The Difficulties of Prospective Elementary School Teachers in Item Problem Solving for Mathematics: Polya’s Steps

Problem-solving in mathematics is one of the skills that have to be mastered by elementary school teacher candidates. This study aimed to analyze the difficulties of prospective elementary school teachers at the Universitas Muhammadiyah Malang (UMM) in item problem solving for mathematics. This research was a descriptive exploratory with a qualitative approach. The subjects were elementary school teacher education students at the UMM, who attended the Elementary School Mathematics Learning course II, totaling of 38 students. The instrument used was a mathematical problem based on HOTS, while the interview and observation referred to problem-solving strategies based on Polya's steps (ability to understand problems, ability to plan problems, ability to act based on a plan, and ability to re-check answers). Data analysis was performed by analyzing the written answer sheets of the subjects while coding and grouping the subject's learning styles. The data from the interview and observation were analyzed with content analysis. The results showed that students still experienced difficulties in all Polya’s steps. The ability of problem-solving based on Polya's steps include understanding the problem, planning, and writing strategies, as well as carrying out activities according to plan. The results of the study stated that only 5.3% of students were in a good category. Students also have had difficulty in re-checking answers, because only 8% of students did the work correctly. It can be concluded that the ability of problem-solving in Mathematics based on Polya's steps was still relatively weak.

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  • Abramovich, S., Grinshpan, A. Z., & Milligan, D. L. (2019). Teaching mathematics through concept motivation and action learning. Education Research International, 3745406, 1–13. https://doi.org/10.1155/2019/3745406
  • Allen, L., & Kelly, B. B. (2015). Transforming the workforce for children birth through age 8: Unifying foundation. https://doi.org/10.17226/19401
  • Anugrahana, A. (2016). Peningkatan kompetensi dasar mahasiswa calon guru SD pada mata kuliah pendidikan matematika dengan model pembelajaran inovatif. Jurnal Penelitian (Edisi Khusus PGSD), 20(12), 182–187. Retrieved from https://e-journal.usd.ac.id/index.php/JP/article/download/875/691
  • Argarini, D. F. (2018). Analisis pemecahan masalah berbasis Polya pada materi perkalian vektor ditinjau dari gaya belajar. Jurnal Matematika Dan Pembelajaran, 6(1), 91–99. Retrieved from http://jurnal.iainambon.ac.id/index.php/INT/article/download/448 /360
  • Avcu, S., & Avcu, R. (2010). Pre-service elementary mathematics teacher’s use of strategies in mathematical problem solving. Procedia - Social and Behavioral Sciences, 9, 1282–1286. https://doi.org/10.1016/j.sbspro.2010.12.321
  • Bal, A. P. (2015). Examination of the mathematical problem-solving beliefs and success levels of primary school teacher candidates through the variables of mathematical success and gender. Educational Sciences: Theory & Practice, 15(5), 1373–1390. https://doi.org/10.12738/estp.2015.5.2573
  • Başkale, H., Bahar, Z., Başer, G., & Ari, M. (2009). Use of Piaget’s theory in preschool nutrition education. Revista de Nutrição, 22(6), 905–917. https://doi.org/10.1590/ s1415-52732009000600012
  • Belland, B. R., Kim, C. M., & Hannafin, M. J. (2013). A framework for designing scaffolds that improve motivation and cognition. Educational Psychologist, 48(4), 243–270. https://doi.org/10.1080/00461520.2013.838920
  • Billstein, R., Libeskind, S., & Lott, J. (2016). A problem solving approach to mathematics for elementary school teachers (12 Eds.). Retrieved from https://www.pearson.com/us/ higher-education/program/Billstein-Problem-Solving-Approach-to-Mathematics-for-Elementary-School-Teachers-A-Plus-My-Lab-Math-Access-Card-Package-12th-Edition/PGM250443.html
  • Borg, E., & Drange, I. (2019). Interprofessional collaboration in school: Effects on teaching and learning. Improving Schools, 22(3), 251–266. https://doi.org/10.1177/13654802198 64812
  • Brame, C. J. (2016). Effective educational videos: Principles and guidelines for maximizing student learning from video content. CBE Life Sciences Education, 15(4), es6.1-es6.6. https://doi.org/10.1187/cbe.16-03-0125
  • Bulut, N., & Karamık, G. (2015). Preservice mathematics teachers’ ways of using problem solving strategies while solving mathematical word problems. International Journal of Human Sciences, 12(2), 1180–1191. https://doi.org/10.14687/ijhs.v12i2.3420
  • Cahyani, H., & Setyawati, R. W. (2016). Pentingnya peningkatan kemampuan pemecahan masalah melalui PBL untuk mempersiapkan generasi unggul menghadapi MEA. PRISMA, Prosiding Seminar Nasional Matematika, 151–160. Retrieved from https://journal.unnes.ac.id/sju/index.php/prisma/article/download/21635/10234/
  • Calder, L., & Carlson, S. (2004). Using “Think alouds” to evaluate deep understanding. In R. L. Swing (Ed.), Proving and improving, volume II: Tools and techniques for assessing the first college year: Vol. II (pp. 35–38). Retrieved from https://files.eric.ed.gov/fulltext/ED503169. pdf#page=64
  • Clark, L. A., Cuthbert, B., Lewis-Fernández, R., Narrow, W. E., & Reed, G. M. (2017). Three approaches to understanding and classifying mental disorder: ICD-11, DSM-5, and the National Institute of Mental Health’s Research Domain Criteria (RDoC). Psychological Science in the Public Interest, 18(2), 72–145. https://doi.org/10.1177/1529100617727266
  • Darling-Hammond, L., Flook, L., Cook-Harvey, C., Barron, B., & Osher, D. (2019). Implications for educational practice of the science of learning and development. Applied Developmental Science, 0(0), 1–44. https://doi.org/10.1080/10888691.2018.153 7791
  • De Sousa, L., Richter, B., & Nel, C. (2017). The effect of multimedia use on the teaching and learning of Social Sciences at tertiary level: a case study. Yesterday and Today, (17), 1–22. https://doi.org/10.17159/2223-0386/2017/n17a1
  • DeJarnette, N. (2016). Changing perceptions of teacher candidates in high-needs schools. School-University Partnerships, 9(1), 71–79. Retrieved from https://files.eric.ed.gov/full text/EJ1107089.pdf
  • Dewi, S. K., Suarjana, M., & Sumantri, M. (2014). Penerapan model Polya untuk meningkatkan hasil belajar dalam memecahkan soal cerita matematika siswa kelas V. Jurnal Mimbar PGSD Universitas Pendidikan Ganesha, 2(1), 1–10. Retrieved from https://ejournal.undiksha.ac.id/index.php/JJPGSD/article/viewFile/2057/1794
  • Dostál, J. (2015). Theory of problem solving. Procedia - Social and Behavioral Sciences, 174, 2798–2805. https://doi.org/10.1016/j.sbspro.2015.01.970
  • Ecevit, T., Yalaki, Y., & Kingir, S. (2018). Improving elementary school teacher candidates’ views of nature of science through intensive education. Journal of Education in Science, Environment and Health, 4(2), 155–171. https://doi.org/10.21891/jeseh.432524
  • Eichmann, B., Goldhammer, F., Greiff, S., Pucite, L., & Naumann, J. (2019). The role of planning in complex problem solving. Computers and Education, 128, 1–12. https://doi.org/10.1016/j.compedu.2018.08.004
  • Ersoy, E., & Bal-Incebacak, B. (2017). The evaluation of the problem solving in mathematics course according to student views. ITM Web of Conferences, 13, 01012. https://doi.org/10.1051/itmconf/20171301012
  • Esan, F. (2015). Cooperative problem-solving strategy and students’ learning outcomes in algebraic word problems: A Nigerian case. International Journal for Infonomics, 8(1), 986–989. https://doi.org/10.20533/iji.1742.4712.2015.0116
  • Foshay, R., & Kirkley, J. (1998). Principles for teaching problem solving (No. ED464604). Retrieved from https://eric.ed.gov/?id=ED464604
  • Gaudiano, B. A. (2008). Cognitive-behavioral therapies: Achievements and challenges. Evidence-Based Mental Health, 11(1), 5–7. https://doi.org/10.1136/ebmh.11.1.5
  • Goldhammer, F., Naumann, J., Stelter, A., Tóth, K., Rölke, H., & Klieme, E. (2014). The time on task effect in reading and problem solving is moderated by task difficulty and skill: Insights from a computer-based large-scale assessment. Journal of Educational Psychology, Vol. 106, pp. 608–626. https://doi.org/10.1037/a0034716
  • Gomez, M. L. (1993). Prospective Teachers’ Perspectives on Teaching Diverse Children: A Review with Implications for Teacher Education and Practice. The Journal of Negro Education, 62(4), 459–474. https://doi.org/10.2307/2295517
  • Gulacar, O., Bowman, C. R., & Feakes, D. a. (2013). Observational investigation of student problem solving: The role and importance of habits. Science Education International, 24(2), 344–360. Retrieved from https://files.eric.ed.gov/fulltext/EJ1022260.pdf
  • Hadi, S., & Radiyatul, R. (2014). Metode pemecahan masalah menurut Polya untuk mengembangkan kemampuan siswa dalam pemecahan masalah matematis di sekolah menengah pertama. EDU-MAT: Jurnal Pendidikan Matematika, 2(1), 53–61. https://doi.org/10.20527/edumat.v2i1.603
  • Hapizah, H. (2017). Kemampuan mahasiswa menyelesaikan soal problem-solving mata pelajaran matematika tingkat sekolah menengah pertama. Jurnal Pendidikan Dan Pembelajaran (JPP), 23(2), 124–131. Retrieved from http://journal.um.ac.id/index.php/ pendidikan-dan-pembelajaran/article/view/10163/4850
  • Herranen, J., & Aksela, M. (2019). Student-question-based inquiry in science education. Studies in Science Education, 55(1), 1–36. https://doi.org/10.1080/03057267.2019.1658 059
  • Hu, H. W., Chiu, C. H., & Chiou, G. F. (2019). Effects of question stem on pupils’ online questioning, science learning, and critical thinking. Journal of Educational Research, 112(4), 564–573. https://doi.org/10.1080/00220671.2019.1608896
  • Hudha, A. M., Amin, M., Sumitro, S. B., & Akbar, S. (2018). The effectiveness of OIDDE learning model in the improvement of bioethics knowledge, ethical decision, and ethical attitude of biology pre- service teachers. Journal of Baltic Science Education, 17(6), 960–971.
  • Husamah, H., Fatmawati, D., & Setyawan, D. (2018). OIDDE learning model: Improving higher order thinking skills of biology teacher candidates. International Journal of Instruction, 11(2), 249–264. https://doi.org/10.12973/iji.2018.11217a
  • Ichsan, I. Z., Sigit, D. V., Miarsyah, M., Ali, A., Arif, W. P., & Prayitno, T. A. (2019). HOTS-AEP: Higher order thinking skills from elementary to master students in environmental learning. European Journal of Educational Research, 8(4), 935–942. https://doi.org/10.12973/eu-jer.8.4.935
  • Irwanto, Saputro, A. D., Rohaeti, E., & Prodjosantoso, A. K. (2018). Promoting critical thinking and problem solving skills of preservice elementary teachers through process-oriented guided-inquiry learning (POGIL). International Journal of Instruction, 11(4), 777–794. https://doi.org/10.12973/iji.2018.11449a
  • Jacques, L. A., Cian, H., Herro, D. C., & Quigley, C. (2019). The impact of questioning techniques on STEAM instruction. Action in Teacher Education, 0(0), 1–19. https://doi.org/10.1080/01626620.2019.1638848
  • Kania, N. (2019). Analisis kesulitan calon guru sekolah dasar dalam menyelesaikan soal pemecahan masalah matematis berdasarkan prosedur Newman. SJME (Supremum Journal of Mathematics Education), 3(1), 57–66. Retrieved from https://osf.io/brwgs/ download/?format=pdf
  • Kaya, D., Izgiol, D., & Kesan, C. (2014). The investigation of elementary mathematics teacher candidates’ problem solving skills according to various variables. International Electronic Journal of Elementary Education, 6(2), 295–313. Retrieved from https://core.ac. uk/download/pdf/26673028.pdf
  • Khoiriyah, A. J., & Husamah, H. (2018). Problem-based learning: Creative thinking skills, problem-solving skills, and learning outcome of seventh grade students. JPBI (Jurnal Pendidikan Biologi Indonesia), 4(2), 151–160. https://doi.org/10.22219/jpbi.v4i2.5804
  • Kloser, M., Wilsey, M., Madkins, T. C., & Windschitl, M. (2019). Connecting the dots: Secondary science teacher candidates’ uptake of the core practice of facilitating sensemaking discussions from teacher education experiences. Teaching and Teacher Education, 80, 115–127. https://doi.org/10.1016/j.tate.2019.01.006
  • Knight, M., & Cooper, R. (2019). Taking on a new grading system: The interconnected effects of standards-based grading on teaching, learning, assessment, and student behavior. NASSP Bulletin, 103(1), 65–92. https://doi.org/10.1177/0192636519826 709
  • Komariah, K. (2011). Penerapan metode pembelajaran problem solving model Polya untuk meningkatkan kemampuan memecahkan masalah bagi siswa kelas IX J di SMPN 3 Cimahi. Prosiding Seminar Nasional Penelitian, Pendidikan Dan Penerapan MIPA, Fakultas MIPA, Universitas Negeri Yogyakarta, 1. Retrieved from https://eprints.uny.ac.id/ 7195/1/PM-25 - Kokom Komariah.pdf
  • Liakopoulou, M. (2011). The professional competence of teachers: Which qualities , attitudes, skills and knowledge contribute to a teacher’s effectivenes? International Journal of Humanities and Social Science, 1(21), 66–78. Retrieved from https://pdfs. semanticscholar.org/c757/316940222c52ca17fa53a9172a7f2fa93094.pdf
  • Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. In Problem Solving in Mathematics Education (pp. 1–39). https://doi.org/10.1007/978-3-319-40730-2_1
  • Liljedahl, Peter, & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/ download?doi=10.1.1.604.7943&rep=rep1&type=pdf
  • Lindholm, M. (2018). Promoting curiosity?: Possibilities and pitfalls in science education. Science and Education, 27(9–10), 987–1002. https://doi.org/10.1007/s11191-018-0015-7
  • Loughran, J. (2013). Pedagogy: Making sense of the complex relationship between teaching and learning. Curriculum Inquiry, 43(1), 118–141. https://doi.org/10.1111/curi.12003
  • Mahardhikawati, E., Mardiyana, & Setiawan, R. (2017). Analisis kemampuan pemecahan masalah berdasarkan langkah-langkah Polya pada materi turunan fungsi ditinjau dari kecerdasan logis-matematis siswa kelas XI IPA SMA Negeri 7 Surakarta tahun Ajaran 2013/2014. Jurnal Pendidikan Matematika Dan Matematika (JPMM) Solusi, 1(4), 119–128. Retrieved from http://www.jurnal.fkip.uns.ac.id/index.php/matematika/article/ view/11608
  • Mehmood, S. T. (2014). Effect of Polya’s problem solving method of teaching on achievement of revised Bloom’s taxonomy in mathematics at elementary level (Department of Education Faculty of Social Sciences International Islamic University). Retrieved from http://prr.hec.gov.pk/jspui/bitstream/123456789/6780/1/Sheikh_Tariq_Mahmood_Education_IIU_2015.pdf
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methodes sourcebook (3rd Ed.). Retrieved from http://www.theculturelab.umd.edu/ uploads/1/4/2/2/14225661/miles-huberman-saldana-designing-matrix-and-networ k-displays.pdf
  • Muhlisin, A. (2019). Reading, mind mapping, and sharing(RMS): Innovation of new learning model on science lecture to improve understanding concepts. Journal for the Education of Gifted Young Scientists, 7(2), 323–340. https://doi.org/10.17478/jegys.570501
  • Muhlisin, A., Susilo, H., Amin, M., & Rohman, F. (2016). Improving critical thinking skills of college students through RMS model for learning basic concepts in science. Asia-Pacific Forum on Science Learning and Teaching, 17(1).
  • Muhlisin, A., Susilo, H., Amin, M., & Rohman, F. (2018). The effectiveness of RMS learning model in improving metacognitive skills on science basic concepts. Journal of Turkish Science Education, 15(4), 1–14. https://doi.org/10.12973/tused.10242a
  • Netriwati, N. (2016). Analisis kemampuan pemecahan masalah matematis berdasarkan teori Polya ditinjau dari pengetahuan awal mahasiswa IAIN Raden Intan Lampung. Al-Jabar: Jurnal Pendidikan Matematika, 7(2), 181–190. Retrieved from http://ejournal.raden intan.ac.id/index.php/al-jabar/article/viewFile/32/27
  • OECD. (2005). Teachers matter: attracting, retaining and developing effective teachers. Learning, 304. https://doi.org/10.1787/9789264022157-ja
  • OECD. (2009). The professional development of teachers. In Creating effective teaching and learning environments: First results from TALIS (pp. 47–86). Retrieved from http://www.oecd.org/education/school/43023606.pdf
  • Osmanoglu, A., Isiksal, M., & Koc, Y. (2015). Getting ready for the profession: Prospective teachers’ noticing related to teacher actions. Australian Journal of Teacher Education, 40(2), 29–51. Retrieved from https://ro.ecu.edu.au/cgi/viewcontent.cgi?article=2527&con text=ajte
  • Oyama, Y., Manalo, E., & Nakatani, Y. (2018). The Hemingway effect: How failing to finish a task can have a positive effect on motivation. Thinking Skills and Creativity, 30(February), 7–18. https://doi.org/10.1016/j.tsc.2018.01.001
  • Patnani, M. (2013). Upaya meningkatkan kemampuan problem solving pada mahasiswa. Jurnal Psikogenesis, 1(2), 130–142. Retrieved from http://academicjournal.yarsi.ac.id/ index.php/Jurnal-Online-Psikogenesis/article/download/43/pdf
  • Polya, G. (1981). Mathematical discovery on understanding, learning and teaching problem solving: Combined edition. Retrieved from https://pdfs.semanticscholar.org/a275/1e87f24544 6e4b0e09e31c0efa6f33e9bd4d.pdf
  • Polya, G. (1988). How to solve it, a new aspect of mathematical method (2nd Ed.). Retrieved from https://www.scirp.org/(S(i43dyn45teexjx455qlt3d2q))/reference/ReferencesPapers.aspx?ReferenceID=2131905
  • Ramdiah, S., Abidinsyah, A., Royani, M., & Husamah, H. (2019). Understanding, planning, and implementation of HOTS by senior high school biology teachers in Banjarmasin-Indonesia. International Journal of Instruction, 12(1), 425–440. https://doi.org/10.29333/ iji.2019.12128a
  • Ramdiah, S., Abidinsyah, H., & Mayasari, R. (2018). Problem-based learning: Generates higher-order thinking skills of tenth graders in ecosystem concept. JPBI (Jurnal Pendidikan Biologi Indonesia), 4(1), 29–34. https://doi.org/10.22219/jpbi.v4i1.5490
  • Reuter, T., Schnotz, W., & Rasch, R. (2015). Drawings and tables as cognitive tools for solving non-routine word problems in primary school. American Journal of Educational Research, 3(11), 1387–1397. https://doi.org/10.12691/education-3-11-7
  • Rudtin, N. A. (2013). Penerapan langkah Polya dalam model problem based instruction untuk meningkatkan kemampuan siswa menyelesaikan soal cerita persegi panjang. Jurnal Elektronik Pendidikan Matematika Tadulako, 1(1), 17–31. Retrieved from http://jurnal.untad.ac.id/jurnal/index.php/JEPMT/article/viewFile/1706/1123
  • Rustina, R., & Heryani, Y. (2017). Analisis kesulitan kemampuan pemecahan masalah matematik mahasiswa dengan menggunakan model creative problem solving. Jurnal
  • Siliwangi, 3(2), 237–240. Retrieved from http://jurnal.unsil.ac.id/index.php/ jspendidikan/article/view/266/246
  • Sam, H. N., & Qohar, A. (2016). Pembelajaran berbasis masalah berdasarkan langkah-langkah Polya untuk meningkatkan kemampuan menyelesaikan soal cerita matematika. Kreano, Jurnal Matematika Kreatif-Inovatif, 6(2), 156. https://doi.org/10.15294/kreano. v6i2.5188
  • Santos Trigo, M. (2011). La Educación Matemática, resolución de problemas, y el empleo de herramientas computacionales. Cuadernos de Investigación y Formación En Educación Matemática, 0(8), 35–54. Retrieved from https://revistas.ucr.ac.cr/index.php/cifem/ article/download/6949/6635/
  • Saputri, R. A. (2019). Analisis pemecahan masalah soal cerita materi perbandingan ditinjau dari aspek merencanakan Polya. Wacana Akademika: Majalah Ilmiah Kependidikan, 3(1), 21–38. Retrieved from http://jurnal.ustjogja.ac.id/index.php/wacanaakademika/ article/download/3267/2335
  • Schmidt, H. G., Wagener, S. L., Smeets, G. A. C. M., Keemink, L. M., & van der Molen, H. T. (2015). On the use and misuse of lectures in higher education. Health Professions Education, 1(1), 12–18. https://doi.org/10.1016/j.hpe.2015.11.010
  • Serdyukov, P. (2017). Innovation in education: What works, what doesn’t, and what to do about it? Journal of Research in Innovative Teaching & Learning, 10(1), 4–33. https:// doi.org/10.1108/jrit-10-2016-0007
  • Silberman, M. L. (1996). Active learning: 101 strategies to teach any subject. Retrieved from https://eric.ed.gov/?id=ED424243
  • Someren, M. W. van, Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: A practical guide to modelling cognitive processes. Retrieved from http://citeseerx.ist.psu.edu/ viewdoc/download?doi=10.1.1.98.7738&rep=rep1&type=pdf
  • Stacey Donaldson. (2010). Teachers of the future: Using new skills to prepare students. Retrieved August 19, 2019, from The Source website: http://www.advanc-ed.org/source/teachers-future-using-new-skills-prepare-students
  • Tarusu, D. T. (2018). Kemampuan pedagogik matematika SD pada mahasiswa PGSD FIP UNIMA. Mosharafa: Jurnal Pendidikan Matematika, 7(2), 251–262. https://doi.org/ 10.31980/mosharafa.v7i2.32
  • Umar, W. (2016). Strategi pemecahan masalah matematis versi George Polya dan penerapannya dalam pembelajaran matematika. KALAMATIKA Jurnal Pendidikan Matematika, I(1), 59–70. https://doi.org/10.22236/KALAMATIKA.vol1no1.2016 pp59-70
  • Uyanik, G. (2016). Examining of the elementary teacher candidates’ knowledge levels regarding fourth grade science course units in elementary school. Cumhuriyet International Journal of Education, 5(4), 1–15. https://doi.org/10.30703/cije.321410
  • Whimbey, A., Lochhead, J., & Narode, R. (2013). Problem solving & comprehension (7th ed.). https://doi.org/10.4324/9780203130810
  • Widaninggar, N. N., Mardiyana, M., & Kurniawati, I. (2017). Proses berpikir siswa dalam memecahkan soal cerita pada pokok bahasan lingkaran berdasarkan langkah- langkah Polya ditinjau dari kecemasan matematika (Penelitian dilakukan di SMPN 16 Surakarta tahun ajaran 2015/2016). Jurnal Pendidikan Matematika Dan Matematika (JPMM) Solusi, 1(1), 117–130. Retrieved from http://jurnal.fkip.uns.ac.id/index.php/matematika/ article/download/11206/7992
  • Worden, D. (2015). The development of content knowledge through teaching practice. Ilha Do Desterro, 68(1), 105–119. https://doi.org/10.5007/2175-8026.2015v68n1p105
  • Yayuk, E., Ekowati, D. W., Suwandayani, B. I., & Ulum, B. (2018). Pembelajaran matematika yang menyenangkan. Retrieved from http://eprints.umm.ac.id/44948/20/Yayuk Ekowati Suwandayani Ulum - Pembelajaran Matematika yang Menyenangkan.pdf
  • Yenice, N., Ozden, B., & Evren, B. (2012). Examining of problem solving skills according to different variables for science teachers candidates. Procedia - Social and Behavioral Sciences, 46, 3880–3884. https://doi.org/10.1016/j.sbspro.2012.06.165