Analysis of Pre-service Mathematics Teachers' Representational Ability Regarding the Prime Numbers Concept
), Sutji Rochaminah(2), Hajerina Hajerina(3)
| 
Country:
(1) Department of Science Education, Universitas Tadulako, Indonesia Department of Mathematics Education, Universitas Alkhairaat, Indonesia, Indonesia
(2) Department of Mathematics Education, Universitas Tadulako, Indonesia, Indonesia
(3) Department of Mathematics Education, Universitas Alkhairaat, Indonesia, Indonesia
Corresponding Author
10.23960/jpmipa.v26i2.pp1253-1273
| Metrics→ |
| Indexing Site→ |  |
 |
 |
 |
Copyright (c) 2025 Indah Suciati, Sutji Rochaminah, Hajerina Hajerina
Abstract
A deep understanding of prime numbers remains a significant challenge, particularly for pre-service mathematics teachers responsible for conveying this essential knowledge to their students. Prime numbers have an essential role in mathematics, including in factorization, proof, and cryptography. Therefore, this study aims to describe and analyze the representational abilities of prospective mathematics teacher students at Alkhairaat University, regarding the prime numbers in Number Theory. This study uses a descriptive exploratory method with a mixed-methods approach based on a sequential explanatory design. Data collection was carried out through diagnostic tests, semi-structured interviews, and documentation, which were then analyzed using descriptive statistics for quantitative data and the Miles & Huberman model for qualitative data. Triangulation of methods and time was used to ensure the validity of the data. The findings showed that out of 17 students, only 29.41% were able to provide accurate verbal representations related to the prime and composite numbers, and only 5.88% were able to link the two meaningfully. In addition, while students were able to mention definitions, most of them had difficulties applying the prime numbers in the abstract problem context, including examples in algebraic notation. This study concludes that there is still a significant gap in the representation ability of prime number concepts of pre-service mathematics teachers. The implications emphasize the need for integrating multidimensional representation learning strategies into the mathematics education curriculum so that prospective teachers are better prepared to teach prime numbers in a comprehensive and meaningful way.
Keywords: representation, prime numbers, number theory, pre-service mathematics teachers.
References
Akkurt, Y. Y., & Durmuş, S. (2022). Tracing proof schemes: some patterns and new perspectives. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 7(1), 1–16. https://doi.org/10.23917/jramathedu.v7i1.15740
Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., Gobel, S. M., Hannula-Sormunen, M., Hodgen, J., Inglis, M., Jones, I., Mazzocco, M., McNeil, N., Schneider, M., Simms, V., & Weber, K. (2016). Challenges in mathematical cognition : A collaboratively-derived research agenda. Journal of Numerical Cognition, 2(1), 20–41. https://doi.org/doi:10.5964/jnc.v2i1.10
Aziz, T. A., Supiat, & Soenarto, Y. (2019). Pre-service secondary mathematics teachers’ understanding of absolute value. Cakrawala Pendidikan, 38(1), 203–214. https://doi.org/10.21831/cp.v38i1.21945
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Barbarani, V. (2021). Combinatorial models of the distribution of prime numbers. Mathematics, 9(11), 1–50. https://doi.org/10.3390/math9111224
Bascones, G. Y., Yunzal, J., A. N., & Casinillo, L. F. (2024). Exploring contextual factors affecting student performance in mathematics: A sequential explanatory research. Canadian Journal of Family and Youth / Le Journal Canadien de Famille et de La Jeunesse, 16(3), 210–234. https://doi.org/10.29173/cjfy30045
Brookhart, S. M. (2024). Educational assessment knowledge and skills for teachers revisited. Education Sciences, 14(7). https://doi.org/10.3390/educsci14070751
Curtis, M., & Tularam, G. A. (2011). The importance of numbers and the need to study primes: The prime questions. Journal of Mathematics and Statistics, 7(4), 262–269. https://doi.org/10.3844/jmssp.2011.262.269
David, E. J., Hah Roh, K., & Sellers, M. E. (2020). Teaching the representations of concepts in calculus: The case of the intermediate value theorem. Primus, 30(2), 191–210. https://doi.org/10.1080/10511970.2018.1540023
Dehmeche, F. M., Mihoubi, D., & Ladjelat, L. (2024). Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing. Notes on Number Theory and Discrete Mathematics, 30(1), 163–169. https://doi.org/10.7546/nntdm.2024.30.1.163-169
Funeme, C., & Lopez, L. (2022). Didactic-mathematical knowledge of some teachers about prime numbers. Alteridad-Revista De Educacion, 17(2), 208–223.
Ganeeva, A. R., & Anisimova, T. I. (2020). Continuing professional education for pre-service teachers of mental arithmetic. Universal Journal of Educational Research, 8(9), 3989–3996. https://doi.org/10.13189/ujer.2020.080924
Gürefe, N., & Aktaş, G. S. (2020). The concept of prime number and the strategies used in explaining prime numbers. South African Journal of Education, 40(3), 1–9. https://doi.org/10.15700/saje.v40n3a1741
Hajerina, H., Suciati, I., & H. Mailili, W. (2022). Analisis kesalahan mahasiswa pada mata kuliah kalkulus diferensial materi turunan [Analysis of student errors in the differential calculus course on derivative material]. EQUALS: Jurnal Ilmiah Pendidikan Matematika, 5(1), 24–33. https://doi.org/10.46918/equals.v5i1.1238
Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of mathematical reasoning addressed in empirical research in mathematics education: A systematic review. Education Sciences, 10(10), 1–15. https://doi.org/10.3390/educsci10100289
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Khalil, I., Al Zahrani, A., Awaji, B., & Mohsen, M. (2024). Teachers’ perceptions of teaching mathematics topics based on STEM educational philosophy: A sequential explanatory design. STEM Education, 4(4), 421–444. https://doi.org/10.3934/steme.2024023
Kong, S. (2019). Learning composite and prime numbers through developing an app: An example of computational thinking development through primary mathematics learning. In Computational Thinking Education. Springer Singapore. https://doi.org/https://doi.org/10.1007/978-981-13-6528-7_9
Li, X. (2020). Investigating u.s. preschool teachers’ math teaching knowledge in counting and numbers. Early Education and Development, 1–19. https://doi.org/10.1080/10409289.2020.1785226
Loconsole, M., & Regolin, L. (2022). Are prime numbers special? Insights from the life sciences. Biology Direct, 17(1), 1–9. https://doi.org/10.1186/s13062-022-00326-w
Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21.
Martin, H. (2021). Multiplicative reasoning task design in teacher education with student teachers in Scottish schools: valuing diversity, developing flexibility and making connections. Teacher Development, 25(3), 317–339. https://doi.org/10.1080/ 13664530.2021.1887922
Nabayra, L. J. M., & Jr, R. G. S. (2022). The mathematics teaching performance of scholar education graduates in selected public schools in the Philippines: An explanatory sequential mixed-method study. Canadian Journal of Educational and Social Studies, 2(4), 23–36. https://doi.org/10.53103/cjess.v2i4.47
Nurdiana, A., Tanod, M. J., & Adirakasiwi, A. G. (2021). Assessing didactic mathematical knowledge for teaching geometry transformation. Journal of Physics: Conference Series, 1764(1). https://doi.org/10.1088/1742-6596/1764/1/012129
Picado-Alfaro, M. (2021). Analysis of the representations of the concept of number proposed by a group of pre-service Primary Education teachers in Costa Rica. Acta Scientiae, 23(1), 170–198. https://doi.org/10.17648/acta.scientiae.6152
Piñeiro, J. L., Chapman, O., Castro-Rodríguez, E., & Castro, E. (2021). Prospective elementary teachers’ pedagogical knowledge for mathematical problem solving. Mathematics, 9(15), 1–23. https://doi.org/10.3390/math9151811
Ramsingh, V. (2020). Conceptual and representational confusion: An analysis of three foundation phase teachers’ descriptions of how they teach division. South African Journal of Childhood Education, 10(1), 1–10.
Sánchez-Jiménez, M., Maravé-Vivas, M., Gil-Gómez, J., & Salvador-Garcia, C. (2025). Building pre-service teachers’ resilience through Service-Learning: an explanatory sequential mixed methods study. Frontiers in Psychology, 16(April), 1–11. https://doi.org/10.3389/fpsyg.2025.1568476
Suciati, I., & Wahyuni, D. S. (2018). Analisis kesalahan siswa dalam menyelesaikan soal matematika pada operasi hitung pecahan pada siswa kelas v sdn pengawu [Analysis of student errors in solving mathematical problems on fractional arithmetic operations in class v students of sdn pengawu]. Jurnal Penelitian Dan Pembelajaran Matematika, 11(2), 129–144. https://doi.org/10.30870/ jppm.v11i2.3760
Ustunsoy, S., Ozdemir, A. S., & Unal, H. (2011). The investigation of students' approach to problem solving about some topics of Number Theory. Procedia - Social and Behavioral Sciences, 15, 3422–3425. https://doi.org/10.1016/j.sbspro.2011.04.312
Uyar, A. (2023). 21st century skills of pre-service teachers and visions of faculties of education in acquiring 21st century skills. International Journal of Contemporary Educational Research, 10(1), 262–278. https://doi.org/10.33200/ijcer.1274201
Zaman, B. U. (2024). New prime number theory. Annals of Mathematics and Physics, 7(2), 158–161. https://doi.org/10.17352/amp.000119
Zazkis, R., & Liljedahl, P. (2004). Understanding primes: The role of representation. Journal for Research in Mathematics Education, 35(3), 164–186. https://doi.org/10.2307/30034911
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
The copyright is reserved to The Jurnal Pendidikan MIPA that is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.