International Association of Educators   |  ISSN: 1949-4270   |  e-ISSN: 1949-4289

Original article | Educational Policy Analysis and Strategic Research 2023, Vol. 18(3) 176-196

Teacher Candidates’ Understanding and Appraoches to Errors About Matrices

Şükrü Ilgün, Solmaz Damla Gedik Altun & Alper Cihan Konyalıoğlu

pp. 176 - 196   |  DOI: https://doi.org/10.29329/epasr.2023.600.9   |  Manu. Number: MANU-2305-05-0006.R1

Published online: September 30, 2023  |   Number of Views: 67  |  Number of Download: 179


Abstract

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26 teacher candidates at a university in the Eastern Anatolia Region. They were given a written exam, and their responses were analyzed by two field experts. The results showed that the pre-service teachers did not fully understand the concepts and operations of matrices. They made a variety of errors, including misconceptions and incomplete understanding. They were also not very good at solving proof-based questions. However, they were more successful at solving problems that were based on plain logic or could be solved using rules.

Keywords: Error, Error approximation, Linear Algebra, Matrices


How to Cite this Article?

APA 6th edition
Ilgun, S., Altun, S.D.G. & Konyalioglu, A.C. (2023). Teacher Candidates’ Understanding and Appraoches to Errors About Matrices . Educational Policy Analysis and Strategic Research, 18(3), 176-196. doi: 10.29329/epasr.2023.600.9

Harvard
Ilgun, S., Altun, S. and Konyalioglu, A. (2023). Teacher Candidates’ Understanding and Appraoches to Errors About Matrices . Educational Policy Analysis and Strategic Research, 18(3), pp. 176-196.

Chicago 16th edition
Ilgun, Sukru, Solmaz Damla Gedik Altun and Alper Cihan Konyalioglu (2023). "Teacher Candidates’ Understanding and Appraoches to Errors About Matrices ". Educational Policy Analysis and Strategic Research 18 (3):176-196. doi:10.29329/epasr.2023.600.9.

References
  1. Abidin, S. N. Z., Zain, S. M. M., Hamzah, H. H. M., & Abd Rahim, N. Z. (2016). Mısconceptıons In Usıng Gauss-Jordan Elımınatıon Method By Undergraduate Students. In 6th International Conference on Global Social Entrepreneurship (Kota Bharu) (p. 291) [Google Scholar]
  2. Alpaca, N., Aparicio, V., Sharhorodska, O. & Jaen, D. (2020). Problem based Learning with Information and Communications Technology Support: An Experience in the Teaching-Learning of Matrix Algebra. International Journal of Advanced Computer Science and Applications,(11)3.https://pdfs.semanticscholar.org/1156/a172278afe5b719ffc98009e17780225f2fa.pdf [Google Scholar]
  3. Altıntaş, E., İlgün, Ş., & Daştan, Z. (2020). Reflections from 7th Grade Students Compared to Error Based Questions in Mathematics. In K. A. KIRKIC, Innovative Learning and Teaching Practices (p. 245-279). Ankara: İksad Publishing. [Google Scholar]
  4. Altıntaş, E., İlgün, Ş., & Daştan, Z. (2020). Examining 7th Grade Students with Questions Containing Wrong Solutions in Mathematics. Turkish Studies, 15(6), 3939-3957. DOI: 10.47423/TurkishStudies.46584 [Google Scholar]
  5. Altıntaş, E., İlgün, Ş., Uygun, S., & Angay, M. (2021). Errors and Misconceptions of  7th Grade Students About First-Order Equations With One Unknown. E-Kafkas Journal of Educational Research, 8(3), 788-820. DOI:10.30900/kafkasegt. 1003487 [Google Scholar]
  6. Arnawa, I. M., & Nita, S. (2020). Improvement students’ achievement in elementary linear algebra through APOS theory approach. Journal of Physics: Conference Series, 1567(2), p.022080. IOP Publishing. [Google Scholar]
  7. Arnawa, I., Ginting, B., & Nita, S. (2021). Does the Use of APOS Theory Promote Students' Achievement in Elementary Linear Algebra?. International Journal of Instruction, 14(3), 175-186. https://doi.org/10.29333/iji.2021.14310a [Google Scholar] [Crossref] 
  8. Arnawa, Nita, Yerizon .(2019). Errors and misconceptions in learning elementary linear algebra. Journal of Physics: Conference Series (JPCS), 1321. DOI: 10.1088/1742-6596/1321/2/022095                               [Google Scholar]
  9. Arslan, K. (2021). Investigation of elementary mathematics teaching program students' ability to perceive linear dependency-linear independence and base-dimension concepts in vector spaces (Master's thesis, Graduate School of Sciences/Elementary Mathematics Teaching Department). [Google Scholar]
  10. Aygor, N. & Ozdag, H. (2012). Misconceptions in linear algebra: the case of undergraduate students. Procedia-Social and Behavioral Sciences, 46, 2989-2994. https://doi.org/10.1016/j.sbspro.2012.05.602 [Google Scholar] [Crossref] 
  11. Bağdat, O. & Koparan, M. (2017). Errors of Secondary School Mathematics Teacher Candidates in Problems Using Primitive Line Operations in Linear Algebra Lesson. Route Educational and Social Science Journal, 4(2). [Google Scholar]
  12. Baştürk, S. (2014). The place of student error in mathematics teaching: The concept of error and obstacle. Education in the Light of Science and Reason, 166, 14-23. https://www.researchgate.net/publication/312295181          [Google Scholar]
  13. Bilgili, S., Özkaya, M., Çiltaş, A., & Konyalıoğlu, A. C. (2020). Examination of middle school mathematics teachers' error approaches to modelling. Anemon Mus Alparslan University Journal of Social Sciences, 8(3), 871-882. DOI: 10.7822/omuefd.845782 [Google Scholar]
  14. Birinci, D., Delice, A. & Aydın, E. (2014). University students’ solution processes in systems of linear equation. Procedia-Social and Behavioral Sciences, 153, 563-568. http://dx.doi.org/10.1016/j.sbspro.2014.09.244 [Google Scholar]
  15. Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş. ve Demirel, F. (2018). Scientific Research Methods. (24th Edition). Ankara: Pegem Academy Publications. [Google Scholar]
  16. Gökçek, T. & Davey, L. (2009). Application of Case Study Assessments. Primary education Online , 8 (2) , 1-3 . Retrieved from https://dergipark.org.tr/en/pub/ilkonline/issue/8598/107042 [Google Scholar]
  17. Demirci, Ö., Özkaya, M., & Konyalıoğlu, A. (2017). Error approaches of prospective teachers about probability. Journal of Erzincan University Faculty of Education, 19(2), 153-172. https://doi.org/10.17556/erziefd.310667 [Google Scholar] [Crossref] 
  18. DeVries, D., & Arnon, I. (2004). Solution--What Does It Mean? Helping Linear Algebra Students Develop the Concept While Improving Research Tools. International Group for the Psychology of Mathematics Education, Vol 2, 55-62. https://files.eric.ed.gov/fulltext/ED489680.pdf [Google Scholar]
  19. Dorier, J. L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. The teaching and learning of mathematics at university level (pp. 255-273). Springer, Dordrecht. [Google Scholar]
  20. Durkaya, M., Aksu, Z., Öçal, M. F., Şenel, E. Ö., Konyalıoğlu, A. C., Hızarcı, S., & Kaplan, A. (2011). Secondary school mathematics teachers’ approaches to students’ possible mistakes. Procedia-Social and Behavioral Sciences, 15, 2569-2573. http://dx.doi.org/10.1016/j.sbspro.2011.04.147 [Google Scholar]
  21. Durkaya, M., Şenel, E. Ö., Öçal, M. F., Kaplan, A., Aksu, Z., & Konyalıoğlu, A. C. (2011). Pre-service mathematics teachers’ multiple representation competencies about determinant concept. Procedia-Social and Behavioral Sciences, 15, 2554-2558. http://dx.doi.org/10.1016/j.sbspro.2011.04.144 [Google Scholar]
  22. Erdem, Z. Ç., & Gürbüz, R. (2017). An investigation on students' mistakes and misconceptions: Example of equation. Van Yüzüncü Yıl University Journal of the Faculty of Education, 14(1), 640-670. http://dx.doi.org/10.23891/efdyyu.2017.25 [Google Scholar]
  23. Hidayanti, N. (2020). Analysis of Student Mistakes in Completing Matrix Problems in The Linear Algebra Course. Journal of Physics: Conference Series (JPCS), 1477. DOI:10.1088/1742-6596/1477/4/042046 [Google Scholar]
  24. Kardeş, D. (2010). Examination of mathematics teacher candidates' linear equation systems solution processes in the context of self-efficacy perception and multiple representations. (Doctoral dissertation, Marmara University, Türkiye). [Google Scholar]
  25. Kazunga, C., & Bansilal, S. (2017). Zimbabwean in-service mathematics teachers’ understanding of matrix operations. The Journal of Mathematical Behavior, 47, 81-95. http://dx.doi.org/10.1016/j.jmathb.2017.05.003 [Google Scholar]
  26. Konyalıoğlu, A. C., Özkaya, M., & Altun Gedik, S. D. (2012). Investigation of Pre-Service Mathematics Teachers’ SubjectMatter Knowledge in terms of Their Approaches to Errors. Iğdır University Journal of the Institute of Science and Technology, 2(2), 27-32. [Google Scholar]
  27. Konyalioglu, A. C., Aksu, Z., Senel, E. O., & Tortumlu, N. (2010). The investigation of mathematics teachers cadidates’ skills of interrogating the reasons of errors in the process of solving mathematics questions. Proceedings of the International Symposium on Teacher Education Policies and Issues II, 951-960. [Google Scholar]
  28. Konyalioglu, A. C., İpek, A. S., & Isik, A. (2003). On the teaching linear algebra at the university level: the role of visualization in the teaching vector spaces. Research in Mathematical Education, 7(1), 59-67. [Google Scholar]
  29. Konyalioglu, A. C., Konyaliglu, S., & Isik, A. (2008). Effectıveness Of Vısualızatıon Approach On Student's Conceptual Learnıng. Journal of Qafqaz University, (24). [Google Scholar]
  30. Konyalioglu, S., Konyalioglu, A. C., Ipek, A. S., & Isik, A. (2005). The role of visualization approach on student’s conceptual learning. International Journal for Mathematics Teaching and Learning, 47, 1-9. [Google Scholar]
  31. Köğce, D. (2022). Examination of Mathematical Errors and Mistakes in Calculus Course. Educational Policy Analysis and Strategic Research, 17(1), 295-311. doi: 10.29329/epasr.2022.248.15 [Google Scholar] [Crossref] 
  32. 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), 670. https://doi.org/10.29333/iejme/11474 [Google Scholar] [Crossref] 
  33. Mulyatna, F., & Nurrahmah, A. (2020). Look Same but Different: Misconceptions in Linear Combinations. In Semantık Conference of Mathematics Education (SEMANTIK 2019), 1-5, Atlantis Press. [Google Scholar]
  34. Mutambara, L. H. N., & Bansilal, S. (2022). Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence. International Electronic Journal of Mathematics Education, 17(4), em0716. https://doi.org/10.29333/iejme/12483 [Google Scholar] [Crossref] 
  35. Mutlu, Y., & Söylemez, İ. (2018). Examination of master's and doctoral theses on mathematical misconceptions. Başkent University Journal of Education, 5(2), 187-197. [Google Scholar]
  36. Mutuk, H. (2018). Matrix Algebra with Mathematica. Karadeniz Journal of Science, 8(1), 115-130. https://doi.org/10.31466/kfbd.420864 [Google Scholar] [Crossref] 
  37. Ndlovu, Z. (2019). An analysis of pre-service mathematics mistakes in matrices. International Journal, 75(3/1). http://dx.doi.org/10.21506/j.ponte.2019.3.9 [Google Scholar]
  38. Önal, H. & Aydın, O. (2018). Misconceptions and error examples in primary school mathematics lesson, Journal of Educational Theory and Practice, 4(2), 1-9. https://dergipark.org.tr/tr/pub/ekuad/issue/38280/442698 [Google Scholar]
  39. Önmez, T. (2015). A qualitative study on elementary mathematics teacher candidates' understanding of linear equations (Master's thesis, Necmettin Erbakan Üniversitesi). [Google Scholar]
  40. Principles, N. (2000). Standards for school mathematics Reston, VA National Council Teaching Mathematics. [Google Scholar]
  41. Turgut, M. (2010). The Effect of Technology Supported Linear Algebra Teaching on Primary Mathematics Teacher Candidates' Spatial Abilities. (Master’s thesis, Dokuz Eylül University Institute of Educational Sciences, İzmir.) [Google Scholar]
  42. Yenilmez, K., & Yaşa, E. (2008). Elementary school students' misconceptions in geometry. Journal of Uludag University Faculty of Education, 21(2), 461-483. https://dergipark.org.tr/tr/download/article-file/153350 [Google Scholar]
  43. Yıldırım, A. ve Şimşek, H. (2018). Qualitative research methods in the social sciences. (11th Edition). Ankara: Seçkin Publishing. [Google Scholar]
  44. Zembat, İ, Ö. (2010). What is misconception?. MF. Özmantar, E. Bingölbali and H. Akkoç (Edıtors), Mathematical Misconceptions and Solution Suggestions. Ankara : Pegem A publishing. [Google Scholar]