Ida Lestari (1*)
Nila Kesumawati (2)
Yunika Lestaria Ningsih (3)

(1) Universitas PGRI Palembang
(2) Universitas PGRI Palembang
(3) Universitas PGRI Palembang
(*) Corresponding Author


Set theory has a wide role in mathematical concepts. Students have to understand the set theory before learning other concepts such as algebra and probability. This study aims to determine the effect of the problem-based learning (PBL) model on the students’ mathematical representation in set theory topics. The method used in this study is a quasi-experiment design. The populations in this study were 289 students of 7th grade at Secondary School in Palembang. The sample of this study were students of class 7.8 (control group) and 7.10 (experimental group). Data were collected through tests, interviews, and documentation. Based on data analysis, known that PBL affects the students’ mathematical representation. Students who had the PBL model get the better score of mathematical representation. They could use the symbol of set correctly, represent the set into Venn diagram correctly and they also could explain their answer. Furthermore, the implementation of the PBL model is offered.


Mathematical representation; Problem-based learning; Set theory

Full Text:



Abdullah, N. I., Tarmizi, R. A., & Abu, R. (2010). The effects of problem based learning on mathematics performance and affective attributes in learning statistics at form four secondary level. Procedia Social and Behavioral Science, 8, 370-376.

Ahamad, S. N. S. H., Li, H. C., Shahrill, M., & Prahmana, R. C. I. (2017). Implementation of problem-based learning in geometry lessons. In Journal of Physics: Conference Series, 943(1), 012008.

Andre, R. (2014). Axioms and Set Theory: A first course in Set Theory. Retrieved from

Bagni, G. T. (2006). Some cognitive difficulties related to the representations of two major concepts of set theory. Educational Studies in Mathematics, 62(3), 259-280.

Bolden, D., Barmby, P., Raine, S., & Gardner, M. (2015). How young children view mathematical representations: a study using eye-tracking technology. Educational research, 57(1), 59-79.

Botty, H. M. R. H., Shahrill, M., Jaidin, J. H., Li, H. C., & Chong, M. S. F. (2016). The implementation of problem-based learning (PBL) in a year 9 mathematics classroom: a study in brunei darussalam. International Research in Education, 4(2), 34-47.

Cai, J., S.Jakabcsin, M., & Lane, S. (1996). Assesing students' mathematical communication. Jurnal of Science and Mathematics, 96(5), 238-246.

Dogan-Dunlap, H. (2006). Lack of set theory relevant prerequisite knowledge. International Journal of Mathematical Education in Science and Technology, 37(4), 401-410.

Happy, N., & Widjajanti, D. B. (2014). Keefektifan PBL ditinjau dari kemampuan berpikir kritis dan kreatif matematis, serta self-esteem siswa SMP . Jurnal Riset Pendidikan Matematika, 1(1), 48-57.

Hernawati, F. (2016). Pengembangan perangkat pembelajaran matematika dengan pendekatan PMRI berorientasi pada kemampuan representasi matematis. Jurnal Riset Pendidikan Matematika, 3(1), 34-44.

Hutagaol, K. (2013). Pembelajaran kontekstual untuk meningkatkan kemampuan representasi matematis siswa sekolah menengah pertama. Infinity Journal, 2(1), 85-99.

Johar, R., & Lubis, K. R. (2018). The analysis of students’ mathematical representation errors in solving word problem related to graph. Jurnal Riset Pendidikan Matematika, 5(1), 96-107.

Noto, M. S., Hartono, W., & Sundawan, D. (2016). Analysis of students mathematical representation and connection on analytical geometry subject. Infinity Journal, 5(2), 99-108.

O'Brien, T. C., Wallach, C., & Mash-Duncan, C. (2011). Problem-based learning in mathematics. The Mathematics Enthusiast, 8(1), 147-159.

Padmavathy, R. D., & Mareesh, K. (2013). Effectiveness of problem based learning in mathematics. International Multidisciplinary e-Journal, 2(1), 45-51.

Razmjooei, A. (2013). Investigation of Some Cognitive Difficulties in Set Theory (Dissertation). Retrivied from

Roh, K. H. (2003). Problem-based learning in mathematics. Retrivied from

Zazkis, R., & Gunn, C. (1997). Sets, subsets, and the empty set: students’ constructions and mathematical conventions. Journal of Computers in Mathematics and Science Teaching, 16(1), 133-169.


Article Metrics

Abstract view : 683 times
PDF - 319 times


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.