Article Sidebar

Download
PDF Appendix
Statistic
Read Counter : 265 Download : 56

Downloads

Download data is not yet available.

Main Article Content

Abstract

This study aimed to evaluate the level of proportional reasoning among middle school students in their ability to solve mathematical problems involving proportions. Proportional reasoning is essential for understanding and mastering various mathematical concepts, serving as a fundamental skill for higher-level mathematics. A qualitative case study design was employed, involving 28 eighth-grade students from a school in Bandung, Indonesia. The participants were assessed using a set of proportion-related problems, including numerical comparison, non-proportional (additive), direct proportion, and inverse proportion tasks. The analysis focused on categorizing the students' problem-solving strategies into distinct levels of proportional reasoning, ranging from non-proportional to formal proportional reasoning. Additionally, three students representing high, moderate, and low mathematical performance were selected for in-depth interviews to explore their reasoning processes when addressing proportion problems. Data analysis included administering tests, reviewing students' problem-solving strategies, conducting in-depth interviews, and evaluating their proportional reasoning abilities. The findings revealed that students with high and moderate mathematical performance exhibited proportional reasoning levels ranging from 0 to 3, whereas low-performing students displayed levels ranging from 0 to 2. Moreover, students generally faced difficulties distinguishing between proportional and non-proportional problems. Even when correct answers were provided, many lacked a deep understanding of direct and inverse proportion concepts. The study also discusses several implications for enhancing students' proportional reasoning skills.

Keywords

Middle School Students Proportional Problem Proportional Reasoning Solution Strategies

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Sari, R. N., Rosjanuardi, R., Isharyadi, R., & Nurhayati, A. (2024). Level of students’ proportional reasoning in solving mathematical problems. Journal on Mathematics Education, 15(4), 1095–1114. https://doi.org/10.22342/jme.v15i4.pp1095-1114
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Arican, M. (2018). 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
  2. Arican, M. (2019a). A diagnostic assessment to middle school students’ proportional reasoning. Turkish Journal of Education, 8(4), 237–257. https://doi.org/10.19128/turje.522839
  3. Arican, M. (2019b). 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 (IJRES), 5(1), 102–117.
  4. Artut, P. D., & Pelen, M. S. (2015). 6th Grade Students’ Solution Strategies on Proportional Reasoning Problems. Procedia - Social and Behavioral Sciences, 197(February), 113–119. https://doi.org/10.1016/j.sbspro.2015.07.066
  5. Atabaş, Ş., & Öner, D. (2017). An Examination of Turkish Middle School Students ’ Proportional Reasoning. Boğaziçi University Journal of Education, 33(1), 63–85.
  6. Avcu, R., & Dogan, M. (2014). What Are the Strategies Used by Seventh Grade Students While Solving Proportional Reasoning Problems? International Journal of Educational Studies in Mathematics, 1(2), 34–55. https://doi.org/10.17278/ijesim.2014.02.003
  7. Ayan Civak, R., Işiksal Bostan, M., & Yemen Karpuzcu, S. (2022). Development of a Hypothetical Learning Trajectory for Enhancing Proportional Reasoning. Hacettepe Egitim Dergisi, 37(1), 345–365. https://doi.org/10.16986/HUJE.2020063485
  8. Ayan, R., & Isiksal-Bostan, M. (2019). Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology, 50(1), 65–81. https://doi.org/10.1080/0020739X.2018.1468042
  9. Ben-Chaim, D., Keret, Y., & Ilany, B.-S. (2012). Ratio and Proportion Research and Teaching in Mathematics Teacher’s Education (Pre-and In-Service Mathematics Teachers of Elementary and Middle School Classes). Sense Publishers.
  10. 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), 0–7. https://doi.org/10.1088/1742-6596/1882/1/012083
  11. Boyer, T. W., & Levine, S. C. (2015). Prompting children to reason proportionally: Processing discrete units as continuous amounts. Developmental Psychology, 51(5), 615–620. https://doi.org/10.1037/a0039010
  12. Burgos, M., & Godino, J. D. (2020). 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
  13. Carney, M. B., Smith, E., Hughes, G. R., Brendefur, J. L., & Crawford, A. (2016). Influence of proportional number relationships on item accessibility and students’ strategies. Mathematics Education Research Journal, 28(4), 503–522. https://doi.org/10.1007/s13394-016-0177-z
  14. Crowe, S., Cresswell, K., Robertson, A., Huby, G., Avery, A., & Sheikh, A. (2011). The case study approach. BMC Medical Research Methodology, 11(1), 100. https://doi.org/10.1186/1471-2288-11-100
  15. D’Angela Menduni-Bortoloti, R., & Barbosa, J. C. (2017). A Construção de uma Matemática para o Ensino do Conceito de Proporcionalidade Direta a partir de uma Revisão Sistemática de Literatura. Bolema - Mathematics Education Bulletin, 31(59), 947–967. https://doi.org/10.1590/1980-4415v31n59a05
  16. Dole, S., Hilton, A., & Hilton, G. (2015). Proportional Reasoning as Essential Numeracy. Mathematics Education in the Margins (Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia), 189–196.
  17. Doyle, K. M., Dias, O., Kennis, J. R., Czarnocha, B., & Baker, W. (2015). The rational number sub-constructs as a foundation for problem solving. Adults Learning Mathematics: An International Journal, 11(1), 21–42. https://eric.ed.gov/?id=EJ1091996
  18. Feagin, J. R., Orum, A. M., & Sjoberg, G. (2016). A case for the case study. UNC Press Book. https://uncpress.org/book/9780807843215/a-case-for-the-case-study/
  19. Gea, M. M., Hernández-Solís, L. A., Batanero, C., & Álvarez-Arroyo, R. (2023). Relating students’ proportional reasoning level and their understanding of fair games. Journal on Mathematics Education, 14(4), 663–682. https://doi.org/10.22342/jme.v14i4.pp663-682
  20. Gundogdu, N. S., & Tunc, M. P. (2022). Improving Middle School Students ’ Proportional Reasoning Through STEM Activities. Journal of Pedagogical Research, 6(2), 164–185.
  21. Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016). Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers. Educational Studies in Mathematics, 92(2), 193–219. https://doi.org/10.1007/s10649-016-9694-7
  22. Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of mathematical reasoning addressed in empirical research in mathematics education: A systematic review. Education Sciences, 10(289), 1–15. https://doi.org/10.3390/educsci10100289
  23. Irfan, M., Nusantara, T., Subanji, S., & Sisworo, S. (2018). Why Did the Students Make Mistakes in Solving Direct and Inverse Proportion Problem ? International Journal of Insights for Mathematics Teaching, 1(1), 25–34.
  24. Irfan, M., Nusantara, T., Subanji, S., & Sisworo, S. (2019). Direct proportion or inverse proportion? The occurrence of student thinking interference. International Journal of Scientific and Technology Research, 8(7), 587–590.
  25. Izsák, A., & Jacobson, E. (2017). Preservice teachers’ reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), 300–339. https://doi.org/10.5951/jresematheduc.48.3.0300
  26. Izzatin, M. (2021). Students’ proportional reasoning in solving non-routine problems based on mathematical disposition. In Journal of Physics: Conference Series (Vol. 1918, Issue 4). https://doi.org/10.1088/1742-6596/1918/4/042114
  27. Jitendra, A. K., Dougherty, B., Sanchez, V., Harwell, M. R., & Harbour, S. (2023). Building Conceptual Understanding of Multiplicative Reasoning Content in Third Graders Struggling to Learn Mathematics: A Feasibility Study. Learning Disabilities Research and Practice, 38(4), 285–295. https://doi.org/10.1111/ldrp.12322
  28. Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding Essential Content Knowledge and Instructional Strategies for Teacher. Routledge. https://doi.org/10.4324/9781410617132
  29. Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in The Middle School, 6(4), 254–261.
  30. Lundberg, A. 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
  31. Ministry of Education and Culture. (2022). Capaian Pembelajaran Mata Pelajaran Matematika Fase A - Fase F.
  32. Misnasanti, Utami, R. W., & Suwanto, F. R. (2017). Problem based learning to improve proportional reasoning of students in mathematics learning. AIP Conference Proceedings, 1868. https://doi.org/10.1063/1.4995129
  33. Parameswari, P., Purwanto, P., Sudirman, S., & Susiswo, S. (2023). Correct-Incorrect Proportional Reasoning Strategies on the Proportional Problems and SOLO Taxonomy Correct-Incorrect Proportional Reasoning Strategies on the Proportional Problems and SOLO Taxonomy. Acta Scientiae, 25(5), 86–117. https://doi.org/10.17648/acta.scientiae.7465
  34. Pelen, M. S., & Artut, P. D. (2016). Seventh Grade Students’ Problem Solving Success Rates on Proportional Reasoning Problems. International Journal of Research in Education and Science, 2(1), 30–34. https://doi.org/10.21890/ijres.71245
  35. Prayitno, A., Rossa, A., & Widayanti, F. D. (2019). Level Penalaran Proporsional Siswa dalam Memecahkan Missing Value Problem. Jurnal Riset Pendidikan Matematika, 6(2), 177–187. https://doi.org/10.21831/jrpm.v6i2.19728
  36. Prayitno, A., Rossa, A., Widayanti, F. D., Rahayuningsih, S., Hamid, A., & Baidawi, M. (2018). Characteristics of Students’ Proportional Reasoning in Solving Missing Value Problem. Journal of Physics: Conference Series, 1114(1). https://doi.org/10.1088/1742-6596/1114/1/012021
  37. 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
  38. Putra, H. D. (2014). Tahap Perkembangan Kognitif Matematika Siswa MTs Asy Syifa Kelas IX Berdasarkan Teori Piaget. Prosiding Seminar Nasional Pendidikan Matematika STKIP Siliwangi, 2, 224–230.
  39. Rohaeti, E. E., Putra, H. D., & Primandhika, R. B. (2019). Mathematical understanding and reasoning abilities related to cognitive stage of senior high school students. Journal of Physics: Conference Series, 1318(1). https://doi.org/10.1088/1742-6596/1318/1/012099
  40. Sari, Y. M. (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
  41. Sukirwan, Darhim, D., & Herman, T. (2018). Analysis of students’ mathematical reasoning. Journal of Physics: Conference Series, 948(1). https://doi.org/10.1088/1742-6596/948/1/012036
  42. Thomas, E., & Magilvy, J. K. (2011). Qualitative Rigor or Research Validity in Qualitative Research. Journal for Specialists in Pediatric Nursing, 16(2), 151–155. https://doi.org/10.1111/j.1744-6155.2011.00283.x
  43. Tunc, M. P. (2020). Investigation of Middle School Students’ Solution Strategies in Solving Proportional and Non-proportional Problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 1–14. https://doi.org/10.16949/turkbilmat.560349
  44. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23(1), 57–86. https://doi.org/10.1207/s1532690xci2301_3
  45. 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
  46. Vanluydt, E., Supply, A. S., Verschaffel, L., & Van Dooren, 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
  47. Venkat, H., & Mathews, C. (2018). Improving multiplicative reasoning in a context of low performance. ZDM - Mathematics Education, 51(1), 95–108. https://doi.org/10.1007/s11858-018-0969-6
  48. 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). https://doi.org/10.1088/1742-6596/1320/1/012046
  49. Walle, J. A. Van de, Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics: Teaching Developmentally. Pearson Education Ltd.
  50. Wijayanti, D., & Winslow, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. Journal of Research in Mathematics Education, 6(3), 307–330. https://doi.org/10.17583/redimat.2017.2078