Learning obstacle of proportion learning based on proposional reasoning level: A case study pre-service mathematics teachers

Authors

  • Rani Sugiarni Suryakancana University
  • Tatang Herman Indonesia University of Education
  • Didi Suryadi Indonesia University of Education
  • Sufyani Prabawanto Indonesia University of Education
  • Nia Jusniani Universitas Terbuka

DOI:

https://doi.org/10.29408/jel.v11i1.27418

Keywords:

pre-service mathematics teacher, proportion, learning obtacles, proportion reasoning level

Abstract

The proportion has emerged as an important mathematical topic in high school because of its foundation in other mathematics topics. This study aims to identify the learning barriers of pre-service mathematics teachers (PMT) based on the material proportion and level of reasoning proportion. This study implemented Didactical Design Research (DDR) and used qualitative research methodologies within an interpretive paradigm. The research participants were 25 PMTs from a seventh-semester candidate teacher at a private college in Cianjur, Indonesia. The data collected from the test results and interviews were analyzed using procedures such as identification, clarification, reduction, and verification. We then present the findings in a narrative format. Langrall and Swafford categorized the results of written tests at the proportional-reasoning level. Based on the results, the PMT at the varied proportional level but at the nonproportional level 0 identified learning obstacles, which include ontogenetic obstacles, epistimology obstacles, and didactic obstacles. The results of this study are expected to be used as a basis for designing hypothetical learning for school mathematical research in future PMT.

Author Biographies

Rani Sugiarni, Suryakancana University

Department of Mathematics Education

Tatang Herman, Indonesia University of Education

Department of Mathematics Education

Didi Suryadi, Indonesia University of Education

Department of Mathematics Education

Sufyani Prabawanto, Indonesia University of Education

Department of Mathematics Education

Nia Jusniani, Universitas Terbuka

Department of Mathematics Education

References

Abramovich, S., & Connell, M. L. (2021). Ratio and Proportion (S. Abramovich & M. L. Connell (eds.); pp. 157–182). Springer International Publishing. https://doi.org/10.1007/978-3-030-68564-5_6

Andini, W., & Jupri, A. (2017). Student obstacles in ratio and proportion learning. Journal of Physics: Conference Series, 812(1), 012048. https://doi.org/10.1088/1742-6596/812/1/012048

Arican, M. (2015). Exploring preservice middle and high school mathematics teachers’ understanding of directly and inversely proportional relationships. University of Georgia Attens, Georgia.

Arican, M. (2019a). Facilitating pre-service mathematics teachers’ understanding of directly and inversely proportional relationships using hands-on and real-world problems. International Journal of Research in Education and Science, 5(1), 102–117.

Arican, M. (2019b). Preservice mathematics teachers’ understanding of and abilities to differentiate proportional relationships from nonproportional relationships. International Journal of Science and Mathematics Education, 17(7), 1423–1443. https://doi.org/10.1007/s10763-018-9931-x

Arican, M. (2024). Correction to: Preservice middle and high school mathematics teachers’ strategies when solving proportion problems (International Journal of Science and Mathematics Education, 16(2), 315-335, 10.1007/s10763-016-9775-1). International Journal of Science and Mathematics Education, 22(4), 937-937. https://doi.org/10.1007/s10763-018-09943-2

Arican, M. (2020). Investigating preservice teachers’ determination and representation of proportional and nonproportional relationships in terms of problem contexts. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 14(1), 629–660. https://doi.org/10.17522/balikesirnef.683225

Arican, M., & Özçakır, B. (2020). Facilitating the development of Preservice teachers’ proportional reasoning in geometric similarity problems using augmented reality activities. Education and Information Technologies, 26, 2327–2353. https://doi.org/10.1007/s10639-020-10359-1

Arican, M., Verschaffel, L., & Van Dooren, W. (2023). Preservice middle school mathematics teachers’ strategy repertoire in proportional problem solving. Research in Mathematics Education, 1–21. https://doi.org/10.1080/14794802.2023.2212260

Bintara, I. A., & Suhendra. (2021). Analysis toward learning obstacles of junior high school students on the topic of direct and inverse proportion. Journal of Physics: Conference Series, 1882(1), 012083. https://doi.org/10.1088/1742-6596/1882/1/012083

Biori, H., Dasari, D., Faturohman, I., & Juandi, D. (2022). Analysis of the epistemological obstacle of junior high school students on proportion topic. AIP Conference Proceedings, 2468(1), 0102464. https://doi.org/10.1063/5.0102464

Boyer, T. W., & Levine, S. C. (2012). Child proportional scaling: Is 1/3=2/6=3/9=4/12? Journal of Experimental Child Psychology, 111(3), 516–533. https://doi.org/10.1016/j.jecp.2011.11.001

Brousseau, G. (2002). Theory of didactical situations in mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2

Buforn, À., Llinares, S., & Fernández, C. (2018). Características del conocimiento de los estudiantes para maestro españoles en relación con la fracción, razón y proporción. Revista Mexicana de Investigacion Educativa, 23(76), 229–251.

Burgos, M., Albanese, V., & López-Martín, M. del M. (2022). Prospective primary school teachers’ recognition of proportional reasoning in pupils’ solution to probability comparison tasks. Twelfth Congress of the European Society for Research in Mathematics Education.

Burgos, M., & Godino, J. D. (2022). Prospective primary school teachers’ competence for analysing the difficulties in solving proportionality problem. Mathematics Education Research Journal, 34(2), 269–291. https://doi.org/10.1007/s13394-020-00344-9

Cabero-Fayos, I., Santágueda-Villanueva, M., Villalobos-Antúnez, J. V., & Roig-Albiol, A. I. (2020). Understanding of inverse proportional reasoning in pre-service teachers. Education Sciences, 10(11), 1–19. https://doi.org/10.3390/educsci10110308

Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2018). Early algebra is not the same as algebra early. In Algebra in the early grades (pp. 235–272). Routledge. https://doi.org/10.4324/9781315097435-12

Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. Routledge. https://doi.org/10.4324/9780203520574

Cramer, K. A., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications: Middle grades mathematics. In Research ideas for the classroom: Middle grades mathematics (pp. 159–178). Macmillan Publishing Company.

Creswell, J. W. (2017). Introduction to mixed method research (Trans. Ed.: Sözbilir, M) Ankara. Trn. Ed.: Mustafa Sözbilir. 2nd. Edition, Ankara: Pegem Akademi.

Irfan, M., Nusantara, T., Subanji, Sisworo, Wijayanto, Z., & Widodo, S. A. (2019). Why do pre-service teachers use the two-variable linear equation system concept to solve the proportion problem? Journal of Physics: Conference Series, 1188(1), 12013. https://doi.org/10.1088/1742-6596/1188/1/012013

Johnson, K. (2017). A study of pre-service teachers use of presenting their proportional reasoning. Mathematical Knowledge for Teaching, 551–558.

Joshua, S., & Lee, M. Y. (2022). Incoherencies in elementary pre-service teachers’ understanding of calculations in proportional tasks. International Electronic Journal of Mathematics Education, 17(4), em0698. https://doi.org/10.29333/iejme/12178

Kalu, F. A. (2017). What makes qualitative research good research? An exploratory analysis of critical elements. International Journal of Social Science Research, 5(2), 43. https://doi.org/10.5296/ijssr.v5i2.10711

Karli, M. G., & Yildiz, E. (2022). Incorrect strategies developed by seventh- grade students to solve proportional reasoning problems. Journal of Qualitative Research in Education, 22(29), 111–148. https://doi.org/10.14689/enad.29.5

Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. The Second Handbook of Research on Mathematics Teaching and Learning, 1, 629–668.

Lamon, S. J. (2020a). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.

Lamon, S. J. (2020b). Teaching Fractions and Ratios for Understanding. Routledge. https://doi.org/10.4324/9781003008057

Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254–261.

Langrall, C. W., & Swafford, J. (2020). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254–261. https://doi.org/10.5951/mtms.6.4.0254

Lim, K. H. (2020). Burning the candle at just one end. Mathematics Teaching in the Middle School, 14(8), 492–500. https://doi.org/10.5951/mtms.14.8.0492

Ölmez, İ. B. (2016). Oranlar üzerine iki farklı yaklaşım: Nicelikler arasındaki toplamsal ve çarpımsal ilişkiler. Elementary Education Online, 15(1), 186–203. https://doi.org/10.17051/io.2016.94175

Ölmez, İ. B. (2022). Preservice teachers’ understandings of division and ratios in forming proportional relationships. Mathematics Education Research Journal, 35, 689-713. https://doi.org/10.1007/s13394-022-00410-4

Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. Journal of Mathematical Behavior, 30(4), 333–352. https://doi.org/10.1016/j.jmathb.2011.07.001

Özen Yılmaz, G. (2019). Investigating middle school students’ achievement and strategies in proportional reasoning problems thesis. Progress in Retinal and Eye Research, 561(3), S2–S3). Middle East Technical University.

Pişkin Tunç, M., & Çakıroğlu, E. (2022). Fostering prospective mathematics teachers’ proportional reasoning through a practice-based instruction. International Journal of Mathematical Education in Science and Technology, 53(2), 269–288. https://doi.org/10.1080/0020739X.2020.1844909

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

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

Suryadi, D. (2010). Metapedadidaktik dan didactical design research (DDR): Sintesis hasil pemikiran berdasarkan lesson study [Metapedadidactics and didactical design research (DDR): A synthesis of lesson study-based thinking]. Teori, Paradigma, Prinsip, dan Pendekatan Pembelajaran MIPA dalam Konteks Indonesia, 55–75.

Suryadi, D. (2019). Penelitian desain didaktis (DDR) dan Implementasinya [Didactic design research (DDR) and its implementation]. Gapura Press.

Valverde, G., & Castro, E. (2012). Prospective elementary school teachers’ proportional reasoning. PNA. Revista de Investigación En Didáctica de La Matemática, 7(1), 1–19.

Wahyuningrum, A. S., Suryadi, D., & Turmudi, T. (2019). Learning obstacles among indonesian eighth graders on ratio and proportion. Journal of Physics: Conference Series, 1320(1), 012046. https://doi.org/10.1088/1742-6596/1320/1/012046

Wahyuningrum, A. S., Suryadi, D., & Turmudi, T. (2022). Students’ prior knowledge as an ontogenic obstacle on the topic of ratio and proportion. Jurnal Pendidikan Matematika, 17(1), 55–68. https://doi.org/10.22342/jpm.17.1.18866.55-68

Zulkarnain, I., Hidayanto, T., Zhang, P., Brown, A., Joseph, M., He, J., Zazkis, R., Marmur, O., Zayyadi, M., Nusantara, T., Hidayanto, E., Sulandra, I. M., Sa’Dijah, C., As’ari, A. R., Zapatera Llinares, A., Callejo de la Vega, M. L., Yustitia, V., Siswono, T. Y. E. Y. E., Abadi, A., … Sukamto, I. (2020). Learning as a critical encounter with the other: prospective teachers conversing with the history of mathematics. Journal of Physics: Conference Series, 11(1), 171–184. https://doi.org/10.1007/s11858-022-01393-z

Downloads

Published

01-02-2025

How to Cite

Sugiarni, R., Herman, T., Suryadi, D., Prabawanto, S., & Jusniani, N. (2025). Learning obstacle of proportion learning based on proposional reasoning level: A case study pre-service mathematics teachers. Jurnal Elemen, 11(1), 87–107. https://doi.org/10.29408/jel.v11i1.27418

Issue

Section

Articles

Similar Articles

<< < 4 5 6 7 8 9 10 11 12 13 > >> 

You may also start an advanced similarity search for this article.