logo logo European Journal of Educational Research

EU-JER is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.

Subscribe

Publisher (HQ)

Eurasian Society of Educational Research
Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
Eurasian Society of Educational Research
Headquarters
7321 Parkway Drive South, Hanover, MD 21076, USA
prospective teachers039 expectations mathematical thinking processes polya models mason theory

Prospective Teachers' Expectations of Students' Mathematical Thinking Processes in Solving Problems

Mohammad Tohir , Maswar Maswar , Moh. Atikurrahman , Saiful Saiful , Diyah Ayu Rizki Pradita

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on .

T

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

Keywords: Prospective teachers', expectations, mathematical thinking processes, Polya models, Mason theory.

cloud_download PDF
Cite
Article Metrics
Views
3202
Download
2868
Citations
Crossref
12

Scopus
16

References

Afgani, M. W., Suryadi, D., & Dahlan, J. A. (2019). The enhancement of pre-service mathematics teachers’ mathematical understanding ability through ACE teaching cyclic. Journal of Technology and Science Education, 9(2), 153–167. https://doi.org/10.3926/jotse.441

Ariefia, H. E., As’ari, A. R., & Susanto, H. (2016). Proses berpikir siswa dalam menyelesaikan permasalahan pada materi trigonometri [Students' thinking processes in solving problems in trigonometry materials]. Journal of Mathematics Learnin/Jurnal Pembelajaran Matematika, 1(1), 28-32.

As’ari, A. R., Tohir, M., Valentino, E., Imron, Z., & Taufiq, I. (2017). Buku guru matematika (revisi) [Mathematics teacher handbook (revised)]. Center for Curriculum and Bookkeeping.

Barham, A. I. (2020). Investigating the development of pre-service teachers’ problem-solving strategies via problem-solving mathematics classes. European Journal of Educational Research, 9(1), 129–141. https://doi.org/10.12973/eu-jer.9.1.129

Chasanah, C., Riyadi, R., & Usodo, B. (2020). The effectiveness of learning models on written mathematical communication skills viewed from students’ cognitive styles. European Journal of Educational Research, 9(3), 979–994. https://doi.org/10.12973/eu-jer.9.3.979

Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students’ mathematical generalizations. Journal for Research in Mathematics Education, 42(4), 308–345. https://doi.org/10.5951/jresematheduc.42.4.0308

Farib, P. M., Ikhsan, M., & Subianto, M. (2019). Proses berpikir kritis matematis siswa sekolah menengah pertama melalui discovery learning [The mathematical critical thinking process of junior high school students through discovery learning]. Journal of Mathematics Education Research/Jurnal Riset Pendidikan Matematika, 6(1), 99–117. https://doi.org/10.21831/jrpm.v6i1.21396

Hulaikah, M., Degeng, I, Sulton, S., & Murwani, F. D. (2020). The effect of experiential learning and adversity quotient on problem solving ability. International Journal of Instruction, 13(1), 869–884. https://doi.org/10.29333/iji.2020.13156a

Iswari, I. F., Susanti, E., Hapizah, H., Meryansumayeka, M., & Turidho, A. (2019). Design of problem-solving questions to measure mathematical thinking type abstraction. Journal of Physics: Conference Series, 1318(1), 1–6. https://doi.org/10.1088/1742-6596/1318/1/012104

Kent, L. (2017). Examining mathematics classroom interactions: elevating student roles in teaching and learning. International Journal of Educational Methodology, 3(2), 93–102. https://doi.org/10.12973/ijem.3.2.93

Lane, C. P., & Harkness, S. S. (2012). Game show mathematics: Specializing, conjecturing, generalizing, and convincing. The Journal of Mathematical Behavior, 31(2), 163–173. https://doi.org/10.1016/j.jmathb.2011.12.008 

Lesseig, K. (2016). Conjecturing, generalizing and justifying: Building theory around teacher knowledge of proving. International Journal for Mathematics Teaching and Learning, 17(3), 1–31. http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/27

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. Pearson Education.

Munawwarah, M., Laili, N., & Tohir, M. (2020). Keterampilan berpikir kritis mahasiswa dalam memecahkan masalah matematika berdasarkan keterampilan abad 21 [Students' critical thinking skills in solving mathematical problems based on 21st century skills]. Alifmatika: Journal of Mathematics Education and Learning/Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 2(1), 37–58. https://doi.org/10.35316/alifmatika.2020.v2i1.37-58

Nurhidayah, D. A. (2016). The thinking process of junior high school students’ in solving mathematic problem based on gender. International Seminar on Education, 1(1) 625–629. http://seminar.umpo.ac.id/index.php/ISE2016/article/view/504

Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton University Press.

Primasatya, N. (2016). Analisis kemampuan berpikir matematis calon guru sekolah dasar dalam menyelesaikan masalah matematika [Analysis of mathematical thinking ability of prospective primary school teachers in solving mathematical problems]. JME: Journal of Mathematics Education/JPM: Jurnal Pendidikan Matematika, 2(1), 50–57. http://doi.org/10.33474/jpm.v2i1.206

Rangka, I. B., Kasmanah, K., Solihatun, S., Folastri, S., Sjamsuri, A., Setiadi, A., Prasetyaningtyas, W. E.,  Ifdil, I., Ardi, Z., Helsa, Y., Suranata, K., Parwito, P., Erwinda, L., Fadli, R. P., Zola, N., Rahim, R., Elwan, L. O. M., Jopang, J., & Bakti, B. (2019). Assessing of student’s performance and their math test in Islamic school: A Rasch perspective. Journal of Physics: Conference Series, 1175(1), 1–6. https://doi.org/10.1088/1742-6596/1175/1/012149

Reyes-Cedeno, C. C., Rivas-Cun, H. I., Espinoza-Cevallos, C. E., & Rojas-Garcia, C. R. (2019). Assessment of the practices for early mathematics thinking in preschools of Pasaje City, Ecuador. European Journal of Educational Research, 8(4), 1063–1070. https://doi.org/10.12973/eu-jer.8.4.1063

Santos-Trigo, M., & Reyes-Martínez, I. (2019). High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies. International Journal of Mathematical Education in Science and Technology, 50(2), 182–201. https://doi.org/10.1080/0020739X.2018.1489075

Saiful, S., Hobri, H., & Tohir, M. (2020). Analisis metakognisi siswa berbasis lesson study for learning community (LSLC) ditinjau dari gaya kognitif [Metacognition analysis of students based on lesson study for learning community (LSLC) in terms of cognitive style]. Alifmatika: Journal of Mathematics Education and Learning/Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 2(1), 73–91. https://doi.org/10.35316/alifmatika.2020.v2i1.73-91

Son, A. L., Darhim, D., & Fatimah, S. (2020). Students’ mathematical problem-solving ability based on teaching models intervention and cognitive style. Journal on Mathematics Education, 11(2), 209–222. https://doi.org/10.22342/jme.11.2.10744.209-222

Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715

Sumarna, N., & Herman, T. (2017). The increase of critical thinking skills through mathematical investigation approach. Journal of Physics: Conference Series, 812(1), 1–8. https://doi.org/10.1088/1742-6596/812/1/012067

Tabak, S. (2019). 6th, 7th and 8th grade students’ misconceptions about the order of operations. International Journal of Educational Methodology, 5(3), 363–373. https://doi.org/10.12973/ijem.5.3.363

Thalhah, S. Z., Tohir, M., Nguyen, P. T., Shankar, K., & Rahim, R. (2019). Mathematical issues in data science and applications for health care. International Journal of Recent Technology and Engineering, 8(2), 4153–4156. http://dx.doi.org/10.35940/ijrte.B1599.0982S1119

Tohir, M., Abidin, Z., Dafik, D., & Hobri, H. (2018). Students creative thinking skills in solving two dimensional arithmetic series through research-based learning. Journal of Physics: Conference Series, 1008(1), 1-11. https://doi.org/10.1088/1742-6596/1008/1/012072 

Tohir, M. (2017). Pengembangan bahan ajar olimpiade matematika berdasarkan model pemecahan masalah untuk meningkatkan kemampuan penalaran matematis siswa [Development of instructional materials based problem-solving mathematical olympiad for students improves mathematical reasoning ability] [Unpublished master's thesis]. University of Jember.

Tohir, M. (2019). Keterampilan berpikir kreatif siswa dalam menyelesaikan soal olimpiade matematika berdasarkan level metakognisi [Students' creative thinking skills in solving mathematics olympiad problems based on metacognition levels]. Alifmatika: Journal of Mathematics Education and Learning/Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 1(1), 1–14. https://doi.org/10.35316/alifmatika.2019.v1i1.1-14

Tohir, M., Susanto, S., Hobri, H., Suharto, S., & Dafik, D. (2018). Students’ creative thinking skills in solving mathematics olympiad problems based on problem-solving Polya and Krulik-Rudnick model. Advanced Science Letters, 24(11), 8361–8364. https://doi.org/10.1166/asl.2018.12563

Xu, B., Cai, J., Liu, Q., & Hwang, S. (2019). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 4(5), 101427. https://doi.org/10.1016/j.ijer.2019.04.005

Yusnia, D. (2018). Analysis the ability of students problem-solving on counting operations of algebra form. MUST: Journal of Mathematics Education, Science and Technology, 3(1), 1–6. http://doi.org/10.30651/must.v3i1.1017

Yin, R. K. (2017). Case study research and applications: Design and methods. Sage publications.

...