Funkcionalno mišljenje in samozavest: katere napake delajo učenci pri reševanju problemov z rastočimi vzorci in kako pride do teh napak?

  • Suci Yuniati Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia
  • Nunuk Suryanti Universitas Islam Riau, Indonesia
  • Suparjono Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia
Ključne besede: Newmanova analiza napak, funkcionalno mišljenje, samozavest, rastoči vzorec

Povzetek

Obstaja nujna potreba po raziskavi, ki bi opredelila vrste in vzorce napak v funkcionalnem mišljenju učencev v povezavi z njihovimi ravnmi samozavesti. Funkcionalno mišljenje vpliva na uspešno učenje pri učencih, kar zadeva razumevanje pojma funkcije, ki je zapleten matematični vidik in ki zahteva ustrezne pristope pa tudi strategije, da bi učencem pomagali doseči obvladovanje te snovi. Namen te študije je analizirati vrste in vzorce napak v funkcionalnem mišljenju med učenci z različnimi ravnmi samozavesti pri reševanju problemov z rastočimi vzorci. Za analizo napak v funkcionalnem mišljenju učencev je bila uporabljena Newmanova analiza napak. Študija uporablja kvalitativno deskriptivno zasnovo, podprto s kvantitativno kategorizacijo ravni samozavesti, v katero sta vključena dva sodelujoča v raziskavi, izbrana med 34 dijaki drugega letnika srednje šole, ki se razlikujeta v ozadju, spolu in v ravni akademskih zmožnosti. Kot raziskovalni instrument je bila razvita naloga oziroma problem, zasnovan za ugotavljanje zmožnosti funkcionalnega mišljenja. Učence, ki so podali napačno rešitev, smo nato razvrstili v skupine na podlagi podobnih ravni samozavesti in vzorcev napak. Da bi razjasnili napake, ki so se pojavile pri reševanju problema z rastočimi vzorci, je bil za intervju izbran po en predstavnik iz skupine z nižjo ravnjo samozavesti in skupine z višjo ravnjo samozavesti. Z združitvijo funkcionalnega mišljenja, Newmanove analize napak in afektivnih vidikov je raziskava opredelila razlike v napakah med učenci z višjimi in nižjimi ravnmi samozavesti. Samozavest, samoregulacija in tesnoba so dejavniki, ki vplivajo na napake učencev. Ugotovitve poudarjajo pomembnost učenja, ki uravnoteženo združuje kognitivne in afektivne vidike.

Prenosi

Podatki o prenosih še niso na voljo.

Literatura

Acosta-Gonzaga, E. (2023). The effects of self-esteem and academic engagement on university students’ performance. Behavioral Sciences, 13(4), 1–12. https://doi.org/10.3390/bs13040348

Angco, R. J. (2021). Error analysis in integral calculus: A modified Newman’s approach. American Research Journal of Humanities Social Science, 4(09), 38–52.

Arhin, J., & Hokor, E. (2021). Analysis of high school students’ errors in solving trigonometry problems. Journal of Mathematics and Science Teacher, 1(1), 1–16. https://doi.org/10.29333/mathsciteacher/11076

Astuik, E. P., & Purwasih, S. M. (2023). Field dependent student errors in solving linear algebra problems based on Newman’s procedure. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 169–180. https://doi.org/10.31980/mosharafa.v12i1.1684

Ayeh, I. G. (2025). Students’ mathematics conceptual challenges: Exploring students’ thinking, understanding, and misconceptions in functions and graphs. European Journal of Science and Mathematics Education, 13(3), 191–206. https://doi.org/10.30935/scimath/16596

Capane, R., Filiberti, F., & Lemmo, A. (2021). Analyzing difficulties in arithmetic word problem solving: An epistemological case study in primary school. Education Sciences, 11(10), 1–20. https://doi.org/10.3390/educsci11100596

Celik, E., Süler, M., Söylemez, A., & Koçak, L. (2023). The mediating role of time attitude in the relationship between self-esteem and resilience in high school students. Journal of Pedagogical Research, 7(1), 82–102. https://doi.org/10.33902/JPR.202317971

Chiphambo, S. M., & Mtsi, N. (2021). Exploring grade 8 students’ errors when learning about the surface area of prisms. Eurasia Journal of Mathematics Science and Technology Education, 17(8), 1–10.

Chung, K. K. H., Lam, C. B., Chan, K. Lee, A. Liu, C., & Wang, L. (2024). Are general anxiety, reading anxiety, and reading self-concept linked to reading skills among Chinese adolescents with and with out dyslexia? Journal of Learning Disabilities, 57(2), 106–119. https://doi.org/10.1177/00222194231181914

Deng, X., Ding, R., & Huang, R. (2025). Investigating a learning progression of functional thinking for elementary students. Educational Studies in Mathematics, 120(1), 81–107.

Dewantara, A. H., Istiyono, E., Retnawati, H., & Suyanto, S. (2024). Investigating pre-service primary school teachers’ difficulties in solving context-based mathematics problems: An error analysis. Mathematics Teaching Research Journal, 16(2), 28–47.

Dodur, H. M., & Ceylan, M. (2025). Academic self-concept and reading comprehension among students with learning disabilities: Serial mediating effect of reading anxiety and reading motivation. British Journal of Educational Psychology, 9(5), 836–848. https://doi/.org/10.1111/bjep.12763

Frey, K., Sproesser, U., & Veldhuis, M. (2022). What is functional thinking? Theoretical considerations and first results of an international interview study. In Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). HAL Open Science. https://hal.science/hal-03744607v1/document

Gashlan, B. M. (2025). Exploring the relationship between academic self-concept and academic success in King Faisal University students. International Journal of Innovative Research and Scientific Studies, 8(8), 65–76. https://doi:org/10.53894/ijirss.v8i8.10545

Granello, F., Cuder, A., Doz, E., Pellizzoni, S., & Passolunghi, M. C. (2025). Improving math self efficacy and math self-concept in middle school: A narrative systematic review. European Journal of Psychology of Education, 40(1), 1–25. https://doi.org/10.1007/s10212-025-00939-5

Gunster, S. M., & Weigand, H. G. (2020). Designing digital technology tasks for the development of functional thinking. ZDM - Mathematics Education, 52(7), 1259–1274. https://doi.org/10.1007/s11858-020-01179-1

Halmo, S. M., Yamini, K. A., & Stanton, J. D. (2024). Metacognition and self-efficacy in action: How first-year students monitor and use sefl-coaching to move past metacognitive discomfort during problem solving. CBE-Life Sciences Education, 2(3), 1–7.

Kleka, P., Brycz, H., Zeiba, M., & Fanslau, A. (2024). Longitudinal study of metacognition’s role in self-efficacy and hope development. Scientific Reports, 14, Article 29379. https://doi.org/10.1038/s41598-024-80180-0

Knisfsend, C. A., Green, L. A., & Clifford, K. L. (2020). Extracurricular participation, collective self-esteem, and academic outcomes among college students. Psi Chi Journal, 25(4), 2325–7342. https://doi.org/10.24839/2325-7342.JN25.4.318

Kurniati, U., Setiyani, & Sagita, L. (2021). Error analysis using Newman procedures and the mathematical representation ability of preservice English teachers. Anatolian Journal of Education, 6(2), 135–156. https://doi.org/10.29333/aje.2021.6211a

Levin, M. & Walkoe, J. (2022). Seeds of algebraic thinking: A knowledge in pieces perspective on the development of algebraic thinking. ZDM-Mathematics Education, 54, 1303–1314. https://doi.org/10.1007/s11858-022-01374-2

Makamure, C., & Jojo, Z. (2022). An analysis of errors for pre-service teachers in first order ordinary differential equations. Eurasia Journal of Mathematics Science and Technology, 18(6), 1–11. https://doi.org/10.29333/ejmste/12074

Martins, R., Viseu, F., & Rocha, H. (2023). Functional thinking: A study with 10th-grade students. Education Science, 13(4), 1–22. https://doi.org/10.3390/educsci13040335

Morales, R. & Parra, J. (2022). Strategies employing prospective primary education teachers in a functional relationship task. Acta Scientiae, 24(3), 32–62. https://doi.org/10.17648/acta.scientiae.6959

Msomi, A. M., & Bansilal, S. (2022). Analysis of students’ errors and misconceptions in solving linear ordinary differential equations using the method of laplace transform. International Electronic Journal of Mathematics Education, 17(1), 1–10. https://doi.org/10.29333/iejme/11474

Noutsara, S., Neunjhem, T., & Chemrutsame, W. (2021). Mistakes in mathematics problems solving based on Newman’s error analysis on set materials. Journal La Edusci, 2(1), 20–27. https://doi.org/10.37899/journallaedusci.v2i1.36

O. Colmsee, I.-S., Hank, P., & Bošnjak, M. (2021). Low self-esteem as a risk factor for eating disorders: A meta-analysis. Zeitschrift für Psychologie, 229(1), 48–69. https://doi.org/10.1027/2151-2604/a00043320

Okoko, J. M., Tunison, S., & Walker, K. D. (Eds.). (2023). Varieties of qualitative research methods: Selected contextual perspectives. Springer Nature.

Oliveira H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257–278. https://doi.org/10.22342/jme.12.2.13745.257–278

Pang, J., Leena, L., & Sunwoo, J. (2022). Task development to measure functional thinking: Focusing on third graders’ understanding. The Korean Society of Educational Studies in Mathematics-Journal of Educational Research in Mathematics, 32(3), 351–372. https://doi.org/10.29275/jerm.2022.32.3.351

Pang, J., & Sunwoo, J. (2022). An analysis of teacher knowledge for teaching functional thinking to elementary school students. Asian Journal for Mathematics Education, 1(3), 306–322. https://doi.org/10.1177/27527263221125112

Pittalis, M. (2023). Young students’ arithmetic-algebraic structure sense: An empirical model and profiles of students. International Journal of Science and Mathematics Education, 21(6), 1865–1887. https://doi.org/10.1007/s10763-022-10333-y

Pittalis M., Sproesser, U., Demosthenous, E., & Odysseos, E. (2025). Enhancing functional thinking in grade 5-6 students through a dynamic mathematics intervention program. Education and Information Technologies, 30(1), 1329–1361. https://doi.org/10.1007/s10639-024-12865-y

Pitta-Pantazi D., Chimoni, M., & Christou, C. (2020). Different types of algebraic thinking: An empirical study focusing on middle school students. International Journal of Science and Mathematics Education, 18(5), 965–984. https://doi.org/10.1007/s10763-019-10003-6

Sainz, V., Alvarez-Arjona, J. J., & Gomez-Gutierrez, J. L. (2025). Self-concept and academic performance in students with and without learning difficulties: A longitudinal study in an inclusive school setting. Sage Journal, 15(3), 1–18. https://doi.org/10.1177/215824402513560

Sakarneh, M. (2023). Teachers’ attitudes towards the rights of students with special education needs during the Covid-19 pandemic. Center for Educational Policy Studies Journal, 13(2), 143–162. https://doi.org/10.26529/cepsj.1155

Saleh, K., Yuwono, I., Rahman As’ari, A., & Sa’dijah, C. (2022). Errors analysis solving problems analogies by Newman procedure using analogical reasoning. International Journal of Humanities and Social Sciences, 9(1), 17–26. https://ijhss.net/index.php/ijhss/article/download/253/89

Sari, D. P., Saputra, S., Ardywinata, A. A., Sukmawati, R. A., & Fadhillah, M. N. (2023). Students’ errors and misconceptions in solving fundamental mathematics problem. Mathematics Education Journal (MEJ), 17(3), 313–324. https://doi.org/10.22342/jpm.17.3.21128.313-324

Servidio, R. (2023). Fear of missing out and self-esteem as mediators of the relationship between maximization and problematic smartphone use. Current Psychology, 42(1), 232–242.

Shimizu, Y. (2025). Learning engagement as moderator between self-efficacy, math anxiety, use of diagrams, and complex plane problem-solving. EURASIA Journal of Mathematics Science and Technology Education, 21(2), 1–12. https://doi.org/10.29333/ejmste/15956

Steinberg, O., Kulakow, S., & Raufelder, D. (2024). Academic self-concept, achievement, and goal orientations in different learning environments. European Journal of Psychology of Education, 39, 3893–3917. https://doi.org/10.1007/s10212-024-00825-6

Sun, S., Sun, D., & Xu, T. (2023). The developmental progression of early algebraic thinking of elementary school students. Journal of Intelligence, 11(12), 1–19. https://doi.org/10.3390/jintelligence11120222

Sundayana, R., & Parani, C. E (2023). Analyzing students’ errors in solving trigonometric problems using Newman’s procedure based on students’ cognitive style. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 135–144. https://doi.org/10.31980/mosharafa.v12i1.762

Thomas, D. S., & Mahmud, M. S. (2021). Analysis of students’ error in solving quadratic equations using Newman’s procedure. International Journal of Academic Research in Business and Social Sciences, 11(12), 222–237. https://doi.org/10.6007/IJARBSS/V11-I12/11760

Tisdell, E. J., Merriam, S. B., & Stuckey-Peyrot, H. L. (2025). Qualitative research: A Guide to design and implementation (5th ed.). John Wiley & Sons.

Trujillo, M., Atarés, L. Canet, M. J., & Pérez-Pascual, M. A. (2023). Learning difficulties with the concept of function in maths: A literature review. Education Science, 13(5), 1–13. https://doi.org/10.3390/educsci13050495

Utami, N. S., Prabawanto, S., & Suryadi, D. (2023). How students generate patterns in learning algebra? A focus on functional thinking in secondary school students. European Journal of Educational Research, 12(2), 913–925. https://doi.org/10.12973/eu-jer.12.2.913

Vaughan-Johnston, T. I., Lambe, L., Craig, W., & Jacobson, J. A. (2020). Self-esteem importance beliefs: A new perspective on adolescent self-esteem. Self and Identity, 19(8), 967–988. https://doi.org/10.1080/15298868.2019.1711157

Yuniati, S., Nusantara, T., Sulandra, I., & Suparjono. (2022). Investigating functional thinking processes that impact on function composition problems in Indonesia. Acta Scientiae, 4, 84–118. https://doi.org/10.17648/acta.scientiae.6969

Objavljeno
2026-07-19
Kako citirati
Yuniati, S., Suryanti, N., & Suparjono. (2026). Funkcionalno mišljenje in samozavest: katere napake delajo učenci pri reševanju problemov z rastočimi vzorci in kako pride do teh napak?. Revija Centra Za študij Edukacijskih Strategij . https://doi.org/10.26529/cepsj.2239
Rubrike
VARIA