### What are The Difficulties in Learning Percentages? An Overview of Prospective Mathematics Teachers’ Strategies in Solving Percentage Problems

#### Abstract

Many studies showed that teachers and prospective teachers have difficulty solving percentage problems. This research is a qualitative descriptive study that aims to investigate the prospective teachers’ strategies in solving problems on the topic of percentages. A total of 250 students majoring in Mathematics Education and Primary Education at IAIN Syekh Nurjati and IAIN Pekalongan were purposively selected to participate in this study. The results showed that only less than half of the participants (40.1%) could give the correct answer. Qualitative data on the strategies used by prospective teachers on the percent question show that (1) teacher candidates ignore the importance of the % symbol and consider the % symbol only as a unit of measurement, (2) teacher candidates ignore the essential role of the reference quantity in the percent question, (3 ) teacher candidates are not used to solving percent problems related to determining initial values before discounts and assume that any percent problem can be solved using multiplication or division.

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A. S. Gay, “A study of middle school students’ understanding of number sense related to percent.” Oklahoma State University, 1990.

S. Dole, T. J. Cooper, A. R. Baturo, and Z. Conoplia, “Year 8, 9 and 10 students’ understanding and access of percent knowledge,” 1997.

P. L. Koay, “The knowledge of percent of pre-service teachers,” 1998.

V. L. Kouba, C. A. Brown, T. P. Carpenter, M. M. Lindquist, E. A. Silver, and J. O. Swafford, “Results of the fourth NAEP assessment of mathematics: Number, operations, and word problems,” Arith. Teach., vol. 35, no. 8, pp. 14–19, 1988.

B. H. Ngu, “Solution representations of percentage change problems: The pre-service primary teachers’ mathematical thinking and reasoning,” Int. J. Math. Educ. Sci. Technol., vol. 50, no. 2, pp. 260–276, 2018, doi: 10.1080/0020739X.2018.1494860.

B. H. Ngu, A. S. Yeung, H. P. Phan, K. S. Hong, and H. Usop, “Learning to solve challenging percentage-change problems: a cross-cultural study from a cognitive load perspective,” J. Exp. Educ., vol. 86, no. 3, pp. 362–385, 2017, doi: 10.1080/00220973.2017.1347774.

M. Parker and G. Leinhardt, “Percent: A Privileged Proportion,” Rev. Educ. Res., 1995, doi: 10.3102/00346543065004421.

A. Tomson, “An Interdisciplinary Analysis of the Concept of Percent.” UC Merced, 2021.

F. van Galen, E. Feijs, N. Figueiredo, K. Gravemeijer, E. Van Herpen, and R. Keijzer, Fractions, percentages, decimals and proportions: A learning-teaching trajectory for grade 4, 5 and 6. Brill Sense, 2008.

M. Van Den Heuvel-Panhuizen, “Improvement of (didactical) assessment by improvement of problems: An attempt with respect to percentage,” Educ. Stud. Math., vol. 27, no. 4, pp. 341–372, 1994.

R. K. Sembiring, S. Hadi, and M. Dolk, “Reforming mathematics learning in Indonesian classrooms through RME,” ZDM - Int. J. Math. Educ., vol. 40, no. 6, pp. 927–939, 2008, doi: 10.1007/s11858-008-0125-9.

V. F. Rianasari, I. K. Budayasa, and S. M. Patahuddin, “Supporting students’ understanding of percentage,” J. Math. Educ., 2012, doi: 10.22342/jme.3.1.621.29-40.

S. Saraswati and A. H. Dewantara, “Konteks pemilihan ketua kelas pada materi persentase: desain pembelajaran dengan pendekatan PMRI,” Didakt. J. Kependidikan, vol. 14, no. 1, pp. 30–43, 2020.

N. F. Handayani and N. Astuti, “Pengaruh Penggunaan Metode Pembelajaran Make A Match Terhadap Hasil Belajar Matematika Mengubah Pecahan Kebentuk Persen Kelas V SD,” J. PAHLAWAN, vol. 15, no. 2, pp. 184–192, 2019.

J. A. Jacobs Danan and R. Gelman, “The problem with percentages,” Philos. Trans. R. Soc. B Biol. Sci., vol. 373, no. 1740, p. 20160519, 2018.

C. S. Ngin, “Examining a Teacher’s Use of Multiple Representations in the Teaching of Percentages: A Commognitive Perspective.,” Math. Educ. Res. Gr. Australas., 2018.

A. Yapici and M. K. Altay, “An Investigation of Middle School Students’ Number Sense Regarding The Percent,” Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Derg, vol. 17, no. 4, pp. 2221–2243, 2017.

B. Hancock, E. Ockleford, and K. Windridge, An Introduction to Qualitative Research. The NIHR RDS EM, 2009.

N. Putra, Metode Penelitian Kualitatif Pendidikan. Jakarta: Rajawaali Pers, 2013.

S. Campbell et al., “Purposive sampling: complex or simple? Research case examples,” J. Res. Nurs., vol. 25, no. 8, pp. 652–661, 2020.

L. R. Aiken, “Content validity and reliability of single items or questionnaires,” Educ. Psychol. Meas., vol. 40, no. 4, pp. 955–959, 1980.

B. F. Risacher, “Knowledge growth of percent during the middle school years.” University of Delaware, 1992.

H. T. Lestiana and C. T. Wanita, “Bar Model: A Beneficial Tool in Learning Percentage,” Eduma Math. Educ. Learn. Teach., vol. 8, no. 2, pp. 18–25, 2019.

F. Van Galen and D. Van Eerde, “Solving problems with the percentage bar,” J. Math. Educ., 2013.

E. ERDEM, A. ÖZÇELİK, and R. GÜRBÜZ, “Difficultiıes Encountered By 7th Graders in The Subject’Percent’And Suggestions.,” Inonu Univ. J. Fac. Educ., vol. 19, no. 3, 2018.

W. Baratta, B. Price, K. Stacey, V. Steinle, and E. Gvozdenko, “Percentages: The effect of problem structure, number complexity and calculation format.,” Math. Educ. Res. Gr. Australas., 2010.

C. Rahayu and R. I. I. Putri, “Pembelajaran Tentang Persentase dengan Baterai Handphone di Kelas V SD Negeri 119 Palembang,” J. Pendidik., vol. 17, no. 1, p. 2016, 2016.

DOI: https://doi.org/10.24042/ijsme.v4i3.10132

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