranchi, S., Cossu, G., Sella, F., Testolin, A., & Zorzi, M. (2024). Weaker Number Sense Accounts for Impaired Numerosity Perception in Dyscalculia: Behavioral and computational evidence. Developmental Science, 27(6). https://doi.org/10.1111/desc.13538

Dzhaparova, S. N., & Omurbekova, S. O. (2024). The Technology for Teaching Addition and Subtraction of Numbers Up to 10 in Elementary School. Bulletin of Issyk-Kul University. https://doi.org/10.69722/1694-8211-2024-56-10-16

Fahlevi, M. R. (2022). Upaya Pengembangan Number Sense Melalui Kurikulum Merdeka. Jurnal Kajian Mutu Pendidikan, 5(1), 11–27. https://doi.org/https://doi.org/10.32923/kjmp.v5i1.2308

Fauziah, A., & Pandra, V. (2024). Analyzing Elementary School Students’ Misconceptions in Number Sense Using a Five-Tier Diagnostic Test. Jurnal Riset Pendidikan Matematika, 11(2), 134–144. https://doi.org/https://doi.org/10.21831/jrpm.v11i2.76086.

Fauziah, A., & Putri, R. I. . (2022). Desain Pembelajaran PMRI Melalui Lesson Study pada Materi Menentukan Luas Permukaan Balok. Jurnal Pendidikan Matematika (Judika Education), 5(2), 73–83. https://doi.org/10.31539/judika.v5i2.4048

Fauziah, A., Putri, R. I. ., Zulkardi, Z., & Somakim, S. (2020). Developing PMRI Learning Environment Through Lesson Study for Pre-Service Primary School Teacher. Journal on Mathematics Education, 11(2), 193–208. https://doi.org/10.22342/jme.11.2.10914.193-208

Gaffney, J. D. H. (2023). Learning How to Make “Good Enough” Estimations. CourseSource, 10. https://doi.org/10.24918/cs.2023.23

Gunes, G. (2022). Investigation of The Computational Estimation Skills of and Strategies Employed By Pre-Service Primary School Teacher. International Electronic Journal of Mathematics Education, 17(3), em0689. https://doi.org/10.29333/iejme/12057

Heuvel, V. D., & Drijvers. (2014). Encyclopedia of Mathematics Education (S. Lerman (ed.)). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8

Honda, H., Kagawa, R., & Shirasuna, M. (2022). On the Round Number Bias and Wisdom of Crowds in Different Response Formats for Numerical Estimation. Scientific Reports, 12(1), 8167. https://doi.org/10.1038/s41598-022-11900-7

Islamy, D. P. (2023). Pengembangan Bahan Ajar Pecahan Berbasis PMRI dengan Konteks ”Ular Tangga” di Kelas V SD. FARABI: Jurnal Matematika Dan Pendidikan Matematika, 6(2), 154–161. https://doi.org/10.47662/farabi.v6i2.623

Jordan, N. C., Devlin, B. L., & Botello, M. (2022). Core Foundations of Early Mathematics: Refining The Number Sense Framework. Current Opinion in Behavioral Sciences, 46, 101181. https://doi.org/10.1016/j.cobeha.2022.101181

Lantakay, C. N., Samo, D. D., & Blegur, I. K. S. (2024). Desain Pembelajaran Penjumlahan dan Pengurangan Bilangan Bulat Menggunakan Matematika Realistik Konteks Permainanan Tradisional Congklak di SD Inpres Nunbaun Delha. Fraktal: jurnal matematika dan pendidikan matematika, 5(1), 16–28. https://doi.org/10.35508/fractal.v5i1.13500

Li, H., Hua, X., Yang, Y., Huang, B., & Si, J. (2020). How Does Task Switching Affect Arithmetic Strategy Use in Children with Low Mathematics Achievement? Evidence from Computational Estimation. European Journal of Psychology of Education, 35(1), 225–240. https://doi.org/10.1007/s10212-019-00425-9

McIntosh, A, Reys. B. J, Reys, R. E. (1995). A Proposed Framework for Examining Basic Number Sense. In Subject Learning in Primary Curriculum (pp. 209–221).

Nieder, A. (2025). The Calculating Brain. Physiological Reviews, 105(1), 267–314. https://doi.org/10.1152/physrev.00014.2024

Pittalis, M. (2025). An Empirically Validated Rational Number Sense Framework. Mathematics Education Research Journal, 37(1), 125–160. https://doi.org/10.1007/s13394-024-00484-2

Putri, R. I. I., Zulkardi, Sari, N., Sagita, L., Siligar, E. I. P., & Sukma, Y. (2025). Learning Numeracy using New Pempek Mathematics. Journal on Mathematics Education, 16(1), 1–22. https://doi.org/10.22342/jme.v16i1.pp1-22

Sukma, Y., Somakim, S., & Indaryanti, I. (2021). Students’ Number Sense on Fraction Problems. Journal of Physics: Conference Series, 1882(1), 012055. https://doi.org/10.1088/1742-6596/1882/1/012055

Ulya, H. (2024). The Meta-Analysis of Innovative Mathematics Learning Toward the Mathematics Ability in Various Countries. AL-ISHLAH: Jurnal Pendidikan, 16(4), 4899–4914. https://doi.org/10.35445/alishlah.v16i4.5854

Vessonen, T., Dahlberg, M., Hellstrand, H., Widlund, A., Korhonen, J., Aunio, P., & Laine, A. (2024). Task Characteristics Associated with Mathematical Word Problem-Solving Performance Among Elementary School-Aged Children: A Systematic Review and Meta-Analysis. Educational Psychology Review, 36(4), 117. https://doi.org/10.1007/s10648-024-09954-2

Wulandari, N. ., Apsari, R. A., Tyaningsih, R. Y., Salsabila, N. H., & Hadiyanto, F. R. (2021). Number Sense Ability of Junior High School Students. Journal of Physics: Conference Series, 1778(1), 012024. https://doi.org/10.1088/1742-6596/1778/1/012024

Yeo, D. J., & Price, G. R. (2021). Probing The Mechanisms Underlying Numerosity-to-Numeral Mappings and Their Relation to Math Competence. Psychological Research, 85(3), 1248–1271. https://doi.org/10.1007/s00426-020-01299-z

Zakaria, Z., & Dewantara, A. H. (2024). Understanding Multiplication Concept: Exploring PMRI-Enhanced Thematic Learning Using Traditional Games for Primary Teachers. Jurnal Elemen, 10(1), 55–69. https://doi.org/10.29408/jel.v10i1.19838