Exploring Pre-service Elementary School Teachers' Conceptual Understanding and Problem-Solving Strategies in Basic Mathematical Concepts

Aliya Hidayatika; Unik Ambar Wati; Rahayu Condro Murti

doi:10.56741/IISTR.ijlree.002440

Authors

Aliya Hidayatika
aliyahidayatika.2024@student.uny.ac.id
Universitas Negeri Yogyakarta
Unik Ambar Wati Universitas Negeri Yogyakarta https://orcid.org/0000-0002-2159-048X
Rahayu Condro Murti Universitas Negeri Yogyakarta https://orcid.org/0000-0002-4275-9459

DOI:

https://doi.org/10.56741/IISTR.ijlree.002440

Keywords:

Conceptual understanding, Polya, Pre-service Teachers, Problem-Solving Strategies

Abstract

This study aims to explore pre-service elementary school teachers' conceptual understanding and problem-solving strategies in fundamental mathematics concepts, with a specific focus on arithmetic series and fractions with mixed-methods methodology. A total of 84 pre-service teachers completed a written test covering 10 basic mathematics concepts, and the scores were analyzed to identify the most difficult concepts. Based on these results, six participants representing the high, medium, and low score categories were interviewed to investigate their conceptual reasoning and to analyze their problem-solving strategies using Polya's steps. The findings reveal that arithmetic series and fractions were the most challenging concepts, as evidenced by low scores, recurring errors, and persistent misconceptions. Interview results, particularly through the lens of Polya's framework, show that high-performing participants tended to use structured procedural strategies but often failed at the looking-back stage. In contrast, low-performing participants relied on intuitive, misaligned strategies, indicating weaknesses across multiple Polya steps. Overall, this study highlights the critical need to strengthen pre-service teachers' conceptual understanding through instructional approaches that emphasize representation, reasoning, and the systematic application of problem-solving heuristics.

Downloads

Download data is not yet available.

Author Biographies

Aliya Hidayatika, Universitas Negeri Yogyakarta

is a Master's student in Elementary Education at Universitas Negeri Yogyakarta. Her research interests lie in mathematics education, with a particular focus on elementary mathematics learning. Her work examines various aspects of teaching and learning mathematics, including student motivation, engagement, achievement, and instructional practices in primary education. She is actively involved in academic and research activities within the field of elementary mathematics education. (email: aliyahidayatika.2024@student.uny.ac.id).

Unik Ambar Wati, Universitas Negeri Yogyakarta

is a Lecturer in the Primary Teacher Education Program at Universitas Negeri Yogyakarta. Her research interests focus on elementary education, educational technology, curriculum and instruction, inclusive education, and teacher professional development. She has published extensively on learning innovation, self-efficacy, blended learning, and technology-integrated instruction in elementary education. She actively contributes to research and academic activities aimed at improving the quality of teaching and learning in primary education. (email: unik@uny.ac.id).

Rahayu Condro Murti, Universitas Negeri Yogyakarta

is a Lecturer in the Primary School Teacher Education Department at Universitas Negeri Yogyakarta. Her research interests include elementary mathematics education, culturally responsive teaching, realistic mathematics education, educational technology, and teacher education. She has published numerous studies on mathematics learning, critical thinking, computational thinking, and innovative learning media for elementary schools. She actively contributes to research and academic activities in the field of primary education. (email: rahayu_cm@uny.ac.id).

References

M. Şahal, M. Doğan, and A. Ş. Özdemir, “Examination of types of mathematical connections that pre-service mathematics teachers use in teaching processes,” Int. J. Mod. Educ. Stud., vol. 8, no. 2, Sep. 2024, doi: 10.51383/ijonmes.2024.354.

F. Tuba, D. Övez, and E. Özdemir, “An examination of pre-service teachers’ Van Hiele levels of geometric thinking and proof perception types in terms of thinking processes,” Educ. Res. Rev., vol. 19, no. 1, pp. 26–39, 2024, doi: 10.5897/ERR2023.4386.

T. Nunes, P. Bryant, and A. Watson, “Key understandings in mathematics learning: Summary Papers,” London: Nuttfield Foundation, 2011. [Online]. Available: https://www.nuffieldfoundation.org/project/key-understandings-in-mathematics-learning

K. M. A. Salviejo, E. D. Ibañez, and J. T. Pentang, “Critical thinking disposition and learning approach as predictors of mathematics performance,” J. Educ. Learn., vol. 18, no. 4, pp. 1107–1116, Nov. 2024, doi: 10.11591/edulearn.v18i4.21386.

T. G. Dangkulos, E. D. Ibañez, and J. T. Pentang, “Problem-solving disposition as a predictor of preservice elementary teachers’ problem-solving performance,” J. Educ. Learn., vol. 19, no. 1, pp. 54–62, Feb. 2025, doi: 10.11591/edulearn.v19i1.21387.

A. H. Dewantara, E. Istiyono, H. Retnawati, and S. Suyanto, “Investigating pre-service primary school teachers’ difficulties in solving context-based mathematics problems: An error analysis,” Math. Teach. Res. J., vol. 16, no. 2, pp. 28-47, 2024. [Online]. Available: https://eric.ed.gov/?id=EJ1442288

S. Tfaili, “Pre-service and in-service elementary school teacher's procedural and representational knowledge of fractions,” Int. Conf. Res. Educ. Sci., pp. 701–712, May 2023, [Online]. Available: https://eric.ed.gov/?id=ED654767

Y. Copur-Gencturk, “Teachers’ conceptual understanding of fraction operations: Results from a national sample of elementary school teachers,” Educ. Stud. Math., vol. 107, no. 3, pp. 525–545, Jul. 2021, doi: 10.1007/s10649-021-10033-4.

Y. Copur-gencturk, “Strategic competence for multistep fraction word problems: An overlooked aspect of mathematical knowledge for teaching,” Educ. Stud. Math., vol. 107, pp. 49–70, 2021, doi: 10.1007/s10649-021-10028-1.

M. G. D. Kabar, J. Walkoe, and M. Z. Zimmerman, “Investigating the change of pre-service middle school mathematics teachers’ conceptualization of algebraic thinking,” Proc. Int. Eurasian Educ. Res. Congress (EJER Congr.), pp. 46–53, May 2024, [Online]. Available: https://eric.ed.gov/?id=ED662847

E. M. Lamaizi, L. Zraoula, and B. El Wahbi, “Exploring learning difficulties in convergence of numerical sequences in Morocco: An error analysis study,” Math. Teach. Res. J., vol. 16, no. 2, pp. 63-79, 2024. [Online]. Available: https://eric.ed.gov/?id=EJ1442286

C. Matitaputty, T. Nusantara, E. Hidayanto, and Sukoriyanto, “Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes,” J. Math. Educ., vol. 13, no. 3, pp. 393–414, Sep. 2022, doi: 10.22342/jme.v13i3.pp393-414.

R. Wahyuni, A. Wahyuni, L. M. Angraini, and A. Sthephani, “Exploring problem-solving skills profiles of pre-service mathematics teachers through Polya's four stages: Riau, Indonesia," J. Math-UMB Edu, vol. 13, no. 1, pp. 99-111, 2025. [Online]. Available: https://jurnal.umb.ac.id/index.php/math/article/view/9075

A. Wahab, Y. S. Kusuma, D. Juandi, T. Turmudi, B. Buhaerah, and S. Syaiful, “Understanding students’ struggles in solving mathematical problems: A systematic literature review using Polya’s framework,” J. Pendidik. Progresif, vol. 14, no. 03, pp. 1728-1753, 2024, doi: 10.23960/jpp.v14.i3.202411.

J. J. Fatihah, S. Sudirman, and M. Mellawaty, “Improving geometric thinking skills through learning cycles assisted by interactive geometry books,” Int. J. Math. Sci. Educ., vol. 1, no. 2, pp. 81–85, 2023, doi: 10.59965/ijmsed.v1i2.74.

M. Noviyanti, S. Sudirman, and C. A. Rodríguez-Nieto, “Investigating mathematical knowledge for teaching early childhood education teachers: A starting point for designing a professional development program,” Educ. Process Int. J., vol. 16, e2025210, 2025. [Online]. Available: https://www.ceeol.com/search/article-detail?id=1384662

Masriyah, A. W. Kohar, E. B. Rahaju, D. K. Fardah, and U. Hanifah, “Assessing student teachers’ ability in posing mathematical reasoning problems,” Cent. Educ. Policy Stud. J., vol. 14, no. 2, pp. 9–37, Jun. 2024, doi: 10.26529/cepsj.1368.

F. Ö. Yasar, M. Özden, and E. Yaşar, “Critical and analytical thinking: Unique and overlapping aspects from the perspective of teacher candidates,” Educ. Policy Anal. Strateg. Res., vol. 20, no. 2, pp. 32-57, 2025, doi: 10.29329/epasr.2025.1329.2.

P. A. Facione, “Critical thinking: A statement of expert consensus for purposes of educational assessment and instruction," Research Findings and Recommendations Prepared for the Committee on Pre-College Philosophy of the American Philosophical Association, 1990. [Online]. Available: https://philarchive.org/archive/faccta

M. K. Serin, G. Uyanık, and L. İncikabı, “The relationship between pre-service primary school teachers’ beliefs about mathematics and critical thinking dispositions,” Turkish J. Comput. Math. Educ., vol. 9, no. 3, pp. 513–535, 2018, doi: 10.16949/turkbilmat.311084.

Y. A. Öztürk, “An analysis of the relationship between pre-service secondary mathematics teachers’ epistemological beliefs towards learning, their educational beliefs, and critical thinking dispositions,” Educ. Policy Anal. Strateg. Res., vol. 17, no. 2, pp. 165–207, Jun. 2022, doi: 10.29329/epasr.2022.442.8.

M. D. Pamungkas, S. B. Waluya, S. Mariani, and I. Isnarto, “Dynamic thinking processes in mathematics learning: A systematic literature review,” in Proc. International Conference on Science, Education, and Technology (ISET), vol. 8, Universitas Negeri Semarang, 2022, pp. 149–153.

V. L. G. Rodríguez-García and O. B. Reye-Meza, “Development of mathematical skills at the cognitive level of basic general education students,” Int. Res. J. Manag. IT Soc. Sci., vol. 9, no. 4, pp. 514–523, Jun. 2022, doi: 10.21744/irjmis.v9n4.2112.

H. C. Çelik and F. Özdemir, “Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers,” Int. J. Progress. Educ., vol. 16, no. 4, pp. 81–98, Aug. 2020, doi: 10.29329/ijpe.2020.268.6.

M. Márquez, C. Fernández, and M. L. Callejo, “Pre-service primary school teachers’ knowledge and their interpretation of students’ answers to a measurement division problem with fractions,” Mathematics, vol. 9, no. 24, e3163, Dec. 2021, doi: 10.3390/math9243163.

M. W. Zulu and V. Mudaly, “Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration,” Eurasia J. Math. Sci. Technol. Educ., vol. 19, no. 7, em2299, 2023, doi: 10.29333/ejmste/13344.

P. Jiang, Y. Zhang, Y. Jiang, and B. Xiong, “Preservice mathematics teachers’ perceptions of mathematical problem solving and its teaching: A case from China,” Front. Psychol., vol. 13, e998586, Nov. 2022, doi: 10.3389/fpsyg.2022.998586.

J. J. Aguilar and J. A. Telese, “Mathematics understanding of elementary pre-service teachers: The analysis of their procedural-fluency, conceptual-understanding, and problem-solving strategies,” Math. Teach. Res. J., vol. 10, no. 3-4, pp. 24–37, 2018. [Online]. Available: https://scholarworks.utrgv.edu/tl_fac/27/

S. K. Sulfiah, Y. M. Cholily, and A. Subaidi, “Professional competency: Pre-service mathematics teachers’ understanding toward probability concept,” vol. 6, no. 3, pp. 206–220, 2021, doi: 10.23917/jramathedu.v6i3.13779.

P. Liljedahl, M. Santos-Trigo, U. Malaspina, and R. Bruder, Problem Solving in Mathematics Education. Springer Nature, 2016. doi: 10.1007/978-3-319-40730-2 ISSN.

J. W. Creswell and V. L. P. Clark, Designing and Conducting Mixed Methods Research, 4th ed. Thousand Oaks: CA: Sage Publications, 2020.

N. Duan and K. Hoagwood, “Purposeful sampling for qualitative data collection and analysis in mixed method implementation research,” Adm. Policy Mental Health Mental Health Services Res., vol. 42, no. 5, pp. 533-544, 2013, doi: 10.1007/s10488-013-0528-y.

E. A. O. Zijlmans, J. Tijmstra, L. A. van der Ark, and K. Sijtsma, “Item-score reliability as a selection tool in test construction,” Front. Psychol., vol. 9, e2298, Jan. 2019, doi: 10.3389/fpsyg.2018.02298.

A. D. López-Rueda, J. Jadán-Guerrero, and M. Chacón-Castro, “Metodología de Pólya para fortalecer las habilidades de resolución de problemas en ecuaciones diferenciales: un estudio de caso en Colombia [Pólya’s methodology for strengthening problem-solving skills in differential equations: A case study in Colombia],” Computers, vol. 12, no. 11, e2, Nov. 2023, doi: 10.3390/computers12110239.

L. N. Pradana, “Problem-solving strategy: Mathematical problem-solving model within the Polya’ framework,” KnE Soc. Sci., vol. 9, no. 6, pp. 728-740, Mar. 2024, doi: 10.18502/kss.v9i6.15327.

M. A. Taamneh, J. Díez-Palomar, and A. Mallart-Solaz, “Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem,” Eurasia J. Math. Sci. Technol. Educ., vol. 20, no. 12, em2551, 2024, doi: 10.29333/ejmste/15707.