Article Sidebar

Published
Jan 10, 2024
Download
PDF
Statistic
Read Counter : 1 Download : 428

Main Article Content

Abstract

This research explores the intricate relationship between students' cognitive processes and problem-solving approaches, explicitly focusing on misconceptions in solving quadratic inequalities. This study was conducted among 179 undergraduates in a mathematics education program in Malang, East Java, Indonesia; this mixed-method concurrent explanatory sequential design research employed the DISC questionnaire and quadratic inequality assignments. The DISC questionnaire categorized respondents into Dominance, Influence, Steadiness, and Conscientiousness. Data were generated from these pre-service teacher responses to the questionnaire, task assignment, and follow-up interviews to solicit information. Purposive sampling facilitated in-depth interviews, providing nuanced insights into the interplay between personality types and mathematical misconceptions. The quantitative data analysis results show a significant association between personality type and the type of error experienced by students when completing an open-ended task about quadratic inequalities X2(12) = 26.836, p = 0.008, V = 0.224. Meanwhile, qualitative data analysis findings reveal patterns associating personality types with specific misconceptions. Dominant traits are linked to theoretical misconceptions, while Influence and Conscientiousness traits correspond to conceptual misconceptions. Additionally, Steady traits are associated with classification misconceptions. This study contributes novel perspectives to mathematics education by exploring the influence of personality on mathematical cognition. The aim is to inform tailored teaching strategies for optimized learning outcomes, addressing persistent barriers posed by misconceptions in quadratic inequalities.

Keywords

Misconception Personality type Quadratic inequality

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

References

  1. Agler, L.-M. L., Stricklin, K., & Alfsen, L. K. (2020). Using personality-based propensity as a guide for teaching practice. Journal of Curriculum and Teaching, 9(3), 45-56. https://doi.org/10.5430/jct.v9n3p45

  2. Ahmad, N., & Siddique, J. (2017). Personality assessment using twitter tweets. Procedia Computer Science, 112, 1964-1973. https://doi.org/10.1016/j.procs.2017.08.067

  3. Akubuilo, F. (2012). Holistic assessment of student’s learning outcome. Journal of Education and Practice, 3(12), 56-60.

  4. Ali, C. A., & Wilmot, E. M. (2016). Pre-service teachers’ didactic conceptual structures in the absolute and quadratic inequalities. IOSR Journal of Mathematics (IOSR-JM), 12(4), 62-69. https://doi.org/10.9790/5728-1204026269

  5. Amelia, R., Kadarisma, G., Fitriani, N., & Ahmadi, Y. (2020). The effect of online mathematics learning on junior high school mathematic resilience during covid-19 pandemic. Journal of Physics: Conference Series, 1657(1), 012011. https://doi.org/10.1088/1742-6596/1657/1/012011

  6. Aquino, R. M., Camacho, L. M., Cañete, E. M., Cavalgante, C., & Márquez, A. (2017). Classical properties of algebras using a new graph association. ArXiv: Combinatorics, 1-19. https://doi.org/10.48550/arXiv.1706.00482

  7. Bachmaier, M. (2010). Test and confidence set for the difference of the x-coordinates of the vertices of two quadratic regression models. Statistical Papers, 51(2), 285-296. https://doi.org/10.1007/s00362-008-0159-7

  8. Cohen, L., Manion, L., & Morrison, K. (2017). The ethics of educational and social research. In L. Cohen, L. Manion, & K. Morrison (Eds.), Research methods in education (8th ed., pp. 111-143). Routledge.

  9. Conard, M. A. (2006). Aptitude is not enough: How personality and behavior predict academic performance. Journal of Research in Personality, 40(3), 339-346. https://doi.org/10.1016/j.jrp.2004.10.003

  10. Creswell, J. W. (2020). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Pearson Higher Ed.

  11. Cutler, D. M., Huang, W., & Lleras-Muney, A. (2015). When does education matter? The protective effect of education for cohorts graduating in bad times. Social Science & Medicine, 127, 63-73. https://doi.org/10.1016/j.socscimed.2014.07.056

  12. DeYoung, C. G., & Gray, J. R. (2009). Personality neuroscience: Explaining individual differences in affect, behaviour and cognition. In P. J. Corr & G. Matthews (Eds.), The Cambridge handbook of personality psychology (pp. 323-346).

  13. Godden, H., Mbekwa, M., & Julie, C. (2013). An analysis of errors and misconceptions in the 2010 grade 12 mathematics examination: A focus on quadratic equations and inequalities. In proceedings of the 19th Annual Congress of the Association for Mathematics Education of South Africa (pp. 70-79). Cape Town

  14. Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach. For the learning of Mathematics, 39(1), 38-43.

  15. Grégoire, J. (2016). Understanding creativity in mathematics for improving mathematical education. Journal of Cognitive Education and Psychology, 15(1), 24-36. https://doi.org/10.1891/1945-8959.15.1.24

  16. Gregory, A., & Fergus, E. (2017). Social and emotional learning and equity in school discipline. The future of children, 27(1), 117-136. https://doi.org/10.1353/foc.2017.0006

  17. Herawaty, D., Widada, W., Gede, W., Lusiana, D., Pusvita, Y., Widiarti, Y., & Anggoro, A. F. D. (2021). The cognitive process of students understanding quadratic equations. Journal of Physics: Conference Series, 1731(1), 012053. https://doi.org/10.1088/1742-6596/1731/1/012053

  18. Hillman, J. G., Antoun, J. P., & Hauser, D. J. (2023). The improvement default: People presume improvement when lacking information. Personality and Social Psychology Bulletin. https://doi.org/10.1177/01461672231190719

  19. Hoan, P. K., Hà, T. T., & Hà, V. S. (2022). Phương pháp biến đổi đại số giải phương trình bậc cao trong trường galoa mở rộng [An algebraic transformation method to solving equations in the extended galois field]. Journal of Science and Technique, 17(04), 83-95. https://doi.org/10.56651/lqdtu.jst.v17.n04.405

  20. Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematical Behavior, 31(4), 417-430. https://doi.org/10.1016/j.jmathb.2012.06.001

  21. Jupri, A., Usdiyana, D., & Gozali, S. M. (2022). Pre-service teachers' strategies in solving absolute value equations and inequalities. Education Sciences, 12(11), 743. https://doi.org/10.3390/educsci12110743

  22. Karimah, R. K. N., Kusmayadi, T. A., & Pramudya, I. (2018). Analysis of difficulties in mathematics learning on students with guardian personality type in problem-solving HOTS geometry test. Journal of Physics: Conference Series, 1008(1), 012076. https://doi.org/10.1088/1742-6596/1008/1/012076

  23. Light, A., & Strayer, W. (2000). Determinants of college completion: School quality or student ability? Journal of Human resources, 35(2), 299-332. https://doi.org/10.2307/146327

  24. Locke, H. S., & Braver, T. S. (2008). Motivational influences on cognitive control: Behavior, brain activation, and individual differences. Cognitive, Affective, & Behavioral Neuroscience, 8(1), 99-112. https://doi.org/10.3758/CABN.8.1.99

  25. Luneta, K., & Makonye, P. J. (2010). Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa. Acta Didactica Napocensia, 3(3), 35-46.

  26. Mamba, A. (2013). Learners’ errors when solving algebraic tasks: A case study of grade 12 mathematics examination papers in South Africa. University of Johannesburg.

  27. Mann, E. L., Chamberlin, S. A., & K. Graefe, A. (2017). The prominence of affect in creativity: Expanding the conception of creativity in mathematical problem solving. In R. Leikin & B. Sriraman (Eds.), Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 57-73). Springer International Publishing. https://doi.org/10.1007/978-3-319-38840-3_5

  28. Mehta, Y., Majumder, N., Gelbukh, A., & Cambria, E. (2020). Recent trends in deep learning based personality detection. Artificial Intelligence Review, 53(4), 2313-2339. https://doi.org/10.1007/s10462-019-09770-z

  29. Naseer, M. S. (2015). Analysis of students’ errors and misconceptions in pre-university mathematics courses. In Proceedings: First International Conference on Teaching & Learning (pp. 34-39).

  30. Ndlovu, L., & Ndlovu, M. (2020). The effect of graphing calculator use on learners' achievement and strategies in quadratic inequality problem solving. Pythagoras, 41(1), a552. https://doi.org/10.4102/pythagoras.v41i1.552

  31. Noftle, E. E., & Robins, R. W. (2007). Personality predictors of academic outcomes: Big five correlates of GPA and SAT scores. Journal of Personality and Social Psychology, 93(1), 116-130. https://doi.org/10.1037/0022-3514.93.1.116

  32. Owen, J. E., Mahatmya, D., & Carter, R. (2020). Dominance, influence, steadiness, and conscientiousness (DISC) assessment tool. In V. Zeigler-Hill & T. K. Shackelford (Eds.), Encyclopedia of Personality and Individual Differences (pp. 1186-1189). Springer International Publishing. https://doi.org/10.1007/978-3-319-24612-3_25

  33. Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, mathematics self-efficacy perception, and mathematics attitude as correlates of students’ non-routine mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7), 1042-1058. https://doi.org/10.1080/0020739X.2019.1648893

  34. Quintanilla, J. (2022). Parabolic properties from pieces of string. Math Horizons, 29(3), 20-23. https://doi.org/10.1080/10724117.2021.2001271

  35. Qushem, U. B., Christopoulos, A., & Laakso, M. J. (2022, 23-27 May 2022). The value proposition of an integrated multimodal learning analytics framework. In 2022 45th Jubilee International Convention on Information, Communication and Electronic Technology (MIPRO) (pp. 666-671). https://doi.org/10.23919/MIPRO55190.2022.9803728

  36. Rimfeld, K., Kovas, Y., Dale, P. S., & Plomin, R. (2016). True grit and genetics: Predicting academic achievement from personality. Journal of Personality and Social Psychology, 111(5), 780-789. https://doi.org/10.1037/pspp0000089

  37. Rosidin, U., Kadaritna, N., & Hasnunidah, N. (2019). Can argument-driven inquiry models have impact on critical thinking skills for students with different personality types? Cakrawala Pendidikan, 38(3), 511-526. https://doi.org/10.21831/cp.v38i3.24725

  38. Satriani, S., Wahyuddin, W., 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), 14-19. https://doi.org/10.14445/22315373/IJMTT-V66I10P503

  39. Singh, P., Rasid, S., Akmal, N., Hoon, T. S., & Han, C. T. (2017). How well do university level courses prepare students to be mathematical thinkers? The Social Sciences, 12(9), 1516-1521.

  40. Spooner, M. (2012). Errors and misconceptions in maths at key stage 2: Working Towards Success in SATs (1st ed.). David Fulton Publishers. https://doi.org/10.4324/9780203453728

  41. Srinivasan, V. K. (2013). Normals to a parabola. International Journal of Mathematical Education in Science and Technology, 44(4), 568-579. https://doi.org/10.1080/0020739X.2012.729681

  42. Steger, M. F., Kashdan, T. B., Sullivan, B. A., & Lorentz, D. (2008). Understanding the search for meaning in life: Personality, cognitive style, and the dynamic between seeking and experiencing meaning. Journal of Personality, 76(2), 199-228. https://doi.org/10.1111/j.1467-6494.2007.00484.x

  43. Su, L., Vasil’ev, V. I., & Jiang, T. (2020). Simultaneously identify the leading coefficient and right-hand side in a parabolic equation. Journal of Physics: Conference Series, 1624(3), 032008. https://doi.org/10.1088/1742-6596/1624/3/032008

  44. Tamba, K. P., & Saragih, M. J. (2020). Epistemological obstacles on the quadratic inequality. Al-Jabar: Jurnal Pendidikan Matematika, 11(2), 317-330. https://doi.org/10.24042/ajpm.v11i2.6858

  45. Tisdell, C. C. (2018). Pedagogical alternatives for triple integrals: moving towards more inclusive and personalized learning. International Journal of Mathematical Education in Science and Technology, 49(5), 792-801. https://doi.org/10.1080/0020739X.2017.1408150

  46. Tsamir, P., & Reshef, M. (2006). Students' preferences when solving quadratic inequalities. Focus on Learning Problems in Mathematics, 28(1), 37.

  47. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 521-525). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_170

  48. 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

  49. Weiss, M. (2016). Solving and graphing quadratics with symmetry and transformations. The Mathematics Teacher, 110(5), 394-397. https://doi.org/10.5951/mathteacher.110.5.0394

  50. Wettstein, M., Tauber, B., Kuźma, E., & Wahl, H.-W. (2017). The interplay between personality and cognitive ability across 12 years in middle and late adulthood: Evidence for reciprocal associations. Psychology and Aging, 32(3), 259-277. https://doi.org/10.1037/pag0000166

  51. Wilkie, K. J. (2022). Coordinating visual and algebraic reasoning with quadratic functions. Mathematics Education Research Journal, 1-37. https://doi.org/10.1007/s13394-022-00426-w

  52. Wortman, J., Lucas, R. E., & Donnellan, M. B. (2012). Stability and change in the big five personality domains: evidence from a longitudinal study of Australians. Psychology and aging, 27(4), 867-874. https://doi.org/10.1037/a0029322

  53. Zayas, V., Shoda, Y., & Ayduk, O. N. (2002). Personality in context: An interpersonal systems perspective. Journal of Personality, 70(6), 851-900. https://doi.org/10.1111/1467-6494.05026