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Research on Proportional Reasoning: A Systematic Review

Yıl 2025, Cilt: 9 Sayı: 2, 210 - 231, 30.10.2025
https://doi.org/10.32960/uead.1698505

Öz

The aim of this study is to systematically review research conducted on proportional reasoning skills between 2007 and 2024. Proportional reasoning is a critical competency in mathematics education, serving as the foundation for many advanced mathematical skills. A total of 88 studies obtained from the Web of Science and Scopus databases were analyzed. These studies were examined in terms of their publication year, the journals they appeared in, their objectives, methodologies, sample levels, data collection tools, and findings. The results indicate that research on proportional reasoning has increased in recent years, with a particular focus on middle school students. Additionally, the most commonly employed methods were found to be experimental and correlational studies. The majority of studies showed that the approaches used to develop proportional reasoning skills had positive effects. Future research could focus on conducting more comprehensive and long-term studies that examine the variables used in studies exploring the relationship between proportional reasoning and other mathematical skills. Furthermore, greater attention could be given to the conditions under which effective approaches and methods are applied and how they are implemented in practice.

Kaynakça

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Orantısal Akıl Yürütme Üzerine Yapılan Araştırmalar: Sistematik Derleme

Yıl 2025, Cilt: 9 Sayı: 2, 210 - 231, 30.10.2025
https://doi.org/10.32960/uead.1698505

Öz

Bu çalışmanın amacı, 2007-2024 yılları arasında orantısal akıl yürütme becerileri üzerine yapılan araştırmaların sistematik bir şekilde incelenmesidir. Orantısal akıl yürütme, matematik eğitiminde önemli bir rol oynayan ve birçok ileri düzey matematiksel becerinin temeli olan bir yetkinliktir. Çalışmada Web of Science ve Scopus veri tabanlarından elde edilen 88 araştırma incelenmiştir. Bu araştırmalar, yıllara, yayınlandıkları dergilere, amaçlarına, yöntemlerine, sınıf düzeylerine, veri toplama araçlarına, veri analiz yöntemlerine ve elde edilen sonuçlara göre analiz edilmiştir. Bulgular, orantısal akıl yürütme üzerine yapılan çalışmaların son yıllarda arttığını ve en çok ortaokul düzeyindeki öğrencilere odaklandığını göstermektedir. Ayrıca, en yaygın kullanılan yöntemlerin deneysel ve ilişkisel tarama çalışmaları olduğu tespit edilmiştir. Çalışmaların çoğunluğu, orantısal akıl yürütme becerilerinin geliştirilmesinde kullanılan yaklaşımların olumlu etkiler gösterdiğini ortaya koymuştur. Orantısal akıl yürütmenin, öğrencilerin diğer matematiksel becerileriyle olan bağlantısını inceleyen araştırmalarda kullanılan değişkenlere odaklanarak daha kapsamlı ve uzun süreli çalışmalar yürütülebilir. Etkili olduğu belirlenen yaklaşım ve yöntemlerin hangi koşullarda ve nasıl uygulandığı daha derinlemesine ele alınabilir.

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  • Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261.
  • Liu, C.-J., & Shen, M.-H. (2011). The influence of different representations on solving concentration problems at elementary school. Journal of Science Education and Technology, 20(5), 621-629. https://doi.org/10.1007/s10956-011-9293-4
  • Lundberg, A. L. V. (2022). Encountering proportional reasoning during a single algebra lesson: a microgenetic analysis. International Electronic Journal of Mathematics Education, 17(1), em0673. https://doi.org/10.29333/iejme/11571
  • Lundberg, Anna. L. V., & Kilhamn, C. (2018). Transposition of knowledge: encountering proportionality in an algebra task. International Journal of Science and Mathematics Education, 16(3), 559-579. https://doi.org/10.1007/s10763-016-9781-3
  • Magalhães Teixeira, P. J. (2021). Mobilizando o raciocínio proporcional na resolução de questões percentuais via uso de funções lineares. Perspectivas em Diálogo: revista de educação e sociedade, 8(17), 506-527. https://doi.org/10.55028/pdres.v8i17.12578
  • Miles, M. B. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks.
  • Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1-8. sınıflar).
  • Modestou, M., & Gagatsis, A. (2007). Students’ improper proportional reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology, 27(1), 75-92. https://doi.org/10.1080/01443410601061462
  • Mongeon, P., & Paul-Hus, A. (2016). The journal coverage of Web of Science and Scopus: A comparative analysis. Scientometrics, 106(1), 213-228. https://doi.org/10.1007/s11192-015-1765-5
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
  • Ng, R., Heyman, G. D., & Barner, D. (2011). Collaboration promotes proportional reasoning about resource distribution in young children. Developmental Psychology, 47(5), 1230-1238. https://doi.org/10.1037/a0024923
  • Nunokawa, K. (2012). Multi-relation strategy in students’ use of a representation for proportionalreasoning. EURASIA Journal of Mathematics, Science and Technology Education, 8(4). https://doi.org/10.12973/eurasia.2012.842a
  • Obersteiner, A., Bernhard, M., & Reiss, K. (2015). Primary school children’s strategies in solving contingency table problems: The role of intuition and inhibition. ZDM-Mathematics Education, 47(5), 825-836. https://doi.org/10.1007/s11858-015-0681-8
  • Öz, E. (2020). Ortaöğretim Öğrencilerinin Orantısal Akıl Yürütme Becerilerinin İncelenmesi [Doktora Tezi, Anadolu Üniversitesi].
  • Öztürk, M. (2020). The relationship between self-regulation and proportional reasoning: the mediating role of reflective thinking towards problem solving. TED Eğitim ve Bilim https://doi.org/10.15390/EB.2020.8480
  • Pakmak, G. S. (2014). 6. Sınıf Öğrencilerinin Niceliksel ve Niteliksel Orantısal Akıl Yürütme Problemlerinin Çözümündeki Anlayışlarının İncelenmesi [Yüksek Lisans Tezi, Pamukkale Üniversitesi].
  • Proulx, J. (2023). Relative proportional reasoning: transition from additive to multiplicative thinking through qualitative and quantitative enmeshments. International Journal of Science and Mathematics Education, 22(2), 353-374. https://doi.org/10.1007/s10763-023-10373-y
  • Resnick, I., Newcombe, N., & Goldwater, M. (2023). Reasoning about fraction and decimal magnitudes, reasoning proportionally, and mathematics achievement in Australia and the United States. Journal of Numerical Cognition, 9(1), 222-239. https://doi.org/10.5964/jnc.8249
  • Ricart, M., & Estrada, A. (2022). Combinatorial and proportional task: looking for ıntuitive strategies in primary education. Mathematics, 10(8), 1340. https://doi.org/10.3390/math10081340
  • Riehl, S. M., & Steinthorsdottir, O. B. (2019). Missing-value proportion problems: The effects of number structure characteristics. Investigations in Mathematics Learning, 11(1), 56-68. https://doi.org/10.1080/19477503.2017.1375361
  • Sari, Y. M., Fiangga, S., Milla, Y. I. E., & Puspaningtyas, N. D. (2023). Exploring students’ proportional reasoning in solving guided-unguided area conservation problem: A case of Indonesian students. Journal on Mathematics Education, 14(2), 375-394. https://doi.org/10.22342/jme.v14i2.pp375-394
  • Scheibling-Sève, C., Gvozdic, K., Pasquinelli, E., & Sander, E. (2022). Enhancing cognitive flexibility through a training based on multiple categorization: Developing proportional reasoning in primary school. Journal of Numerical Cognition, 8(3), 443-472. https://doi.org/10.5964/jnc.7661
  • Schwarz, B. B., & Linchevski, L. (2007). The role of task design and argumentation in cognitive development during peer interaction: The case of proportional reasoning. Learning and Instruction, 17(5), 510-531. https://doi.org/10.1016/j.learninstruc.2007.09.009
  • Shin, J., Lee, S. J., & Steffe, L. P. (2020). Problem solving activities of two middle school students with distinct levels of units coordination. The Journal of Mathematical Behavior, 59, 100793. https://doi.org/10.1016/j.jmathb.2020.100793
  • Steinthorsdottir, O. B., & Sriraman, B. (2009). Icelandic 5th-grade girls’ developmental trajectories in proportional reasoning. Mathematics Education Research Journal, 21(1), 6-30. https://doi.org/10.1007/BF03217536
  • Stemn, B. S. (2008). Building middle school students’ understanding of proportional reasoning through mathematical investigation. Education 3-13, 36(4), 383-392. https://doi.org/10.1080/03004270801959734
  • Supply, A.-S., Vanluydt, E., Van Dooren, W., & Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educational Studies in Mathematics, 113(3), 371-388. https://doi.org/10.1007/s10649-023-10212-5
  • Tall, D., & Razali, M. R. (1993). Diagnosing Students’ Difficulties In Learning Mathematics. International Journal of Mathematical Education in Science and Technology, 24(2), 209-222. https://doi.org/10.1080/0020739930240206
  • Taylor, A., & Jones, G. (2009). Proportional Reasoning Ability and Concepts of Scale: Surface area to volume relationships in science. International Journal of Science Education, 31(9), 1231-1247. https://doi.org/10.1080/09500690802017545
  • Ter Vrugte, J., De Jong, T., Vandercruysse, S., Wouters, P., Van Oostendorp, H., & Elen, J. (2017). Computer game-based mathematics education: Embedded faded worked examples facilitate knowledge acquisition. Learning and Instruction, 50, 44-53. https://doi.org/10.1016/j.learninstruc.2016.11.007
  • Ter Vrugte, J., De Jong, T., Wouters, P., Vandercruysse, S., Elen, J., & Van Oostendorp, H. (2015). When a game supports prevocational math education but integrated reflection does not. Journal of Computer Assisted Learning, 31(5), 462-480. https://doi.org/10.1111/jcal.12104
  • Thurn, C., Nussbaumer, D., Schumacher, R., & Stern, E. (2022). The Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning. Journal of Intelligence, 10(2), 31. https://doi.org/10.3390/jintelligence10020031
  • Tjoe, H., & De La Torre, J. (2014). On recognizing proportionality: Does the ability to solve missing value proportional problems presuppose the conception of proportional reasoning? The Journal of Mathematical Behavior, 33, 1-7. https://doi.org/10.1016/j.jmathb.2013.09.002
  • Tomaz, V. S., & David, M. M. (2015). How students’ everyday situations modify classroom mathematical activity: the case of water consumption. Journal for Research in Mathematics Education, 46(4), 455-496. https://doi.org/10.5951/jresematheduc.46.4.0455
  • Uçar, R. (2022). Orantısal Akıl Yürütme Üzerine Sistematik Derleme Çalışması [Yüksek Lisans Tezi, Necmettin Erbakan Üniversitesi].
  • Uçar, Z., & Bozkuş, F. (2016). İlkokul ve ortaokul öğrencilerinin orantısal durumları orantısal olmayan durumlardan ayırt edebilme becerileri. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 17(3), 281-299.
  • Vanluydt, E., De Keyser, L., Verschaffel, L., & Van Dooren, W. (2023). Stimulating early proportional reasoning: An intervention study in second graders. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-023-00696-3
  • Vanluydt, E., Degrande, T., Verschaffel, L., & Van Dooren, W. (2020). Early stages of proportional reasoning: A cross-sectional study with 5- to 9-year-olds. European Journal of Psychology of Education, 35(3), 529-547. https://doi.org/10.1007/s10212-019-00434-8
  • Vanluydt, E., Supply, A.-S., Verschaffel, L., & Van, W. (2021). The importance of specific mathematical language for early proportional reasoning. Early Childhood Research Quarterly, 55, 193-200. https://doi.org/10.1016/j.ecresq.2020.12.003
  • Vanluydt, E., Verschaffel, L., & Van Dooren, W. (2022a). The early development of proportional reasoning: A longitudinal study of 5- to 8-year-olds. Journal of Educational Psychology, 114(6), 1343-1358. https://doi.org/10.1037/edu0000734
  • Vanluydt, E., Verschaffel, L., & Van Dooren, W. (2022b). The role of relational preference in word-problem solving in 6-to 7-year-olds. Educational Studies In Mathematics, 110(3), 393-411. https://doi.org/10.1007/s10649-021-10139-9
  • Vanluydt, E., Wijns, N., Torbeyns, J., & Van Dooren, W. (2021). Early childhood mathematical development: The association between patterning and proportional reasoning. Educational Studies in Mathematics, 107(1), 93-110. https://doi.org/10.1007/s10649-020-10017-w
  • Verdú, F. (2012). Característıcas Del Desarrollo Del Razonamıento Proporcıonal En La Educacıón Prımarıa Y Secundarıa. enseñanza de las ciencias, 30(1), 129-142.
  • Warshauer, H. K. (2015). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18(4), 375-400. https://doi.org/10.1007/s10857-014-9286-3
  • Wilkie, K. J. (2016). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333-361. https://doi.org/10.1007/s10649-016-9703-x
  • Zhu, J., & Liu, W. (2020). A tale of two databases: The use of Web of Science and Scopus in academic papers. Scientometrics, 123(1), 321-335. https://doi.org/10.1007/s11192-020-03387-8
Toplam 122 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Hatice Çetin 0000-0003-0686-8049

Aleyna Koç 0000-0002-2337-9629

Gönderilme Tarihi 13 Mayıs 2025
Kabul Tarihi 25 Ekim 2025
Erken Görünüm Tarihi 30 Ekim 2025
Yayımlanma Tarihi 30 Ekim 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 9 Sayı: 2

Kaynak Göster

APA Çetin, H., & Koç, A. (2025). Orantısal Akıl Yürütme Üzerine Yapılan Araştırmalar: Sistematik Derleme. Ulusal Eğitim Akademisi Dergisi, 9(2), 210-231. https://doi.org/10.32960/uead.1698505