Analysis the proportional reasoning abilities of senior high school students in solving mathematical problems:

Dhuwi Novita Sari; Helti Lygia Mampouw

doi:10.33654/math.v5i2.569

Dhuwi Novita Sari Universitas Kristen Satya Wacana https://orcid.org/0000-0002-5278-6135
Helti Lygia Mampouw Universitas Kristen Satya Wacana

DOI: https://doi.org/10.33654/math.v5i2.569

Keywords: Mathematics, Problem solving, Proportional reasoning

Abstract

This research aims to analyze the proportional reasoning abilities of high school students in solving mathematical problems. Subject of this qualitative descriptive research were 3 of tenth grade students of SMA Negeri 2 Salatiga who have high mathematical abilities. The researchers are the main instrument, supported by test instruments and interview guidelines. Data from the test and interview results were analyzed using steps data reduction, data display, and conclusion drawing. The results showed that the three subjects had different proportional reasoning abilities in solving mathematical problems. The proportional reasoning ability of subject S tends to be at level 1 by showing strategies using images and making qualitative comparisons. The proportional reasoning ability of subject F tends to be at level 2 by showing strategies of connecting models through numerical calculations, using composite units, and using quantitative reasoning. The proportional reasoning ability of subject M tends to be at level 3 by showing strategies using formal methods and knowing invariant and covariant relationships. The three subjects showed proportional reasoning ability at level 0 in solving problems that needed additive and multiplicative comparisons by simply describing the change situation in additive view.

Downloads

Download data is not yet available.

References

Acton, M. (2009). Teenage well-being. Retrieved from https://www.tusla.ie/uploads/content/Teenagers_Wellbeing_d3.pdf

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.

Căprioară, D. (2015). Problem Solving - Purpose and Means of Learning Mathematics in School. Procedia - Social and Behavioral Sciences, 191, 1859–1864.

Cetin, H., & Ertekin, E. (2011). The relationship between eighth-grade primary school students’ proportional reasoning skills and success in solving equations. International Journal of Instruction, 4(1), 47–62.

Dole, S., Clarke, D., Wright, T., & Hilton, G. (2012). Students’ proportional reasoning in mathematics and science. In Tso, T.Y. (Ed). Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, 2, 195–202. Taipei, Taiwan: PME.

Dole, S., Wright, T., & Clarke, D. (n.d.). Proportional Reasoning. Making Connections in Science and Mathematics, 1–18. https://doi.org/10.1027/1618-3169.56.2.92

Dooley, K. B. (2006). an Investigation of Proportional Thinking Among High School Students. (December).

Frith, V., & Lloyd, P. (2016). Investigating Proportional Reasoning in a University Quantitative Literacy Course. 9(1).

Isroil, A., Budayasa, I.K., & Masriyah, M. (2018). Profil Berpikir Siswa SMP dalam Menyelesaikan Masalah Matematika Ditinjau dari Kemampuan Matematika. Jurnal Review Pembelajaran Matematika, 2(2), 93.

Jung, S. P., Jee, H. P., & Oh, N. K. (2010). Characterizing the Proportional Reasoning of Middle School Students. The SNU Journal Of Education Research, 119–144.

Langrall, C. W., & Swafford, J. (2000). Three Balloons for Two Dollars: Developing Proportional Reasoning. Mathematics Teaching in the Middle School, 6(4), 254–261.

Lewis, E.T. (2012). Qualitative Data Analysis: A Participatory View. Retrieved from http://emmathereselewis.com/Papers/Data Analysis Feb12.pdf

Montague, M. (2004). Math Problem Solving for Middle School Students with Disabilities. American Institutes for Research, 1–13.

Nugraha, Y., Sujadi, I., & Pangadi. (2016). Penalaran proporsional siswa kelas VII. Beta - Jurnal Tadris Matematika, 9(1), 34–47.

OECD. (2013). PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy.

Ojose, B. (2015). Proportional Reasoning and Related Concepts: Analysis of Gaps and Understandings of Middle-Grade Students. Universal Journal of Educational Research, 3(2), 104–112.

Ortiz, A. M. (2015). Examining Students’ Proportional Reasoning Strategy Levels as Evidence of the Impact of an Integrated LEGO Robotics and Mathematics Learning Experience. Journal of Technology Education, 26(2), 46–69.

Parish, L. (2010). Facilitating the Development of Proportional Reasoning through Teaching Ratio. In L. Sparrow, B. Kissane, & C. Hurst (Eds.). Shaping the Future of Mathematics Education: Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia., 469–476. Fremantle: MERGA.

Prayitno, A., Rossa, A., Widayanti, F. D., Rahayuningsih, S., Hamid, A. A., & Baidawi, M. (2018). Characteristics of Students ’ Proportional Reasoning In Solving Missing Value Problem. Journal of Physics: Conference Series, 0–6.

Şen, C., & Güler, G. (2017). Effect of Strategy Teaching For the Solution of Ratio Problems on Students ’ Proportional Reasoning Skills. Malaysian Online Journal of Educational Sciences, 5(2), 1–15.

Syahlan. (2017). Sepuluh strategi dalam pemecahan masalah matematika. Indonesian Digital Journal of Mathematics and Education, 4(6), 358–369.

Thompson, C. S., & Bush, W. S. (2003). Improving middle school teachers’ reasoning about proportional reasoning. Mathematics Teaching in the Middle School, 8(8), 398–403.

Utami, R. W., & Wutsqa, D. U. (2017). Analisis Kemampuan Pemecahan Masalah Matematika dan Self-Efficacy Siswa SMP Negeri di Kabupaten Ciamis. Jurnal Riset Pendidikan Matematika, 4(2), 166–176.

Walle, J.A.V. (2007). Matematika Sekolah Dasar dan Menengah. (Terjemahan Suyono). Jakarta: Penerbit Erlangga.

Analisis kemampuan penalaran proporsional siswa SMA dalam memecahkan masalah matematika