Understanding High School Students’ Errors in solving Mathematics Problems: A Phenomenological Research

Authors

  • Ahmad Naufal Aljura Faculty of Mathematics and Science, Universitas Negeri Yogyakarta
    Indonesia
  • Heri Retnawati Faculty of Mathematics and Science, Universitas Negeri Yogyakarta
    Indonesia
  • Hutkemri Zulnaidi Faculty of Education, University of Malaya
    Malaysia
  • Vianney Mbazumutima Faculty of Natural Sciences, École Normale Supérieure du Burundi
    Burundi

DOI:

https://doi.org/10.23917/ijolae.v7i1.24005

Keywords:

cognition domain, educational intervention, education policies, educational standars, learning engagement, mathematical problem solving, phenomenology research, technology-assisted learning model

Abstract

This research aims to understand a phenomenon regarding high school students’ errors in solving mathematics problems using a qualitative approach with phenomenology as the analysis framework. Data were collected through tests, classroom observations, documentation (students’ answer sheets, list of attendees, and students’ score lists), and unstructured phenomenological interviews with four purposively selected participants who met the selection criteria. The researchers used the mathematical problem-solving (MPS) model by Rott-Specht-Knipping and Aguas’ phenomenological data analysis steps using the NVIVO 12 software to analyze the students’ MPS process and identify their errors and the factors contributing to these errors. Errors were predominantly found in problems solved without engaging in the exploration phase. Analysis errors were the most common, while errors due to carelessness were the rarest. Factors contributing to these errors were identified across five domains: MPS Ability (MPSA), cognition, affection, motivation, and self-awareness. This research provides valuable insights into student errors in MPS for researchers and educators, particularly teachers, and provides recommendations for mathematics education policies and future research.

Downloads

Download data is not yet available.

References

Aagaard, J. (2017). Introducing postphenom-enological research: a brief and selective sketch of phenomenological research methods. International Journal of Quali-tative Studies in Education, 30(6), 519–533. https://doi.org/10.1080/09518398.2016.1263884

Adinda, A., Purwanto, P., Parta, I. N., & Chandra, T. D. (2021). Investigation Of Students’ Metacognitive Awareness Failures About Solving Absolute Value Problems in Mathematics Education. Eurasian Journal of Educational Re-search, 2021(95). https://doi.org/10.14689/ejer.2021.95.2

Aguas, P. (2022). Fusing Approaches in Ed-ucational Research: Data Collection and Data Analysis in Phenomenological Re-search. The Qualitative Report. https://doi.org/10.46743/2160-3715/2022.5027

Alexander, I. W. (1970). What is Phenome-nology? Journal of the British Society for Phenomenology, 1(1), 3–3. https://doi.org/10.1080/00071773.1970.11006091

Anderson, J. R., Lee, H. S., & Fincham, J. M. (2014). Discovering the structure of mathematical problem solving. Neu-roImage, 97, 163–177. https://doi.org/10.1016/j.neuroimage.2014.04.031

Bartholomew, T. T., Joy, E. E., Kang, E., & Brown, J. (2021). A choir or cacopho-ny? Sample sizes and quality of convey-ing participants’ voices in phenomeno-logical research. Methodological Innova-tions, 14(2). https://doi.org/10.1177/20597991211040063

Blakemore, S. J., & Frith, C. (2003). Self-awareness and action. Current Opinion in Neurobiology, 13(2), 219–224. https://doi.org/10.1016/S0959-4388(03)00043-6

Böswald, V., & Schukajlow, S. (2023). I val-ue the problem, but I don’t think my stu-dents will: preservice teachers’ judg-ments of task value and self-efficacy for modelling, word, and intramathematical problems. ZDM - Mathematics Educa-tion, 55(2), 331–344. https://doi.org/10.1007/s11858-022-01412-z

BSKAP. (2022). Copy of Appendix I of the Decree of the Head of the Educational Standards, Curriculum and Assessment Agency of the Ministry of Education, Culture, Research and Technology Number 033/H/Kr/2022 concerning Learning Achievements in Early Child-hood Education, Basic Education Levels and Secondary Education Levels in Merdeka Curriculum (p. 133). https://kurikulum.kemdikbud.go.id/rujukan

Carter, N., Bryant-Lukosius, D., DiCenso, A., Blythe, J., & Neville, A. J. (2014). The Use of Triangulation in Qualitative Research. Oncology Nursing Forum, 41(5), 545–547. https://doi.org/10.1188/14.ONF.545-547

Cleary, T. J., & Chen, P. P. (2009). Self-regulation, motivation, and math achievement in middle school: Variations across grade level and math context. Journal of School Psychology, 47(5), 291–314. https://doi.org/10.1016/j.jsp.2009.04.002

Clements, M. A. (1982). Careless Errors Made by Sixth-Grade Children on Writ-ten Mathematical Tasks. Journal for Re-search in Mathematics Education, 13(2), 136. https://doi.org/10.2307/748360

Darmawan, E., & Suparman, S. (2019). Design of Mathematics Learning Media based on Discovery Learning to Improve Problem Solving Ability. Indonesian Journal on Learning and Advanced Education (IJOLAE), 1(2), 20-28. doi:https://doi.org/10.23917/ijolae.v1i2.7564

DeBellis, V. A., & Goldin, G. A. (2006). Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective. Educational Studies in Mathematics, 63(2), 131–147. https://doi.org/10.1007/s10649-006-9026-4

Demetriou, A., & Kazi, S. (2006). Self-awareness in g (with processing efficien-cy and reasoning). Intelligence, 34(3), 297–317. https://doi.org/10.1016/j.intell.2005.10.002

Díaz, V., Aravena, M., & Fores, G. (2020). Solving Problem Types Contextualized to the Quadratic Function and Error Analysis: A Case Study. Eurasia Jour-nal of Mathematics, Science and Tech-nology Education, 16(11), em1896. https://doi.org/10.29333/ejmste/8547

Dwita, A., & Retnawati, H. (2022). Students’ errors in solving mathematical problems. AIP Conference Proceedings, 2575. https://doi.org/10.1063/5.0107794

Eggen, P. D., & Kauchak, D. P. (1996). Strategy for Teacher: Teaching Content and Thinking Skills. Allyn & Bacon.

Etikan, I. (2016). Comparison of Convenience Sampling and Purposive Sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1. https://doi.org/10.11648/j.ajtas.20160501.11

Fatimah, Ms., Nurhidayah, Ms., Ahmad, H., Febryanti, Ms., & P., M. A. (2019). Ef-fect of Motivation and Gender on Prob-lem-solving in Student Mathematics. Proceedings of the 1st International Conference on Advanced Multidiscipli-nary Research (ICAMR 2018). https://doi.org/10.2991/icamr-18.2019.26

Furinghetti, F., & Morselli, F. (2009). Every unsuccessful problem solver is unsuc-cessful in his or her own way: affective and cognitive factors in proving. Educa-tional Studies in Mathematics, 70(1), 71–90. https://doi.org/10.1007/s10649-008-9134-4

García, T., Boom, J., Kroesbergen, E. H., Núñez, J. C., & Rodríguez, C. (2019). Planning, execution, and revision in mathematics problem solving: Does the order of the phases matter? Studies in Educational Evaluation, 61, 83–93. https://doi.org/10.1016/j.stueduc.2019.03.001

García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students’ meta-cognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 11(2), 139–170. https://doi.org/10.1007/s11409-015-9139-1

Groenewald, T. (2004). A Phenomenological Research Design Illustrated. Internation-al Journal of Qualitative Methods, 3(1), 42–55. https://doi.org/10.1177/160940690400300104

Hardini, R., Prahmana, R., Akib, I., & Shahrill, M. (2021). Learning Social Arithmetic of Low-Ability Student through the Context of Snacks and Money. Indonesian Journal on Learning and Advanced Education (IJOLAE), 4(1), 21-33. doi:https://doi.org/10.23917/ijolae.v4i1.14308

Hasan, N., Subanji, S., & Sukorianto, S. (2019). Analisis Kesalahan Siswa Kelas VIII dalam Menyelesaikan Soal Cerita Terkait Teorema Pythagoras. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(4), 468. https://doi.org/10.17977/jptpp.v4i4.12264

Howard, D. C. P. (1994). Human‐computer interactions: a phenomenological exami-nation of the adult first‐time computer experience. International Journal of Qualitative Studies in Education, 7(1), 33–49. https://doi.org/10.1080/0951839940070103

Irhamna, I., Amry, Z., & Syahputra, H. (2020). Contribution of Mathematical Anxiety, Learning Motivation and Self-Confidence to Student’s Mathematical Problem Solving. Budapest International Research and Critics in Linguistics and Education (BirLE) Journal, 3(4), 1759–1772. https://doi.org/10.33258/birle.v3i4.1343

Kalkan, F., & Dağlı, E. (2021). Views of sec-ondary school students on ideal teacher qualifications: A phenomenological anal-ysis. International Journal of Evaluation and Research in Education (IJERE), 10(1), 317. https://doi.org/10.11591/ijere.v10i1.20565

Karaali, G. (2015). Metacognition in the Classroom: Motivation and Self-Awareness of Mathematics Learners. PRIMUS, 25(5), 439–452. https://doi.org/10.1080/10511970.2015.1027837

(Ken) Clements, M. A. (1980). Analyzing children’s errors on written mathematical tasks. Educational Studies in Mathemat-ics, 11(1), 1–21. https://doi.org/10.1007/BF00369157

Khusnani, A., Husein, R., Jufriansah, A., Thalo, O., Rahmawati, K., Fitri, M., & Adina, C. (2023). Identification of Understanding of Disaster Preparedness in the School Environment. Indonesian Journal on Learning and Advanced Education (IJOLAE), 5(3), 233-248. doi:https://doi.org/10.23917/ijolae.v5i3.22974

Kingsdorf, S., & Krawec, J. (2014). Error Analysis of Mathematical Word Problem Solving Across Students with and with-out Learning Disabilities. Learning Dis-abilities Research & Practice, 29(2), 66–74. https://doi.org/10.1111/ldrp.12029

Krawec, J. L. (2014). Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability. Jour-nal of Learning Disabilities, 47(2), 103–115. https://doi.org/10.1177/0022219412436976

Kurniawan, D., Astalini, A., Darmaji, D., Tanti, T., & Maryani, S. (2022). Innovative Learning: Gender Perception of e-Module Linear Equations in Mathematics and Physics. Indonesian Journal on Learning and Advanced Education (IJOLAE), 4(2), 92-106. doi:https://doi.org/10.23917/ijolae.v4i2.16610

Kwon, K., & Jonassen, D. H. (2011). The Influence of Reflective Self-Explanations on Problem-Solving Performance. Jour-nal of Educational Computing Research, 44(3), 247–263. https://doi.org/10.2190/EC.44.3.a

Leong, Y. H., Dindyal, J., Toh, T. L., Quek, K. S., Tay, E. G., & Lou, S. T. (2011). Teacher preparation for a problem-solving curriculum in Singapore. ZDM, 43(6–7), 819–831. https://doi.org/10.1007/s11858-011-0356-z

Lestari, A. R. A., Minggi, I., & Qadry, I. K. (2019). Analisis Kesalahan dalam Me-nyelesaikan Soal Cerita Materi Bangun Ruang Sisi Datar Berdasarkan Prosedur Newman. SIGMA (Suara Intelektual Gaya Mtematika), 11(2), 122–129.

Liu, D. W. Y., & Winder, B. (2014). Explor-ing foreign undergraduate students’ ex-periences of university. International Journal of Qualitative Studies in Educa-tion, 27(1), 42–64. https://doi.org/10.1080/09518398.2012.736643

Lopez, V., & Whitehead, D. (2014). Sampling data and data collection in qualitative re-search. In Nursing and Midwifery Re-search (3rd ed.). Elsevier.

Lukman, L., Marsigit, M., Istiyono, E., Kartowagiran, B., Retnawati, H., Kistoro, H. C. A., & Putranta, H. (2021). Effective teachers’ personality in strengthening character education. Inter-national Journal of Evaluation and Re-search in Education (IJERE), 10(2), 512. https://doi.org/10.11591/ijere.v10i2.21629

Milazoni, T. R., Maison, M., & Nizlel, N. (2022). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Matematika Berdasarkan Teori Pemrosesan Informa-si dan Pemberian Scaffolding. AKSIO-MA: Jurnal Program Studi Pendidikan Matematika, 11(1), 654–666. https://doi.org/10.24127/ajpm.v11i1.4705

Muis, K. R., Psaradellis, C., Lajoie, S. P., Di Leo, I., & Chevrier, M. (2015). The role of epistemic emotions in mathematics problem solving. Contemporary Educa-tional Psychology, 42, 172–185. https://doi.org/10.1016/j.cedpsych.2015.06.003

NCTM. (2000). Principles and Standards for School Mathematics. NCTM.

Novak, E., & Tassell, J. L. (2017). Studying preservice teacher math anxiety and mathematics performance in geometry, word, and non-word problem solving. Learning and Individual Differences, 54, 20–29. https://doi.org/10.1016/j.lindif.2017.01.005

Özcan, Z. Ç., & Eren Gümüş, A. (2019). A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety. Australian Journal of Edu-cation, 63(1), 116–134. https://doi.org/10.1177/0004944119840073

Pavlin-Bernardić, N., Rovan, D., & Pavlović, J. (2017). Academic Cheating in Mathe-matics Classes: A Motivational Perspec-tive. Ethics & Behavior, 27(6), 486–501. https://doi.org/10.1080/10508422.2016.1265891

Pólya, G. (2004). How to solve it: A new as-pect of mathematical method (Vol. 5). Princeton university press.

Pomalato, S. W. D., Ili, L., Ningsi, B. A., Fadhilaturrahmi, F., Hasibuan, A. T., & Primayana, K. H. (2020). Student Error Analysis in Solving Mathematical Prob-lems. Universal Journal of Educational Research, 8(11), 5183–5187. https://doi.org/10.13189/ujer.2020.081118

Priyani, H. A., & Ekawati, R. (2018). Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students. IOP Conference Series: Mate-rials Science and Engineering, 296, 012010. https://doi.org/10.1088/1757-899X/296/1/012010

Pugalee, D. K. (2001). Writing, Mathematics, and Metacognition: Looking for Connec-tions Through Students’ Work in Math-ematical Problem Solving. School Sci-ence and Mathematics, 101(5), 236–245. https://doi.org/10.1111/j.1949-8594.2001.tb18026.x

Radatz, H. (1979). Error Analysis in Mathe-matics Education. Journal for Research in Mathematics Education, 10(3), 163. https://doi.org/10.2307/748804

Radatz, H. (1980). Students’ Errors in the Mathematical Learning Process: A Sur-vey. For the Learning of Mathematics, 1(1), 16–20. https://www.jstor.org/stable/40247696

Retnawati, H. (2016). Analisis Kuantitatif Instrumen Penelitian (First). Parama Publishing. www.nuhamedika.gu.ma

Rhodes, F. (1987). Carelessness? The Math-ematical Gazette, 71(458), 285–292. https://doi.org/10.2307/3617047

Rofi’ah, N., Ansori, H., & Mawaddah, S. (2019). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Cerita Matematika Berdasarkan Langkah Penyelesaian Pol-ya. EDU-MAT: Jurnal Pendidikan Ma-tematika, 7(2), 120. https://doi.org/10.20527/edumat.v7i2.7379

Rott, B., Specht, B., & Knipping, C. (2021). A descriptive phase model of problem-solving processes. ZDM – Mathematics Education, 53(4), 737–752. https://doi.org/10.1007/s11858-021-01244-3

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

Solso, R. L. (1995). Cognitive Psychology. Allyn & Bacon.

Son, A. L., Darhim, & Fatimah, S. (2019). An analysis to student error of algebraic problem solving based on polya and newman theory. Journal of Physics: Conference Series, 1315(1), 012069. https://doi.org/10.1088/1742-6596/1315/1/012069

Svenson, I. F., Lawrence, J. A., & Willis, S. G. (1983). Distance university students’ processing of mathematics exercises. Educational Studies in Mathematics, 14(1), 73–85. https://doi.org/10.1007/BF00704703

Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1016/0364-0213(88)90023-7

Trezise, K., & Reeve, R. A. (2014). Cogni-tion-emotion interactions: patterns of change and implications for math prob-lem solving. Frontiers in Psychology, 5. https://doi.org/10.3389/fpsyg.2014.00840

Ulya, H. (2015). Hubungan Gaya Kognitif Dengan Kemampuan Pemecahan Masa-lah Matematika Siswa. Jurnal Konseling Gusjigang, 1(2). https://doi.org/10.24176/jkg.v1i2.410

Vagle, M. D. (2009). Validity as intended: ‘bursting forth toward’ bridling in phe-nomenological research. International Journal of Qualitative Studies in Educa-tion, 22(5), 585–605. https://doi.org/10.1080/09518390903048784

Veloo, A., Krishnasamy, H. N., & Wan Ab-dullah, W. S. (2015). Types of Student Errors in Mathematical Symbols, Graphs and Problem-Solving. Asian Social Sci-ence, 11(15). https://doi.org/10.5539/ass.v11n15p324

Verschaffel, L., Greer, B., & Corte, E. (2000). Making sense of word problems. Swets and Zeitlinger.

Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM, 52(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4

Wa-Mbaleka, S. (2020). The Researcher as an Instrument. In A. P. Costa, L. P. Reis, & A. Moreira (Eds.), Computer Supported Qualitative Research (Vol. 1068). Springer International Publishing. https://doi.org/10.1007/978-3-030-31787-4

White, A. L. (2005). Active Mathematics In Classrooms: Finding Out Why Children Make Mistakes-And Then Doing Some-thing To Help Them. Square One, 15(4).

Yazıcı, S., & Fidan, N. K. (2020). Value pref-erences and requirements of the students attending the regional boarding second-ary schools. International Journal of Evaluation and Research in Education (IJERE), 9(3), 635. https://doi.org/10.11591/ijere.v9i3.20539

Yüksel, P., & Yıldırım, S. (2015). Theoretical Frameworks, Methods, and Procedures for Conducting Phenomenological Stud-ies. Turkish Online Journal of Qualita-tive Inquiry, 6(1). https://doi.org/10.17569/tojqi.59813

Downloads

Submitted

2025-03-13

Published

2025-01-30

Issue

Section

Articles