Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem

Muntasir A. Taamneh; Javier Díez-Palomar; Albert Mallart-Solaz

doi:10.29333/ejmste/15707

Full Text (PDF)

Muntasir A. Taamneh ¹ , Javier Díez-Palomar ¹ ^* , Albert Mallart-Solaz ²

More Detail

¹ University of Barcelona, Barcelona, SPAIN² Autonomous University of Barcelona, Barcelona, SPAIN^* Corresponding Author

Abstract

This study uses Polya’s problem-solving strategy to explore student errors and causal factors in Pythagorean theorem problem-solving. The sample was drawn from tenth-grade students at Al Hosn Secondary School in Abu Dhabi, United Arab Emirates in the academic year 2023/2024. Data were collected using two methods: written examinations, as outlined in Polya’s strategy, and interviews with students who committed errors. The research test instrument consists of 3 trigonometric problem-solving. From 30 students of Al Hosn Secondary School, there were 48.9% of data errors, 50% of concept errors, 57.8% of strategy errors, 47.8% of calculation errors, and 14.4% of careless errors. The errors made by the students originated from their inability to comprehend the geometric interpretation of the Pythagorean theorem, difficulties in applying algebraic operations, and challenges in modelling the data provided in the problems.

Keywords

Trigonometric
Error
Pythagorean theorem
Polya's strategy
Problem-Solving

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 20, Issue 12, December 2024, Article No: em2551

https://doi.org/10.29333/ejmste/15707

Publication date: 11 Dec 2024

Article Views: 105

Article Downloads: 40

Open Access References How to cite this article

References

Ahmad, H., Febryanti, Muthmainnah, Al Yakin, A., & Sarbi, S. (2018). The analysis of student error in solve the problem of spherical trigonometry application. Journal of Physics: Conference Series, 1114, Article 012114. https://doi.org/10.1088/1742-6596/1114/1/012114
Antara, P. Y., Sudiarta, G. P., & Suweken, G. (2020). Error analysis in solving trigonometry questions for high school students class X. International Journal of Science and Research, 10(10), 1151-1154.
Arivina, A. N., & Jailani. (2022). An analysis of high school students’ error in completing trigonometry problems based on Movshovitz-Hadar, Zaslavsky, and Inbar categories. AIP Conference Proceedings, 2575, Article 040008. https://doi.org/10.1063/5.0110888
Barlow, A. T., Watson, L. A., Tessema, A. A., Lischka, A. E., & Strayer, J. F. (2018). Inspection-worthy mistakes: Which? And why? Teaching Children Mathematics, 24(6), 384-391. https://doi.org/10.5951/teacchilmath.24.6.0384
BSNP. (2006). Curriculum for unit-level competencies and basic competencies in mathematics for junior high schools. National Education Standards Body.
Castro, W. F., & Herrera-Restrepo, C. (2024). Mathematical thinking of fifth-grade students when inventing and solving problems. Journal of Research in Mathematics, 13(2), 132-163 https://doi.org/10.17583/redimat.14302
De Almeida, L. M. W., & de Castro, E. M. V. (2023). Metacognitive strategies in mathematical modelling activities: Structuring an identification instrument. Journal of Research in Mathematics Education, 12(3), 210-228. https://doi.org/10.17583/redimat.12926
Fahrudin, D., Mardiyana, & Pramudya, I. (2019). Profile of students’ errors in trigonometry equations. Journal of Physics: Conference Series, 1188, Article 012044. https://doi.org/10.1088/1742-6596/1188/1/012044
Gee, J. P. (2014). An introduction to discourse analysis: Theory and method. Routledge. https://doi.org/10.4324/9781315819679
Hanggara, Y., Agustyaningrum, N., & Ismayanti. (2024). Analysis of students’ errors in solving trigonometry problems. AIP Conference Proceedings, 3046, Article 020004. https://doi.org/10.1063/5.0194586
Hasan, N., Subanji, S., & Sukorianto, S. (2019a). Analisis kesalahan siswa kelas VIII dalam menyelesaikan soal cerita terkait teorema Pythagoras [Analysis of class VIII students’ errors in solving story problems related to the Pythagorean theorem]. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(4), 468-477. https://doi.org/10.17977/jptpp.v4i4.12264
Hasan, R., Lukitasari, M., Juniarti, V., & Irwandi. (2019b). Improving student problem-solving skill and cognitive learning outcome through the implementation of problem-based learning. Jurnal Bioedukatika, 7(1), 18-26. https://doi.org/10.26555/bioedukatika.v7i1.12323
Hidayati, U. (2020). Analysis of student errors in solving trigonometry problems. Journal of Mathematics Education, 5(1), 54-60. https://doi.org/10.31327/jme.v5i1.1181
Hutapea, M. L., Suryadi, D., & Nurlaelah, E. (2015). Analysis of students’ epistemological obstacles on the subject of Pythagorean theorem. Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam, 20(1), 1-10. https://doi.org/10.18269/jpmipa.v20i1.555
Moradi, F., Rahimi, Z., & Nekouee, Z. (2023). Analysis of Engineering students’ errors and misunderstandings of integration methods during the COVID-19. Tuning Journal for Higher Education, 11(1), 369-368. https://doi.org/10.18543/tjhe.2434
Nurmeidina, R., & Rafidiyah, D. (2019). Analysis of students’ difficulties in solving trigonometry problems. In Proceedings of the 4^th Progressive and Fun Education International Conference. European Alliance for Innovation. https://doi.org/10.4108/eai.7-8-2019.2288422
Polya, G. (1971). How to solve it: A new aspect of mathematical method. Princeton University Press.
Pratikno, H., & Retnowati, E. (2018). How Indonesian students use the Polya’s general problem-solving steps. Southeast Asian Mathematics Education Journal, 8(1), 39-48. https://doi.org/10.46517/seamej.v8i1.62
Puspitarani, & Retnawati, H. (2020). Diagnosis of learning difficulties in mathematics for students resolving problems related to material in the Pythagorean theorem for 8th grade students in SMP 1 Todanan and SMP Muhammadiyah 9 Todanan, academic year 2018/2019. Journal of Physics: Conference Series, 1581, Article 012026. https://doi.org/10.1088/1742-6596/1581/1/012026
Rizka, B., & Lismalinda. (2021). The effect of problem-based learning model on the sociolinguistics learning outcomes of private university students in Aceh. Getsempena English Education Journal, 8(1), 14-25. https://doi.org/10.46244/geej.v8i1.1197
Rohimah, S. M., & Prabawanto, S. (2020). Students’ difficulties in solving trigonometric equations and identities. Journal of Physics: Conference Series, 1521, Article 032002. https://doi.org/10.1088/1742-6596/1521/3/032002
Rudi, R., Suryadi, D., & Rosjanuardi, R. (2020). Identifying students’ difficulties in understanding and applying the Pythagorean theorem with an onto-semiotic approach. MaPan: Jurnal Matematika dan Pembelajaran, 8(1), 1-18. https://doi.org/10.24252/mapan.2020v8n1a1
Sari, R. H. Y., & Wutsqa, D. U. (2019). Analysis of student’s error in resolving the Pythagoras problems. Journal of Physics: Conference Series, 1320, Article 012056. https://doi.org/10.1088/1742-6596/1320/1/012056
Satriani, S., Wahyuddin, Halim, N. H., & Syamsuadi, A. (2020). The analysis of compliance type students error in resolving integral challenge of trigonometry function. International Journal of Mathematics Trends and Technology, 66(10), Article IJMTT-V66I10P503. https://doi.org/10.14445/22315373/IJMTT-V66I10P503
Sekgoma, A., & Salani, E. (2023). Analyzing common trigonometric errors among first-year primary school student teachers at the university of Botswana. European Journal of Education Studies, 10(12), 362-380. https://doi.org/10.46827/ejes.v10i12.5128
Setiawan, Y. E. (2022). Analysis of error in determining the distance between two points in the cartesian plane in the first semester students. Jurnal Pendidikan Matematika dan IPA, 13(1), 25-39. https://doi.org/10.26418/jpmipa.v13i1.43259
Sulistyorini, Y. (2018). Error analysis in solving geometry problems on pseudo-thinking’s students. In Proceedings of the University of Muhammadiyah Malang’s 1^st International Conference of Mathematics Education (pp. 103-107). Atlantis Press. https://doi.org/10.2991/incomed-17.2018.22
Supardi, L., Zayyadi, M., Lanya, H., Hasanah, S. I., & Hidayati, S. N. (2021). Commognitive analysis of students’ errors in solving high order thinking skills problems. Turkish Journal of Computer and Mathematics Education, 12(6), 950-961. https://doi.org/10.17762/turcomat.v12i6.2373
Veloo, A., Krishnasamy, H. N., & Wan Abdullah, W. S. (2015). Types of student errors in mathematical symbols, graphs and problem-solving. Asian Social Science, 11(15), 324-334. https://doi.org/10.5539/ass.v11n15p324
Wardhani, T. A. W., & Argaswari, D. P. A. D. (2022). High school students’ error in solving word problem of trigonometry based on Newman error hierarchical model. Infinity Journal, 11(1), 87-102. https://doi.org/10.22460/infinity.v11i1.p87-102
Zulyanty, M., & Mardia, A. (2022). Do students’ errors still occur in mathematical word problem-solving? A Newman error analysis. Al-Jabar Jurnal Pendidikan Matematika, 13(2), 343-353. https://doi.org/10.24042/ajpm.v13i2.13519

How to cite this article

APA

Taamneh, M. A., Díez-Palomar, J., & Mallart-Solaz, A. (2024). Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), em2551. https://doi.org/10.29333/ejmste/15707

Vancouver

Taamneh MA, Díez-Palomar J, Mallart-Solaz A. Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. EURASIA J Math Sci Tech Ed. 2024;20(12):em2551. https://doi.org/10.29333/ejmste/15707

AMA

Taamneh MA, Díez-Palomar J, Mallart-Solaz A. Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. EURASIA J Math Sci Tech Ed. 2024;20(12), em2551. https://doi.org/10.29333/ejmste/15707

Chicago

Taamneh, Muntasir A., Javier Díez-Palomar, and Albert Mallart-Solaz. "Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 12 (2024): em2551. https://doi.org/10.29333/ejmste/15707

Harvard

Taamneh, M. A., Díez-Palomar, J., and Mallart-Solaz, A. (2024). Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), em2551. https://doi.org/10.29333/ejmste/15707

MLA

Taamneh, Muntasir A. et al. "Examining tenth-grade students’ errors in applying Polya’s problem-solving approach to Pythagorean theorem". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 12, 2024, em2551. https://doi.org/10.29333/ejmste/15707