Problem posing ability among prospective mathematics teachers

Ibnu Rafi; Sugiman Sugiman

doi:10.21831/pg.v14i2.29976

Problem posing ability among prospective mathematics teachers

Ibnu Rafi, Program Study of Mathematics Education, Graduate School, Universitas Negeri Yogyakarta, Indonesia
Sugiman Sugiman, Department of Mathematics Education, Universitas Negeri Yogyakarta, Indonesia

10.21831/pg.v14i2.29976

Abstract

Posing mathematics problem is perceived as one of the learning strategies to promote students’ skills in mathematics problem-solving as well as one of the crucial competencies that should be mastered by prospective mathematics teachers. Some people argued that for prospective mathematics teachers, posing mathematics problem itself is as important as solving mathematics problem because when they become mathematics teachers, there exist necessity for them to pose mathematics problem as a means for assessing students’ understanding or achievement. The aim of this article, therefore, was to focus on the investigation into the prospective mathematics teachers’ ability in posing mathematics problems. Relevant literature from several electronic databases such as SpringerLink, ScienceDirect, ResearchGate, and Google Scholar was searched based on the following keywords: ‘pre-service mathematics teacher’, ‘problem-posing’, ‘prospective mathematics teacher problem-posing’, and ‘posing mathematics problem’. There was a total of 16 articles which were included into this review according to the determined inclusion criteria as follow: an empirical study that was published in journal or conference proceeding with the publication date from years of 2009 to 2019, written in English, full text, and discussing about prospective mathematics teachers’ ability in posing problem-related to mathematics. There were as many as three themes that deal with the prospective mathematics teachers’ ability to pose the mathematics problem, i.e. type of posed problem, ability in posing mathematics problem, and the difficulty which was experienced by prospective mathematics teachers in posing mathematics problem. These three themes and their implications are discussed in this article.

Kemampuan calon guru matematika dalam mengajukan masalah

Abstrak

Pengajuan masalah matematika dapat dianggap sebagai salah satu strategi pembelajaran untuk mengembangkan keterampilan siswa dalam memecahkan masalah matematika serta sebagai salah satu kompetensi yang penting yang seharusnya dikuasai oleh calon guru matematika. Beberapa orang berpendapat bahwa untuk calon guru matematika, mengajukan masalah matematika itu sama pentingnya dengan memecahkan masalah matematika karena ketika mereka menjadi guru matematika, ada suatu keharusan bagi mereka untuk mengajukan masalah matematika sebagai saran untuk menilai pemahaman atau pencapaian siswa. Tujuan artikel ini, oleh karena itu, adalah untuk fokus pada penyelidikan kemampuan calon guru matematika dalam mengajukan masalah matematika. Literatur yang relevan dari beberapa basis data elektronik seperti SpringerLink, ScienceDirect, ResearchGate, dan Google Scholar dicari berdasarkan kata kunci berikut: ‘pre-service mathematics teacher’, ‘problem-posing’, ‘prospective mathematics teacher problem-posing’, dan ‘posing mathematics problem’. Ada total 16 artikel yang dimasukkan ke dalam tinjauan ini sesuai dengan kriteria inklusi yang ditentukan sebagai berikut: studi empiris yang diterbitkan dalam jurnal atau prosiding seminar dengan tanggal publikasi dari tahun 2009 hingga 2019, ditulis dalam bahasa Inggris, teks lengkap, dan membahas tentang kemampuan calon guru matematika dalam mengajukan masalah yang berkaitan dengan matematika. Ada tiga tema yang berhubungan dengan kemampuan calon guru matematika untuk mengajukan masalah matematika, yaitu jenis masalah yang diajukan, kemampuan dalam mengajukan masalah matematika, dan kesulitan yang dialami oleh calon guru matematika dalam mengajukan masalah matematika. Ketiga tema dan implikasinya dibahas dalam artikel ini.

Keywords

Problem-posing ability; prospective teacher; mathematics problem-posing; kemampuan mengajukan masalah; calon guru

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References

Al-Absi, M. (2013). The effect of open-ended tasks–as an assessment tool–on fourth graders’ mathematics achievement, and assessing students’ perspectives about it. Jordan Journal of Educational Sciences, 9(3), 345–351. Retrieved from http://journals.yu.edu.jo/jjes/Issues/2013/Vol9No3/8.pdf

Amiluddin, R., & Sugiman, S. (2016). Pengaruh problem posing dan PBL terhadap prestasi belajar, dan motivasi belajar mahasiswa pendidikan matematika [Effects of problem posing and PBL towards learning achievement and motivation of prospective mathematics teachers]. Jurnal Riset Pendidikan Matematika, 3(1), 100–108. doi: https://doi.org/10.21831/jrpm.v3i1.7303

Apino, E., & Retnawati, H. (2017). Developing instructional design to improve mathematical higher order thinking skills of students. Journal of Physics: Conference Series, 812(1), 1–7. doi: https://doi.org/10.1088/1742-6596/812/1/012100

Becker, J. P., & Epstein, J. (2006). The “open approach” to teaching school mathematics. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 10(3), 151–167. Retrieved from http://www.ksme.info/eng/html/sub03_06.asp

Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA: Journal of Research in Mathematics Teaching, 6(4), 135–146. Retrieved from https://revistaseug.ugr.es/index.php/pna/article/view/6137/5453

Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. Lumat: International Journal on Math, Science and Technology Education, 3(1), 19–36. Retrieved from https://www.lumat.fi/index.php/lumat-old/article/view/38/28

Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415. doi: https://doi.org/10.1007/s10857-008-9081-0

Cronin, P., Ryan, F., & Coughlan, M. (2008). Undertaking a literature review: A step-by-step approach. British Journal of Nursing, 17(1), 38–43. doi: https://doi.org/10.12968/bjon.2008.17.1.28059

El Sayed, R. A. E. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56–69. Retrieved from https://inst.eecs.berkeley.edu/~cs301/fa18/resources/Oman-problemssolving.pdf

Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. doi: https://doi.org/10.1007/s10649-012-9449-z

Fardah, D. K. (2018). Preservice teachers’ techniques for generating new problems. Jurnal Ilmiah: Soulmath, 6(1), 37–45. doi: https://doi.org/10.25139/sm.v6i1.778

Fatah, A., Suryadi, D., Sabandar, J., & Turmudi, T. (2016). Open-ended approach: An effort in cultivating students’ mathematical creative thinking ability and self-esteem in mathematics. Journal on Mathematics Education, 7(1), 11–20. doi: https://doi.org/10.22342/jme.7.1.2813.9-18

Hadi, S., Retnawati, H., Munadi, S., Apino, E., & Wulandari, N. F. (2018). The difficulties of high school students in solving higher-order thinking skills problems. Problems of Education in the 21st Century, 76(4), 520–532. Retrieved from http://oaji.net/articles/2017/457-1533495738.pdf

Isik, C., & Kar, T. (2012). The analysis of the problems posed by the pre-service teachers about equations. Australian Journal of Teacher Education, 37(9), 93–113. doi: https://doi.org/10.14221/ajte.2012v37n9.1

Işik, C., Kar, T., Yalçin, T., & Zehir, K. (2011). Prospective teachers’ skills in problem posing with regard to different problem posing models. Procedia - Social and Behavioral Sciences, 15, 485–489. doi: https://doi.org/10.1016/j.sbspro.2011.03.127

Jailani, J., Sugiman, S., & Apino, E. (2017). Implementing the problem-based learning in order to improve the students’ HOTS and characters. Jurnal Riset Pendidikan Matematika, 4(2), 247–259. doi: https://doi.org/10.21831/jrpm.v4i2.17674

Kar, T., Özdemir, E., Ipek, A. S., & Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Procedia - Social and Behavioral Sciences, 2, 1577–1583. doi: https://doi.org/10.1016/j.sbspro.2010.03.239

Kiliç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. Asia-Pacific Education Researcher, 22(4), 677–686. doi: https://doi.org/10.1007/s40299-013-0073-1

Linda, L. (2017). Analisis penguasaan kompetensi pedagogik dan profesional mahasiswa calon guru matematika dalam mata kuliah micro-teaching [Analysis of the mastery of pedagogical competency and professional competency of prospective mathematics teachers in the course of micro-teaching]. Pythagoras: Jurnal Pendidikan Matematika, 12(1), 65–75. doi: https://doi.org/10.21831/pg.v12i1.14053

Mallart, A., Font, V., & Diez, J. (2018). Case study on mathematics pre-service teachers’ difficulties in problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1465–1481. doi: https://doi.org/10.29333/ejmste/83682

Masriyah, M., Kurniasari, I., & Palupi, E. L. W. (2018). Characteristics of pre-service teachers’ performance in problem posing. Journal of Physics: Conference Series, 1088(1), 1–5. doi: https://doi.org/10.1088/1742-6596/1088/1/012115

Ministry of Education and Culture of Republic of Indonesia. (2012). Regulation No. 57 Year 2012 on Teacher Competency Test. Jakarta. Retrieved from http://www.kopertis12.or.id/wp-content/uploads/2012/08/PermendikbudNo57tahun2012-UjiKompetensiGuru.pdf

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054. doi: https://doi.org/10.1111/j.1467-9620.2006.00684.x

Nessipbayeva, O. (2012). The competencies of the modern teacher. In N. Popov, C. Wolhuter, B. Leutwyler, G. Hilton, J. Ogunleye, & P. Almeida (Eds.), International perspectives on education (pp. 148–154). Sofia, Bulgaria: Bulgarian Comparative Education Society (BCES). Retrieved from https://files.eric.ed.gov/fulltext/ED567040.pdf

Nicol, C., & Bragg, L. A. (2009). Designing problems: What kinds of open-ended problems do preservice teachers pose? In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of 33rd Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 225–232). Thessaloniki, Greece: PME. Retrieved from http://dro.deakin.edu.au/eserv/DU:30024772/bragg-designingproblems-2009.pdf

Prayitno, L. L., & Budiyono, S. C. (2018). Error analysis of problem posed by pre-service primary teachers based on semantic structures. Advances in Social Science, Education and Humanities Research, 174, 398–401. doi: https://doi.org/10.2991/ice-17.2018.84

President of Republic of Indonesia. (2005). Law of the Republic of Indonesia No.14/2005 on Teacher and Lecturer. Jakarta. Retrieved from http://sumberdaya.ristekdikti.go.id/wp-content/uploads/2016/02/uu-nomor-14-tahun-2005-ttg-guru-dan-dosen.pdf

Retnawati, H., Djidu, H., Kartianom, K., Apino, E., & Anazifa, R. D. (2018). Teachers’ knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215–230. Retrieved from http://oaji.net/articles/2017/457-1524597598.pd

Sariningsih, R., & Herdiman, I. (2017). Mengembangkan kemampuan penalaran statistik dan berpikir kreatif matematis mahasiswa melalui pendekatan open-ended [Developing statistical reasoning and critical thinking skills of undergraduate students through open-ended approach]. Jurnal Riset Pendidikan Matematika, 4(2), 239–246. doi: https://doi.org/10.21831/jrpm.v4i2.16685

Şengül, S., & Katranci, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the ‘sets’ subject. Procedia - Social and Behavioral Sciences, 69, 1650–1655. doi: https://doi.org/10.1016/j.sbspro.2012.12.111

Şengül, S., & Katranci, Y. (2014). Structured problem posing cases of prospective mathematics teachers: Experiences and suggestions. International Journal on New Trends in Education and Their Implications, 5(4), 190–204. Retrieved from http://www.ijonte.org/FileUpload/ks63207/File/17..sengul.pdf

Şengül, S., & Katranci, Y. (2015a). Free problem posing cases of prospective mathematics teachers: difficulties and solutions. Procedia - Social and Behavioral Sciences, 174, 1983–1990. doi: https://doi.org/10.1016/j.sbspro.2015.01.864

Şengül, S., & Katranci, Y. (2015b). The analysis of the problems posed by prospective mathematics teachers about ‘ratio and proportion’ subject. Procedia - Social and Behavioral Sciences, 174, 1364–1370. doi: https://doi.org/10.1016/j.sbspro.2015.01.760

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. doi: https://doi.org/10.3102/0013189X015002004

Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: new questions and directions. Educational Studies in Mathematics, 83, 1–7. doi: https://doi.org/10.1007/s10649-013-9478-2

Soeyono, Y. (2014). Pengembangan bahan ajar matematika dengan pendekatan open-ended untuk meningkatkan kemampuan berpikir kritis dan kreatif siswa SMA [Developing mathematics instructional materials by using open-ended approach to enhance critical thinking and creative thinking of Senior High School students]. Pythagoras: Jurnal Pendidikan Matematika, 9(2), 205–218. Retrieved from https://doi.org/10.21831/pg.v9i2.9081

Sugiman, S. (2013). Student’s competency in solving and creating mathematical problem in pre-service training program. Jurnal Teknologi (Social Sciences), 63(2), 117–121. Retrieved from https://doi.org/10.11113/jt.v63.2021

Sullivan, P., & Lilburn, P. (2002). Good questions for math teaching: Why ask them and what to ask, grades K-6. Sausalito, CA: Math Solutions Publications.

Sullivan, P., Warren, E., & White, P. (2000). Students’ responses to content specific open-ended mathematical tasks. Mathematics Education Research Journal, 12(1), 2–17. doi: https://doi.org/10.1007/bf03217071

Wijaya, A. (2018). How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem. Journal of Physics: Conference Series, 983(1), 1–6. doi: https://doi.org/10.1088/1742-6596/983/1/012114

Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101–118. doi: https://doi.org/10.1007/s10649-017-9760-9

DOI: https://doi.org/10.21831/pg.v14i2.29976